Q.1 What type of filter allows low-frequency signals to pass while blocking high-frequency signals?
High-pass filter
Band-pass filter
Low-pass filter
Band-stop filter
Explanation - A low-pass filter passes signals with frequencies lower than its cutoff frequency and attenuates higher frequencies.
Correct answer is: Low-pass filter
Q.2 Which component is most commonly used in a simple RC low-pass filter?
Capacitor
Inductor
Resistor
Transistor
Explanation - In an RC low-pass filter, the capacitor blocks high frequencies while allowing low frequencies to pass through the resistor.
Correct answer is: Capacitor
Q.3 The frequency at which a filter's output is reduced to 70.7% of its maximum is called?
Cutoff frequency
Resonant frequency
Bandwidth
Peak frequency
Explanation - The cutoff frequency is defined where the output power drops to half (70.7% amplitude) of its maximum.
Correct answer is: Cutoff frequency
Q.4 Which filter type removes a single unwanted frequency from a signal?
High-pass filter
Low-pass filter
Band-pass filter
Band-stop filter
Explanation - A band-stop filter (notch filter) attenuates signals within a specified frequency band while passing frequencies outside that band.
Correct answer is: Band-stop filter
Q.5 What does the symbol 'R' represent in an RC low-pass filter diagram?
Resistor
Resonator
Relay
Regulator
Explanation - In an RC filter, 'R' denotes a resistor which, along with a capacitor, shapes the filter's frequency response.
Correct answer is: Resistor
Q.6 If a filter has a cutoff frequency of 1 kHz, which of these statements is true?
Signals above 1 kHz pass with no attenuation
Signals below 1 kHz are completely blocked
Signals near 1 kHz start to be attenuated
All signals are blocked regardless of frequency
Explanation - Near the cutoff frequency, the filter begins to reduce the amplitude of signals; below it signals pass largely unattenuated.
Correct answer is: Signals near 1 kHz start to be attenuated
Q.7 Which of the following is NOT a common component used in filters?
Resistor
Capacitor
Inductor
Light bulb
Explanation - Resistors, capacitors, and inductors are the primary passive components for designing filters; a light bulb is not typically used in filter circuits.
Correct answer is: Light bulb
Q.8 The graph that shows a filter's gain versus frequency is called what?
Time response plot
Voltage divider chart
Frequency response plot
Phase angle diagram
Explanation - A frequency response plot displays how the amplitude (gain) of a filter changes across different input frequencies.
Correct answer is: Frequency response plot
Q.9 In a simple RC high-pass filter, which component primarily determines the cutoff frequency?
Resistor value
Capacitor value
Both equally
Neither
Explanation - The cutoff frequency of an RC high-pass filter is inversely proportional to the capacitance; larger C lowers the cutoff.
Correct answer is: Capacitor value
Q.10 What is the main purpose of adding a filter to an audio amplifier circuit?
Increase volume
Reduce noise
Add color to sound
Change speaker size
Explanation - Filters in audio circuits help remove unwanted frequency components (noise) to improve sound quality.
Correct answer is: Reduce noise
Q.11 Which filter type would you use to isolate a signal only between 100 Hz and 300 Hz?
High-pass filter
Low-pass filter
Band-pass filter
All-pass filter
Explanation - A band-pass filter allows signals within a specified frequency band to pass while blocking frequencies outside that band.
Correct answer is: Band-pass filter
Q.12 In a filter, the 'roll-off rate' refers to how quickly the attenuation increases beyond the cutoff frequency. A steeper roll-off means?
The filter is less selective
The filter is more selective
The filter's power consumption increases
The filter's size decreases
Explanation - A steeper roll-off (e.g., -20 dB/octave) means the filter quickly rejects unwanted frequencies, making it more selective.
Correct answer is: The filter is more selective
Q.13 Which of these is a common real-world example of a low-pass filter?
A microphone
A radio tuner
A headphone cable
A car alarm
Explanation - A headphone cable acts as a low-pass filter, allowing low-frequency sounds to pass while attenuating high frequencies.
Correct answer is: A headphone cable
Q.14 A filter that allows only high-frequency signals to pass is known as?
Band-stop filter
High-pass filter
Low-pass filter
Band-pass filter
Explanation - High-pass filters transmit signals above the cutoff frequency and block lower-frequency signals.
Correct answer is: High-pass filter
Q.15 In the context of filters, what does the term 'passband' refer to?
Frequency range that is blocked
Frequency range that is allowed
The cutoff frequency itself
The time delay of the filter
Explanation - Passband is the range of frequencies that the filter lets through with minimal attenuation.
Correct answer is: Frequency range that is allowed
Q.16 Which component is most critical for creating a high-frequency cutoff in an RC low-pass filter?
Capacitor
Resistor
Inductor
Diode
Explanation - The capacitor’s impedance decreases with frequency, thus controlling the cutoff point of the filter.
Correct answer is: Capacitor
Q.17 The quality factor Q of a filter is a measure of?
Its power consumption
Its selectivity or sharpness of the frequency response
Its temperature stability
Its cost
Explanation - A higher Q indicates a sharper resonance peak and a narrower bandwidth around the cutoff frequency.
Correct answer is: Its selectivity or sharpness of the frequency response
Q.18 Which type of filter would be suitable to eliminate a 60 Hz hum from a power line noise?
Band-pass filter at 60 Hz
High-pass filter at 1 kHz
Band-stop filter at 60 Hz
Low-pass filter at 60 Hz
Explanation - A band-stop filter (notch) at 60 Hz removes that specific frequency while letting others pass.
Correct answer is: Band-stop filter at 60 Hz
Q.19 What is the primary benefit of using an active filter over a passive filter?
Lower cost
No power required
Higher output signal gain
Simpler design
Explanation - Active filters use op-amps or other active components to provide signal amplification in addition to filtering.
Correct answer is: Higher output signal gain
Q.20 In a simple RC circuit, the time constant τ is equal to?
R + C
R - C
R × C
R ÷ C
Explanation - The time constant τ = RC determines how quickly the capacitor charges or discharges in an RC circuit.
Correct answer is: R × C
Q.21 Which filter type is most commonly used in radio receivers to isolate a single channel?
Band-pass filter
Band-stop filter
Low-pass filter
High-pass filter
Explanation - Band-pass filters isolate the desired frequency band (channel) while rejecting others.
Correct answer is: Band-pass filter
Q.22 Which of the following is NOT an example of a real-world filter?
Water purification system
Audio equalizer
Telephone handset
Light bulb
Explanation - A water filter, audio equalizer, and telephone handset all perform filtering; a light bulb does not.
Correct answer is: Light bulb
Q.23 When designing a filter, what does increasing the order of the filter typically do?
Makes the filter faster
Makes the filter more selective
Reduces the filter’s size
Increases the cutoff frequency
Explanation - Higher-order filters have steeper roll-off slopes and more precise frequency rejection characteristics.
Correct answer is: Makes the filter more selective
Q.24 In a low-pass RC filter, as the frequency increases, the impedance of the capacitor:
Increases
Decreases
Remains constant
First increases then decreases
Explanation - Capacitive reactance Xc = 1/(2πfC) decreases with higher frequency, allowing less attenuation of high frequencies.
Correct answer is: Decreases
Q.25 Which filter configuration uses a resistor, capacitor, and inductor together?
RC filter
LC filter
RLC filter
RL filter
Explanation - RLC filters combine resistance, inductance, and capacitance to achieve desired frequency response characteristics.
Correct answer is: RLC filter
Q.26 What is the purpose of a Bode plot in filter analysis?
To show the physical size of the filter
To display the filter’s gain and phase versus frequency
To illustrate the filter’s manufacturing cost
To compare different filter brands
Explanation - Bode plots provide a visual representation of the magnitude and phase response across frequencies.
Correct answer is: To display the filter’s gain and phase versus frequency
Q.27 In an RC low-pass filter, when the input frequency is much lower than the cutoff frequency, the output voltage:
Is zero
Is the same as the input voltage
Is twice the input voltage
Is half the input voltage
Explanation - At low frequencies, the capacitor behaves like an open circuit, allowing the signal to pass with minimal loss.
Correct answer is: Is the same as the input voltage
Q.28 Which of the following is a key design parameter for an active low-pass filter using an op-amp?
Gain of the op-amp
Power rating of the op-amp
Package size of the op-amp
Color of the op-amp casing
Explanation - The op-amp’s gain influences the filter’s overall transfer function and frequency response.
Correct answer is: Gain of the op-amp
Q.29 In a filter design, what does the term 'bandwidth' refer to?
The physical width of the filter component
The range of frequencies that are allowed through the filter
The maximum voltage the filter can handle
The time taken for the filter to react to changes
Explanation - Bandwidth is the difference between the upper and lower cutoff frequencies of a filter.
Correct answer is: The range of frequencies that are allowed through the filter
Q.30 Which filter type would you use to allow a signal to pass only below 10 Hz?
High-pass filter
Low-pass filter
Band-pass filter
Band-stop filter
Explanation - A low-pass filter blocks frequencies above its cutoff, allowing only low-frequency signals to pass.
Correct answer is: Low-pass filter
Q.31 What is the main effect of a filter on the phase of a signal?
Filters always increase phase
Filters can introduce a frequency-dependent phase shift
Filters eliminate phase shift completely
Filters double the phase shift
Explanation - Different filter orders and components cause the phase of the output to vary with frequency.
Correct answer is: Filters can introduce a frequency-dependent phase shift
Q.32 Which of the following statements best describes an all-pass filter?
It blocks all frequencies
It passes all frequencies with equal magnitude but alters phase
It passes only a narrow band of frequencies
It stops signals at high frequencies only
Explanation - All-pass filters have a flat magnitude response but introduce a frequency-dependent phase shift.
Correct answer is: It passes all frequencies with equal magnitude but alters phase
Q.33 If a filter's attenuation is 3 dB at a certain frequency, what does that mean about its output voltage?
Output is 3 dB higher than input
Output is 3 dB lower than input
Output voltage is 70.7% of input voltage
Output voltage is 50% of input voltage
Explanation - A 3 dB attenuation corresponds to the output being 70.7% of the input amplitude.
Correct answer is: Output voltage is 70.7% of input voltage
Q.34 Which component in an LC filter provides the energy storage necessary for filtering?
Resistor
Capacitor
Inductor
Diode
Explanation - The inductor stores magnetic energy and helps shape the frequency response of LC filters.
Correct answer is: Inductor
Q.35 What happens to the phase shift introduced by a first-order RC filter as frequency increases?
Phase shift increases and approaches 90 degrees
Phase shift decreases to zero
Phase shift remains constant
Phase shift becomes negative infinity
Explanation - For a first-order RC filter, the phase shift asymptotically approaches 90° at very high frequencies.
Correct answer is: Phase shift increases and approaches 90 degrees
Q.36 Which type of filter would you use to allow frequencies from 100 Hz to 200 Hz while blocking frequencies outside this range?
Low-pass filter
High-pass filter
Band-pass filter
Band-stop filter
Explanation - Band-pass filters pass signals only within a specific frequency band and block those outside it.
Correct answer is: Band-pass filter
Q.37 When an RC filter's cutoff frequency is increased by decreasing the resistor value, the filter’s bandwidth:
Increases
Decreases
Remains unchanged
Becomes infinite
Explanation - Lowering resistance raises the cutoff frequency, effectively widening the frequency range that passes.
Correct answer is: Increases
Q.38 Which component is primarily used in a digital filter implemented on a microcontroller?
Discrete-time algorithm
Capacitor
Inductor
Resistor
Explanation - Digital filters rely on numerical algorithms rather than physical components like capacitors or inductors.
Correct answer is: Discrete-time algorithm
Q.39 In a second-order low-pass filter, what is the typical roll-off rate?
-10 dB/octave
-20 dB/octave
-30 dB/octave
-40 dB/octave
Explanation - Each additional pole in a filter adds approximately -20 dB/octave to the roll-off, so a second-order has -40 dB/octave.
Correct answer is: -40 dB/octave
Q.40 What does the term 'phase margin' describe in filter design?
The amount of phase shift before the filter becomes unstable
The maximum output voltage
The filter’s size
The cost of the filter
Explanation - Phase margin is the difference between the system’s phase at unity gain and -180°, indicating stability margin.
Correct answer is: The amount of phase shift before the filter becomes unstable
Q.41 Which of the following is a typical application of a band-stop filter?
Removing a specific interference frequency from a signal
Increasing signal strength
Reducing power consumption
Improving color accuracy in displays
Explanation - Band-stop filters eliminate unwanted frequency components, such as noise spikes, from signals.
Correct answer is: Removing a specific interference frequency from a signal
Q.42 In the context of filter theory, what does 'attenuation' mean?
Increase in signal amplitude
Decrease in signal amplitude
Change in signal frequency
Change in signal phase
Explanation - Attenuation refers to the reduction of signal magnitude as it passes through a filter.
Correct answer is: Decrease in signal amplitude
Q.43 Which of these is a common type of active filter that uses operational amplifiers?
Butterworth filter
Chebyshev filter
Low-pass RC filter
High-pass inductor filter
Explanation - Butterworth filters are widely used in active designs for their flat passband characteristics using op-amps.
Correct answer is: Butterworth filter
Q.44 What is the main difference between analog and digital filters?
Analog filters use continuous signals; digital filters use discrete-time signals
Digital filters are always better
Analog filters are faster
Digital filters do not require any components
Explanation - Analog filters process continuous signals in real-time, whereas digital filters operate on sampled data.
Correct answer is: Analog filters use continuous signals; digital filters use discrete-time signals
Q.45 Which parameter of a filter determines the sharpness of its transition from passband to stopband?
Quality factor (Q)
Resistor value
Capacitor value
Inductor value
Explanation - Higher Q values lead to steeper roll-off and sharper transition bands in filter responses.
Correct answer is: Quality factor (Q)
Q.46 The transfer function H(s) of a first-order low-pass RC filter is:
H(s) = 1/(RCs + 1)
H(s) = RCs + 1
H(s) = s/(RC + s)
H(s) = (RC + s)/1
Explanation - The transfer function describes the output-to-input ratio in the Laplace domain for a low-pass RC filter.
Correct answer is: H(s) = 1/(RCs + 1)
Q.47 In a Butterworth filter, which property is maximized in the passband?
Flatness of gain
Peak amplitude
Phase delay
Bandwidth
Explanation - Butterworth filters are designed to have a maximally flat magnitude response in the passband.
Correct answer is: Flatness of gain
Q.48 What is the purpose of a pole in a filter’s transfer function?
To represent an energy source
To determine the frequency response shape
To provide mechanical stability
To reduce power consumption
Explanation - Poles in a transfer function dictate where the magnitude decreases and the phase shifts occur.
Correct answer is: To determine the frequency response shape
Q.49 Which of the following is a characteristic of an underdamped second-order system?
No oscillation in the step response
Oscillatory step response
Instantaneous response
Purely exponential decay
Explanation - Underdamped systems exhibit oscillations due to complex conjugate poles.
Correct answer is: Oscillatory step response
Q.50 What does the symbol 's' represent in the Laplace domain transfer function?
Frequency
Time
Complex frequency variable
Voltage
Explanation - 's' is the complex frequency variable used in Laplace transforms for analyzing linear systems.
Correct answer is: Complex frequency variable
Q.51 Which filter type uses a Chebyshev polynomial to achieve a sharper cutoff?
Butterworth filter
Chebyshev filter
Elliptic filter
Bessel filter
Explanation - Chebyshev filters employ Chebyshev polynomials to provide a steeper roll-off at the expense of ripple in the passband.
Correct answer is: Chebyshev filter
Q.52 In an RC high-pass filter, the cutoff frequency f_c is given by:
f_c = 1/(2πRC)
f_c = 2πRC
f_c = RC
f_c = R/C
Explanation - The cutoff frequency of a first-order RC high-pass filter follows f_c = 1/(2πRC).
Correct answer is: f_c = 1/(2πRC)
Q.53 What effect does increasing the number of poles in a digital filter typically have?
Decrease the computational complexity
Increase the filter's memory usage
Reduce the filter's order
Decrease the filter's bandwidth
Explanation - Adding poles increases the filter order, leading to more coefficients and higher memory requirements.
Correct answer is: Increase the filter's memory usage
Q.54 Which of the following is NOT a common type of digital filter?
FIR (Finite Impulse Response)
IIR (Infinite Impulse Response)
Bessel filter
Moving average filter
Explanation - Bessel filters are primarily analog; the other options are digital filter types.
Correct answer is: Bessel filter
Q.55 In frequency response analysis, what does a Bode plot's magnitude plot represent?
Signal phase shift
Signal amplitude versus frequency
Signal time delay
Signal power consumption
Explanation - The magnitude plot shows how the output amplitude changes with frequency, expressed in dB.
Correct answer is: Signal amplitude versus frequency
Q.56 Which type of filter provides the flattest passband but a less steep roll-off?
Chebyshev filter
Butterworth filter
Elliptic filter
Bessel filter
Explanation - Butterworth filters offer a maximally flat magnitude response with a moderate roll-off.
Correct answer is: Butterworth filter
Q.57 What does the term 'group delay' refer to in filter analysis?
Delay of the group of components
Time delay experienced by different frequency components
Delay due to group velocity
Delay caused by the filter's physical size
Explanation - Group delay is the derivative of the phase response with respect to angular frequency, indicating time lag per frequency.
Correct answer is: Time delay experienced by different frequency components
Q.58 In a second-order low-pass filter, the cutoff frequency is also known as the?
Resonant frequency
Unity frequency
Half-power frequency
Peak frequency
Explanation - The cutoff or half-power point is where the output power drops to half the input power.
Correct answer is: Half-power frequency
Q.59 What is the main advantage of a digital filter over an analog filter?
No need for any physical components
Unlimited precision in amplitude response
Infinite memory capacity
Instantaneous response
Explanation - Digital filters can be designed with arbitrary precision and adjustable characteristics via software.
Correct answer is: Unlimited precision in amplitude response
Q.60 Which filter topology is commonly used for anti-aliasing in analog-to-digital converters?
High-pass filter
Band-stop filter
Low-pass filter
Band-pass filter
Explanation - An anti-aliasing filter removes high-frequency components before sampling to avoid aliasing artifacts.
Correct answer is: Low-pass filter
Q.61 Which component is essential in an active filter to provide gain?
Resistor
Capacitor
Op-amp
Inductor
Explanation - Operational amplifiers are used to amplify signals within active filter designs.
Correct answer is: Op-amp
Q.62 Which filter design technique uses a linear phase response to avoid signal distortion?
Butterworth design
Chebyshev design
Bessel design
Elliptic design
Explanation - Bessel filters maintain a linear phase response, minimizing signal distortion.
Correct answer is: Bessel design
Q.63 A filter with a 3 dB bandwidth of 1 kHz and a Q factor of 1 would have a bandwidth of?
1 kHz
0.5 kHz
2 kHz
3 kHz
Explanation - For a resonant frequency of 1 kHz and Q=1, the bandwidth equals the resonant frequency / Q, which is 1 kHz.
Correct answer is: 1 kHz
Q.64 The transfer function H(s) of a second-order bandpass filter can be expressed as:
H(s) = s/(s^2 + ω0/Q s + ω0^2)
H(s) = ω0^2/(s^2 + ω0/Q s + ω0^2)
H(s) = 1/(s^2 + ω0/Q s + ω0^2)
H(s) = s^2/(s^2 + ω0/Q s + ω0^2)
Explanation - The standard form for a second-order bandpass filter includes a numerator of 's' and a second-order denominator.
Correct answer is: H(s) = s/(s^2 + ω0/Q s + ω0^2)
Q.65 Which filter type is known for having the steepest roll-off at the lowest filter order?
Butterworth
Chebyshev Type I
Elliptic
Bessel
Explanation - Elliptic filters provide the steepest roll-off for a given filter order due to ripples in both passband and stopband.
Correct answer is: Elliptic
Q.66 The phase margin of a closed-loop system is 45 degrees. This indicates that the system:
Will be unstable
Has a stable margin of 45 degrees
Is critically damped
Has a damping ratio of 0.45
Explanation - A phase margin of 45° provides a buffer before reaching the instability threshold of 180°.
Correct answer is: Has a stable margin of 45 degrees
Q.67 In filter synthesis, what does 'synthesis' refer to?
Measuring the filter's response
Designing a filter from scratch
Testing filter prototypes
Manufacturing filter components
Explanation - Filter synthesis involves deriving component values and architecture to meet desired specifications.
Correct answer is: Designing a filter from scratch
Q.68 Which filter is best suited for preserving the time-domain shape of a signal with minimal phase distortion?
Butterworth
Chebyshev
Bessel
Elliptic
Explanation - Bessel filters provide the most linear phase response, preserving signal shapes.
Correct answer is: Bessel
Q.69 An op-amp based active low-pass filter with a cutoff frequency of 10 kHz uses a resistor of 1 kΩ. What capacitor value is needed?
15.9 nF
159 nF
1.59 μF
15.9 μF
Explanation - Using f_c = 1/(2πRC), C = 1/(2πfR) ≈ 15.9 nF.
Correct answer is: 15.9 nF
Q.70 The magnitude of the transfer function |H(jω)| for a second-order low-pass filter peaks at the resonant frequency when Q > 1.5. This is known as?
Resonance
Cutoff
Bandwidth
Ripple
Explanation - When Q exceeds 1.5, the filter exhibits a resonant peak at its natural frequency.
Correct answer is: Resonance
Q.71 Which of the following best describes a Butterworth filter’s stopband attenuation?
Linear decrease
Exponential decrease
Quadratic decrease
No attenuation
Explanation - Butterworth filters have a smooth, exponential roll-off beyond the cutoff frequency.
Correct answer is: Exponential decrease
Q.72 The phase shift of a second-order bandpass filter near its resonant frequency is approximately:
0°
±45°
±90°
±180°
Explanation - At resonance, a second-order bandpass filter introduces a ±90° phase shift.
Correct answer is: ±90°
Q.73 In designing a digital FIR filter using the window method, what determines the filter’s length?
Desired frequency resolution
Hardware constraints
Maximum input voltage
Number of analog components
Explanation - A longer filter length yields higher frequency resolution and steeper roll-off.
Correct answer is: Desired frequency resolution
Q.74 Which filter design method is based on transforming an analog prototype into a digital filter via bilinear transformation?
Impulse invariance
Zero-order hold
Bilinear transformation
Least squares
Explanation - Bilinear transformation maps analog poles and zeros to the digital z-plane, preserving stability.
Correct answer is: Bilinear transformation
Q.75 For a second-order Butterworth low-pass filter, what is the value of the Q factor?
0.707
1
0.5
1.5
Explanation - A second-order Butterworth filter has a Q of 1/√2 ≈ 0.707 for a maximally flat response.
Correct answer is: 0.707
Q.76 In a digital filter, which algorithm is used to compute the convolution of the input signal with the filter coefficients?
Fast Fourier Transform (FFT)
Direct Form I
Least Mean Squares (LMS)
Zero Crossing
Explanation - Direct Form I is one of the standard structures for implementing IIR filters in time-domain convolution.
Correct answer is: Direct Form I
Q.77 Which filter type is primarily used in audio equalizers to adjust specific frequency bands?
Band-stop filter
Band-pass filter
Low-pass filter
High-pass filter
Explanation - Band-pass filters allow tuning of particular frequency ranges for audio enhancement.
Correct answer is: Band-pass filter
Q.78 A digital low-pass filter has a cutoff frequency of 0.3π rad/sample. What is the corresponding cutoff frequency in Hz if the sampling rate is 48 kHz?
7200 Hz
72000 Hz
1440 Hz
2400 Hz
Explanation - f_c = (0.3π/π) * 48kHz/2 = 0.3 * 24kHz = 7200 Hz.
Correct answer is: 7200 Hz
Q.79 In the context of filter design, what is meant by 'synthesis'?
Testing the filter’s performance
Building the filter from components
Creating a filter design from specifications
Measuring the filter’s frequency response
Explanation - Synthesis involves determining component values and topology to meet the desired frequency characteristics.
Correct answer is: Creating a filter design from specifications
Q.80 Which filter type has the property of maintaining a constant group delay across its passband?
Butterworth
Chebyshev
Bessel
Elliptic
Explanation - Bessel filters are designed for a linear phase response, providing a constant group delay.
Correct answer is: Bessel
Q.81 A digital filter uses a feedback structure to achieve a sharp cutoff. This type of filter is known as a(n):
FIR filter
IIR filter
Digital-to-analog converter
Analog-to-digital converter
Explanation - Infinite Impulse Response (IIR) filters use feedback to achieve sharp cutoff characteristics.
Correct answer is: IIR filter
Q.82 Which parameter indicates how much the output phase of a filter lags the input phase?
Amplitude
Quality factor
Phase margin
Group delay
Explanation - Group delay measures the derivative of phase with respect to frequency, indicating how the phase lags.
Correct answer is: Group delay
Q.83 In a second-order bandstop filter, the transfer function H(s) has a zero at s = 0. What is the physical implication of this zero?
The filter completely blocks DC components
The filter passes DC components unaltered
The filter has infinite gain at DC
The filter introduces a 180° phase shift at DC
Explanation - A zero at the origin means the output is zero for a DC input, effectively blocking DC signals.
Correct answer is: The filter completely blocks DC components
Q.84 Which filter design technique is known for optimizing the magnitude response while constraining the phase response?
Chebyshev Type I
Bessel
Elliptic
Linear Phase Design
Explanation - Linear Phase Design methods focus on achieving a linear phase response at the cost of magnitude ripple.
Correct answer is: Linear Phase Design
Q.85 A filter's Q factor is related to its bandwidth (BW) and resonant frequency (f0) by which equation?
Q = BW / f0
Q = f0 / BW
Q = BW * f0
Q = f0 + BW
Explanation - Quality factor Q equals resonant frequency divided by bandwidth, indicating selectivity.
Correct answer is: Q = f0 / BW
Q.86 Which of the following is a characteristic of a Chebyshev Type I filter?
No ripple in passband
No ripple in stopband
Ripple only in passband
Ripple only in stopband
Explanation - Chebyshev Type I filters have equiripple behavior in the passband and monotonic stopband.
Correct answer is: Ripple only in passband
Q.87 Which filter topology is used in a classic RC anti-aliasing filter preceding an ADC?
High-pass
Low-pass
Band-pass
Band-stop
Explanation - Anti-aliasing requires a low-pass filter to remove frequencies above Nyquist before sampling.
Correct answer is: Low-pass
Q.88 What is the typical use of a notch filter in power electronics?
Boosting the output voltage
Filtering out the 60 Hz power line frequency
Increasing the switching frequency
Reducing the output current
Explanation - Notch filters remove specific unwanted frequencies like mains hum from signals.
Correct answer is: Filtering out the 60 Hz power line frequency
Q.89 In a digital FIR filter, the impulse response length is directly related to which performance metric?
Phase distortion
Group delay
Computational load
Power consumption
Explanation - A longer impulse response requires more multiplications per output sample, increasing computational load.
Correct answer is: Computational load
Q.90 A second-order Butterworth filter has a cutoff frequency of 5 kHz. What is the pole magnitude in radians per second?
5000
31416
15708
62832
Explanation - Pole magnitude = ω0 = 2πf_c ≈ 2π*5000 = 31416 rad/s. The magnitude of each pole in a Butterworth is ω0/√2 ≈ 15708.
Correct answer is: 15708
Q.91 Which filter design method uses Chebyshev polynomials to provide equal ripple in both passband and stopband?
Butterworth
Chebyshev Type I
Chebyshev Type II
Elliptic
Explanation - Elliptic filters have equiripple in both passband and stopband, achieved using elliptic polynomials.
Correct answer is: Elliptic
Q.92 The term 'group delay' is most relevant to:
Magnitude response
Phase response
Stability analysis
Power consumption
Explanation - Group delay measures the phase shift per unit frequency, affecting signal timing.
Correct answer is: Phase response
Q.93 In a digital filter implemented in a microcontroller, which of the following is a key consideration?
Availability of analog components
Memory usage for filter coefficients
Physical size of the filter
Color of the microcontroller casing
Explanation - Microcontroller-based digital filters must manage memory constraints for storing coefficients and state variables.
Correct answer is: Memory usage for filter coefficients
Q.94 Which of the following filter designs is known for its maximally flat group delay?
Chebyshev
Elliptic
Butterworth
Bessel
Explanation - Bessel filters provide the most linear phase (flat group delay) among standard filter types.
Correct answer is: Bessel
Q.95 A digital low-pass filter with a cutoff frequency of 0.1π rad/sample has a 3 dB attenuation at which normalized frequency?
0.05π
0.1π
0.2π
0.5π
Explanation - The 3 dB point is defined as the cutoff frequency itself in normalized radian frequency.
Correct answer is: 0.1π
Q.96 Which filter topology is best suited for use in a high-speed data communications system to eliminate high-frequency noise?
High-pass filter
Low-pass filter
Band-stop filter
Band-pass filter
Explanation - A low-pass filter removes high-frequency noise that can corrupt digital signals.
Correct answer is: Low-pass filter
Q.97 For an LTI system, the stability of a digital filter depends on:
All poles lying inside the unit circle
All poles lying outside the unit circle
All zeros lying on the unit circle
All zeros lying outside the unit circle
Explanation - Stability requires that all poles of the z-transform lie within the unit circle.
Correct answer is: All poles lying inside the unit circle
Q.98 A Butterworth filter of order N has a magnitude-squared function given by |H(jω)|² = 1 / [1 + (ω/ωc)^(2N)]. What is the slope at the cutoff frequency for a second-order Butterworth filter?
-20 dB/dec
-40 dB/dec
-60 dB/dec
-80 dB/dec
Explanation - Each additional order adds -20 dB/dec, so a second-order filter has a -40 dB/dec slope beyond the cutoff.
Correct answer is: -40 dB/dec
Q.99 Which of the following is a typical application of an elliptic filter?
Audio equalizer with linear phase
High-fidelity recording system
Fast optical communication
Sharp cutoff with minimal order
Explanation - Elliptic filters provide the steepest roll-off for a given filter order, making them ideal for sharp cutoffs.
Correct answer is: Sharp cutoff with minimal order
Q.100 What does the 'zero' of a digital filter represent?
A frequency that is completely passed
A frequency that is completely attenuated
A point of maximum gain
The filter's cutoff frequency
Explanation - Zeros in the transfer function correspond to frequencies that produce zero output.
Correct answer is: A frequency that is completely attenuated
Q.101 The term 'phase lag' refers to the difference between which two phases?
Input and output signals
Output and reference signals
Zero and pole phases
Voltage and current phases
Explanation - Phase lag is the amount by which the output signal lags behind the input signal.
Correct answer is: Input and output signals
Q.102 A second-order all-pass filter with transfer function H(s) = (s^2 - ω0^2) / (s^2 + ω0^2) introduces a phase shift of:
0°
±90°
±180°
±270°
Explanation - All-pass filters introduce a frequency-dependent phase shift, reaching ±180° at the natural frequency.
Correct answer is: ±180°
Q.103 Which filter design approach is best for achieving a flat group delay across the passband?
Butterworth design
Chebyshev design
Bessel design
Elliptic design
Explanation - Bessel filters are specifically designed for a linear phase response, thus providing flat group delay.
Correct answer is: Bessel design
Q.104 In the context of filter design, what is the significance of the 'pole-zero map'?
It indicates the filter's power consumption
It shows the frequency points of maximum gain
It visualizes the filter's frequency response characteristics
It displays the filter's temperature stability
Explanation - Poles and zeros determine the shape of the magnitude and phase response of the filter.
Correct answer is: It visualizes the filter's frequency response characteristics
Q.105 Which of the following is an example of a non-recursive (FIR) digital filter?
IIR filter
FIR filter
Analog filter
Bandpass filter
Explanation - Finite Impulse Response (FIR) filters are non-recursive and rely solely on current and past inputs.
Correct answer is: FIR filter
Q.106 A digital filter with a cutoff frequency of 0.25π rad/sample and a sampling rate of 8 kHz has a cutoff in Hz of:
1000 Hz
2000 Hz
4000 Hz
8000 Hz
Explanation - f_c = (0.25π/π) * fs/2 = 0.25 * 4kHz = 1000 Hz.
Correct answer is: 1000 Hz
Q.107 Which filter type is known for having the steepest roll-off for a given filter order?
Butterworth
Chebyshev
Elliptic
Bessel
Explanation - Elliptic filters provide the sharpest roll-off due to ripples in both passband and stopband.
Correct answer is: Elliptic
Q.108 In a digital filter, the 'noise floor' is related to:
The filter's bandwidth
The number of taps in an FIR filter
The filter's cutoff frequency
The filter's power supply voltage
Explanation - More taps can reduce noise floor by averaging out random noise components.
Correct answer is: The number of taps in an FIR filter
Q.109 The concept of 'insertion loss' is important in:
Power amplifiers
Passive filters
Active filters
All of the above
Explanation - Insertion loss refers to the loss of signal power due to the filter and is relevant in all filter types.
Correct answer is: All of the above
Q.110 A 4th-order Chebyshev Type I low-pass filter with a ripple of 1 dB has what approximate cutoff slope beyond the cutoff frequency?
-40 dB/dec
-80 dB/dec
-100 dB/dec
-120 dB/dec
Explanation - Each Chebyshev pole adds about -20 dB/dec; a 4th-order filter yields -80 dB/dec.
Correct answer is: -80 dB/dec
Q.111 Which filter design technique ensures that the filter's response is linear in the group delay across the entire passband?
Chebyshev design
Butterworth design
Linear Phase FIR design
Elliptic design
Explanation - Linear Phase FIR filters are constructed to maintain constant group delay across the passband.
Correct answer is: Linear Phase FIR design
Q.112 What is the main advantage of using an active filter compared to a passive filter?
No need for power supply
Lower cost
Higher output gain
Simpler design
Explanation - Active filters incorporate amplifiers, enabling signal gain along with filtering.
Correct answer is: Higher output gain
Q.113 In digital signal processing, what does the term 'aliasing' refer to?
The phenomenon of higher frequencies folding back into lower frequencies due to insufficient sampling
The phenomenon of higher frequencies being amplified
The phenomenon of lower frequencies being attenuated
The phenomenon of noise increasing with time
Explanation - Aliasing occurs when the sampling rate is not high enough to capture higher frequency components accurately.
Correct answer is: The phenomenon of higher frequencies folding back into lower frequencies due to insufficient sampling
Q.114 Which of the following filter designs is particularly suitable for applications requiring minimal group delay variation?
Bessel filter
Butterworth filter
Chebyshev filter
Elliptic filter
Explanation - Bessel filters are designed for a linear phase response, minimizing group delay variation.
Correct answer is: Bessel filter
Q.115 A digital filter uses a 'window function' to mitigate spectral leakage. Which window function is commonly used for this purpose?
Rectangular
Hamming
Triangle
Square
Explanation - The Hamming window reduces spectral leakage in FIR filter design.
Correct answer is: Hamming
Q.116 Which of the following statements is true about a 3rd-order Butterworth filter?
It has a cutoff slope of -20 dB/dec
It has a cutoff slope of -40 dB/dec
It has a cutoff slope of -60 dB/dec
It has a cutoff slope of -80 dB/dec
Explanation - A third-order Butterworth filter has a slope of -60 dB per decade beyond the cutoff.
Correct answer is: It has a cutoff slope of -60 dB/dec
Q.117 Which filter type is most suitable for use in a high-frequency RF front-end to suppress out-of-band interference?
High-pass filter
Low-pass filter
Band-stop filter
Band-pass filter
Explanation - Band-stop (notch) filters effectively eliminate specific frequency components that could interfere with the signal.
Correct answer is: Band-stop filter
Q.118 In filter theory, the term 'stability margin' refers to:
The difference between actual and desired filter parameters
The difference between the system's actual phase and the phase at -180°
The difference between the filter's cutoff frequency and the Nyquist frequency
The difference between the filter's passband ripple and stopband attenuation
Explanation - Stability margin indicates how close the system is to the point of instability at -180° phase shift.
Correct answer is: The difference between the system's actual phase and the phase at -180°
Q.119 Which of the following is a key difference between analog and digital filters?
Analog filters are implemented in silicon
Digital filters can only be implemented in hardware
Analog filters use continuous time; digital filters use discrete time
Digital filters are always linear
Explanation - The fundamental difference is that analog filters process continuous signals, while digital filters work on sampled data.
Correct answer is: Analog filters use continuous time; digital filters use discrete time
Q.120 A digital filter's frequency response can be evaluated by applying which transform to its impulse response?
Fourier Transform
Laplace Transform
Z-Transform
Hilbert Transform
Explanation - The z-transform is used for analyzing discrete-time systems and deriving the frequency response.
Correct answer is: Z-Transform
Q.121 In an IIR filter, the coefficient set {b0, b1, …, bN, a1, …, aN} corresponds to which type of system?
Feedforward only
Feedback only
Feedforward and feedback
None of the above
Explanation - IIR filters use both feedforward (b coefficients) and feedback (a coefficients) terms.
Correct answer is: Feedforward and feedback
Q.122 Which of the following describes a 'pole-zero' cancellation in a filter design?
When a zero coincides with a pole, resulting in a net zero effect on the transfer function
When a pole cancels a zero in the numerator, resulting in increased attenuation
When a pole cancels a zero in the denominator, resulting in increased gain
When a pole and zero are placed at infinity
Explanation - Pole-zero cancellation removes the effect of that pole-zero pair from the overall frequency response.
Correct answer is: When a zero coincides with a pole, resulting in a net zero effect on the transfer function
Q.123 The 'Nyquist frequency' in digital signal processing is:
Half of the sampling rate
Double the sampling rate
The frequency at which aliasing first occurs
Both A and C
Explanation - The Nyquist frequency is half the sampling rate and is the highest frequency that can be uniquely represented without aliasing.
Correct answer is: Both A and C
Q.124 A digital filter with a stopband attenuation of 80 dB at 0.5π rad/sample and a passband ripple of 0.1 dB is likely a(n):
Chebyshev Type I filter
Chebyshev Type II filter
Butterworth filter
Elliptic filter
Explanation - Elliptic filters provide high stopband attenuation with a small ripple in the passband.
Correct answer is: Elliptic filter
Q.125 In filter theory, what does the term 'passband ripple' refer to?
Variation in attenuation within the stopband
Variation in attenuation within the passband
Maximum attenuation in the stopband
Minimum attenuation in the passband
Explanation - Passband ripple refers to the small variations in gain that occur within the passband.
Correct answer is: Variation in attenuation within the passband
Q.126 Which digital filter design approach uses the 'Remez exchange algorithm' to optimize the filter's frequency response?
Least-mean squares (LMS)
Chebyshev minimax
FIR filter design
Elliptic filter design
Explanation - The Remez algorithm is used to compute minimax optimal FIR filter coefficients.
Correct answer is: Chebyshev minimax
Q.127 An 'all-pass' filter is used in audio processing primarily for:
Amplitude equalization
Phase shifting
Frequency attenuation
Noise reduction
Explanation - All-pass filters alter the phase of the signal without changing its amplitude.
Correct answer is: Phase shifting
Q.128 In the context of filter design, what is the significance of a filter's 'Bode plot'?
It displays the filter's time-domain response
It shows the magnitude and phase versus frequency
It indicates the filter's physical dimensions
It provides the filter's thermal characteristics
Explanation - Bode plots provide a graphical representation of a filter’s magnitude and phase across frequencies.
Correct answer is: It shows the magnitude and phase versus frequency
Q.129 Which of the following filter topologies is used to implement a steep roll-off with minimal group delay variation?
Chebyshev Type I
Chebyshev Type II
Elliptic
Bessel
Explanation - Bessel filters are chosen for linear phase response, minimizing group delay variation.
Correct answer is: Bessel
Q.130 Which of these is a key parameter in determining the stability of an analog filter?
The filter's cutoff frequency
The filter's poles' location in the s-plane
The filter's physical size
The filter's power rating
Explanation - Poles in the left half of the s-plane indicate stability for analog filters.
Correct answer is: The filter's poles' location in the s-plane
Q.131 In digital filter design, what does the 'z-plane' represent?
The complex frequency plane
The time-domain representation of the filter
The space in which the filter's poles and zeros are plotted
The physical location of the filter on a circuit board
Explanation - The z-plane is used to analyze the stability and frequency response of discrete-time systems.
Correct answer is: The space in which the filter's poles and zeros are plotted
Q.132 Which of the following is NOT a method to reduce the order of a high-order digital filter?
Using a cascaded structure
Implementing a higher-order filter in hardware
Using a lower-order approximation
Using a multi-stage filter with shared coefficients
Explanation - Using a higher-order filter in hardware does not reduce the order; it increases it.
Correct answer is: Implementing a higher-order filter in hardware
Q.133 What is the primary advantage of using a 'cascaded integrator-comb (CIC)' filter in DSP?
High computational complexity
Low power consumption and simple implementation
High group delay
Precise linear phase response
Explanation - CIC filters are efficient for large decimation ratios with minimal arithmetic operations.
Correct answer is: Low power consumption and simple implementation
Q.134 In a Butterworth filter of order N, the magnitude response falls by 3 dB at the cutoff frequency. What is the magnitude response at 10× the cutoff frequency for a 2nd-order filter?
-3 dB
-6 dB
-13 dB
-20 dB
Explanation - For a 2nd-order Butterworth, the attenuation at 10× ωc is approximately -13 dB.
Correct answer is: -13 dB
Q.135 Which of the following statements about a 'digital notch filter' is true?
It has a very wide stopband
It attenuates a narrow band of frequencies
It passes all frequencies equally
It is used only for audio applications
Explanation - A digital notch filter is designed to suppress a specific narrow frequency band.
Correct answer is: It attenuates a narrow band of frequencies
Q.136 Which of the following filter design methods is best suited for minimizing the error between the desired and actual frequency responses over a given interval?
Chebyshev minimax
Least-squares
Bessel optimization
Elliptic optimization
Explanation - Least-squares filter design minimizes the overall error between desired and actual responses.
Correct answer is: Least-squares
Q.137 What is the main purpose of a 'pre-emphasis' filter in digital audio processing?
To reduce low-frequency content
To boost high-frequency content before encoding
To equalize the mid-range frequencies
To suppress DC offsets
Explanation - Pre-emphasis boosts high frequencies to compensate for the loss during compression or transmission.
Correct answer is: To boost high-frequency content before encoding
Q.138 In filter synthesis, the 'prototype filter' is typically chosen as:
A high-pass filter
A low-pass filter
A band-pass filter
A band-stop filter
Explanation - Low-pass prototypes are commonly transformed into other filter types via frequency transformations.
Correct answer is: A low-pass filter
Q.139 The 'Hamming window' is often used in FIR filter design to:
Increase the filter's passband ripple
Reduce the filter's stopband attenuation
Reduce spectral leakage
Increase the filter's group delay
Explanation - Applying a Hamming window smooths the impulse response, minimizing sidelobes and spectral leakage.
Correct answer is: Reduce spectral leakage
Q.140 Which of the following describes the 'zero-order hold' in digital-to-analog conversion?
It holds the last input value until the next sample
It holds a constant zero value between samples
It holds the first sample value throughout
It holds a value that ramps linearly between samples
Explanation - Zero-order hold holds each sample value constant until the next sampling instant, creating a staircase output.
Correct answer is: It holds the last input value until the next sample
Q.141 For a 3rd-order digital IIR filter, if the coefficients are a1 = 0.5, a2 = 0.25, a3 = 0.125, what type of response does the filter exhibit?
Stable
Unstable
Marginally stable
Oscillatory
Explanation - All poles are inside the unit circle, indicating a stable IIR filter.
Correct answer is: Stable
Q.142 Which of the following is a key characteristic of a 'brick-wall' filter?
Gradual roll-off
Sharp cut-off with infinite slope
Large group delay
High stopband ripple
Explanation - 'Brick-wall' filters have an idealized infinite slope at the cutoff, unattainable in practice.
Correct answer is: Sharp cut-off with infinite slope
Q.143 In digital filter implementation, which structure is known for its minimal computational cost but higher sensitivity to coefficient quantization?
Direct form I
Direct form II
Cascade form
Parallel form
Explanation - Direct form I uses more multipliers but has higher quantization sensitivity compared to Direct form II.
Correct answer is: Direct form I
Q.144 Which of the following best describes a 'spectral leakage' problem in digital signal processing?
When high-frequency components are lost during filtering
When energy from a signal spreads into adjacent frequency bins due to finite observation time
When the filter's passband ripple increases over time
When the filter's stopband attenuation decreases
Explanation - Spectral leakage arises from the finite length of the observed data, causing energy spread across frequencies.
Correct answer is: When energy from a signal spreads into adjacent frequency bins due to finite observation time
Q.145 Which of the following is a common application for a 'digital IIR filter' in real-time systems?
Low-power consumption with high precision
High computational cost for complex algorithms
Real-time audio equalization with minimal delay
Offline data processing only
Explanation - IIR filters provide efficient real-time filtering with fewer taps than equivalent FIR filters.
Correct answer is: Real-time audio equalization with minimal delay
Q.146 What is the primary difference between a 'finite impulse response (FIR)' filter and an 'infinite impulse response (IIR)' filter?
FIR filters are non-linear while IIR filters are linear
FIR filters have a finite impulse response, IIR filters have an infinite impulse response
IIR filters are always stable, FIR filters are never stable
FIR filters are analog, IIR filters are digital
Explanation - FIR filters' output depends only on current and past inputs, while IIR filters also depend on past outputs.
Correct answer is: FIR filters have a finite impulse response, IIR filters have an infinite impulse response
Q.147 The 'z-transform' of a discrete-time system is used to analyze which of the following?
The system's power consumption
The system's frequency response and stability
The system's temperature variations
The system's physical layout
Explanation - The z-transform provides a comprehensive tool for analyzing digital filter stability and frequency characteristics.
Correct answer is: The system's frequency response and stability