27 real Digital Signal Processing questions from the ECE Core bank, as asked in Indian campus drives and tech interviews. Every question has a verified answer and an AI-tutor explanation on placd — free to start.
1. What is Discrete Fourier transform?
Junior
A.sustained low-level oscillations in fixed-point recursive filters caused by rounding or overflow in the feedback path even when the input is zero
B.mapping s = (2/T)(1 − z⁻¹)/(1 + z⁻¹) from analog to digital filter that preserves stability but warps frequency, corrected by pre-warping the critical frequencies
C.N-point frequency representation of a finite sequence with bin spacing fs/N, itself periodic in N and computable by fast algorithms
D.sample-rate reduction by integer M that must be preceded by a low-pass filter with cutoff π/M to prevent aliasing of the discarded band
2. Which term means: "N-point frequency representation of a finite sequence with bin spacing fs/N, itself periodic in N and computable by fast algorithms"?
A.Discrete Fourier transform — tapers applied to a truncated impulse response or data record; rectangular gives −13 dB sidelobes, Hamming about −43 dB at the price of a wider main lobe
B.Discrete Fourier transform — sustained low-level oscillations in fixed-point recursive filters caused by rounding or overflow in the feedback path even when the input is zero
C.Discrete Fourier transform — mapping s = (2/T)(1 − z⁻¹)/(1 + z⁻¹) from analog to digital filter that preserves stability but warps frequency, corrected by pre-warping the critical frequencies
D.Discrete Fourier transform — N-point frequency representation of a finite sequence with bin spacing fs/N, itself periodic in N and computable by fast algorithms
A.radix-2 decimation reduces N² complex multiplications to (N/2)·log2 N, requiring the length to be a power of two or zero-padded to one
B.error from finite ADC word length, treated as uniform white noise giving SNR of 6.02N + 1.76 dB for a full-scale sinusoid
C.tapers applied to a truncated impulse response or data record; rectangular gives −13 dB sidelobes, Hamming about −43 dB at the price of a wider main lobe
D.sample-rate reduction by integer M that must be preceded by a low-pass filter with cutoff π/M to prevent aliasing of the discarded band
5. Which term means: "radix-2 decimation reduces N² complex multiplications to (N/2)·log2 N, requiring the length to be a power of two or zero-padded to one"?
A.FFT complexity — finite impulse response filters are always stable and can have exactly linear phase but need many taps; recursive filters need fewer coefficients but risk instability and phase distortion
B.FFT complexity — tapers applied to a truncated impulse response or data record; rectangular gives −13 dB sidelobes, Hamming about −43 dB at the price of a wider main lobe
C.FFT complexity — radix-2 decimation reduces N² complex multiplications to (N/2)·log2 N, requiring the length to be a power of two or zero-padded to one
D.FFT complexity — convolution of two length-N sequences modulo N, which equals linear convolution only when N is at least L1 + L2 − 1, the basis of overlap-add FFT filtering
A.tapers applied to a truncated impulse response or data record; rectangular gives −13 dB sidelobes, Hamming about −43 dB at the price of a wider main lobe
B.N-point frequency representation of a finite sequence with bin spacing fs/N, itself periodic in N and computable by fast algorithms
C.finite impulse response filters are always stable and can have exactly linear phase but need many taps; recursive filters need fewer coefficients but risk instability and phase distortion
D.sample-rate reduction by integer M that must be preceded by a low-pass filter with cutoff π/M to prevent aliasing of the discarded band
8. Which term means: "finite impulse response filters are always stable and can have exactly linear phase but need many taps; recursive filters need fewer coefficients but risk instability and phase distortion"?
A.FIR versus IIR filters — error from finite ADC word length, treated as uniform white noise giving SNR of 6.02N + 1.76 dB for a full-scale sinusoid
B.FIR versus IIR filters — sustained low-level oscillations in fixed-point recursive filters caused by rounding or overflow in the feedback path even when the input is zero
C.FIR versus IIR filters — finite impulse response filters are always stable and can have exactly linear phase but need many taps; recursive filters need fewer coefficients but risk instability and phase distortion
D.FIR versus IIR filters — sample-rate reduction by integer M that must be preceded by a low-pass filter with cutoff π/M to prevent aliasing of the discarded band
A.convolution of two length-N sequences modulo N, which equals linear convolution only when N is at least L1 + L2 − 1, the basis of overlap-add FFT filtering
B.error from finite ADC word length, treated as uniform white noise giving SNR of 6.02N + 1.76 dB for a full-scale sinusoid
C.radix-2 decimation reduces N² complex multiplications to (N/2)·log2 N, requiring the length to be a power of two or zero-padded to one
D.sustained low-level oscillations in fixed-point recursive filters caused by rounding or overflow in the feedback path even when the input is zero
11. Which term means: "convolution of two length-N sequences modulo N, which equals linear convolution only when N is at least L1 + L2 − 1, the basis of overlap-add FFT filtering"?
A.Circular convolution — convolution of two length-N sequences modulo N, which equals linear convolution only when N is at least L1 + L2 − 1, the basis of overlap-add FFT filtering
B.Circular convolution — error from finite ADC word length, treated as uniform white noise giving SNR of 6.02N + 1.76 dB for a full-scale sinusoid
C.Circular convolution — tapers applied to a truncated impulse response or data record; rectangular gives −13 dB sidelobes, Hamming about −43 dB at the price of a wider main lobe
D.Circular convolution — sample-rate reduction by integer M that must be preceded by a low-pass filter with cutoff π/M to prevent aliasing of the discarded band
A.sustained low-level oscillations in fixed-point recursive filters caused by rounding or overflow in the feedback path even when the input is zero
B.radix-2 decimation reduces N² complex multiplications to (N/2)·log2 N, requiring the length to be a power of two or zero-padded to one
C.sample-rate reduction by integer M that must be preceded by a low-pass filter with cutoff π/M to prevent aliasing of the discarded band
D.mapping s = (2/T)(1 − z⁻¹)/(1 + z⁻¹) from analog to digital filter that preserves stability but warps frequency, corrected by pre-warping the critical frequencies
14. Which term means: "mapping s = (2/T)(1 − z⁻¹)/(1 + z⁻¹) from analog to digital filter that preserves stability but warps frequency, corrected by pre-warping the critical frequencies"?
A.Bilinear transform — error from finite ADC word length, treated as uniform white noise giving SNR of 6.02N + 1.76 dB for a full-scale sinusoid
B.Bilinear transform — finite impulse response filters are always stable and can have exactly linear phase but need many taps; recursive filters need fewer coefficients but risk instability and phase distortion
C.Bilinear transform — sustained low-level oscillations in fixed-point recursive filters caused by rounding or overflow in the feedback path even when the input is zero
D.Bilinear transform — mapping s = (2/T)(1 − z⁻¹)/(1 + z⁻¹) from analog to digital filter that preserves stability but warps frequency, corrected by pre-warping the critical frequencies
A.finite impulse response filters are always stable and can have exactly linear phase but need many taps; recursive filters need fewer coefficients but risk instability and phase distortion
B.tapers applied to a truncated impulse response or data record; rectangular gives −13 dB sidelobes, Hamming about −43 dB at the price of a wider main lobe
C.error from finite ADC word length, treated as uniform white noise giving SNR of 6.02N + 1.76 dB for a full-scale sinusoid
D.N-point frequency representation of a finite sequence with bin spacing fs/N, itself periodic in N and computable by fast algorithms
17. Which term means: "tapers applied to a truncated impulse response or data record; rectangular gives −13 dB sidelobes, Hamming about −43 dB at the price of a wider main lobe"?
A.Window functions — tapers applied to a truncated impulse response or data record; rectangular gives −13 dB sidelobes, Hamming about −43 dB at the price of a wider main lobe
B.Window functions — error from finite ADC word length, treated as uniform white noise giving SNR of 6.02N + 1.76 dB for a full-scale sinusoid
C.Window functions — convolution of two length-N sequences modulo N, which equals linear convolution only when N is at least L1 + L2 − 1, the basis of overlap-add FFT filtering
D.Window functions — sample-rate reduction by integer M that must be preceded by a low-pass filter with cutoff π/M to prevent aliasing of the discarded band
A.mapping s = (2/T)(1 − z⁻¹)/(1 + z⁻¹) from analog to digital filter that preserves stability but warps frequency, corrected by pre-warping the critical frequencies
B.N-point frequency representation of a finite sequence with bin spacing fs/N, itself periodic in N and computable by fast algorithms
C.error from finite ADC word length, treated as uniform white noise giving SNR of 6.02N + 1.76 dB for a full-scale sinusoid
D.sample-rate reduction by integer M that must be preceded by a low-pass filter with cutoff π/M to prevent aliasing of the discarded band
20. Which term means: "sample-rate reduction by integer M that must be preceded by a low-pass filter with cutoff π/M to prevent aliasing of the discarded band"?
A.Decimation — tapers applied to a truncated impulse response or data record; rectangular gives −13 dB sidelobes, Hamming about −43 dB at the price of a wider main lobe
B.Decimation — radix-2 decimation reduces N² complex multiplications to (N/2)·log2 N, requiring the length to be a power of two or zero-padded to one
C.Decimation — sample-rate reduction by integer M that must be preceded by a low-pass filter with cutoff π/M to prevent aliasing of the discarded band
D.Decimation — finite impulse response filters are always stable and can have exactly linear phase but need many taps; recursive filters need fewer coefficients but risk instability and phase distortion
A.tapers applied to a truncated impulse response or data record; rectangular gives −13 dB sidelobes, Hamming about −43 dB at the price of a wider main lobe
B.sample-rate reduction by integer M that must be preceded by a low-pass filter with cutoff π/M to prevent aliasing of the discarded band
C.sustained low-level oscillations in fixed-point recursive filters caused by rounding or overflow in the feedback path even when the input is zero
D.error from finite ADC word length, treated as uniform white noise giving SNR of 6.02N + 1.76 dB for a full-scale sinusoid
A.Quantisation noise — finite impulse response filters are always stable and can have exactly linear phase but need many taps; recursive filters need fewer coefficients but risk instability and phase distortion
B.Quantisation noise — tapers applied to a truncated impulse response or data record; rectangular gives −13 dB sidelobes, Hamming about −43 dB at the price of a wider main lobe
C.Quantisation noise — mapping s = (2/T)(1 − z⁻¹)/(1 + z⁻¹) from analog to digital filter that preserves stability but warps frequency, corrected by pre-warping the critical frequencies
D.Quantisation noise — error from finite ADC word length, treated as uniform white noise giving SNR of 6.02N + 1.76 dB for a full-scale sinusoid
A.radix-2 decimation reduces N² complex multiplications to (N/2)·log2 N, requiring the length to be a power of two or zero-padded to one
B.mapping s = (2/T)(1 − z⁻¹)/(1 + z⁻¹) from analog to digital filter that preserves stability but warps frequency, corrected by pre-warping the critical frequencies
C.sustained low-level oscillations in fixed-point recursive filters caused by rounding or overflow in the feedback path even when the input is zero
D.sample-rate reduction by integer M that must be preceded by a low-pass filter with cutoff π/M to prevent aliasing of the discarded band
26. Which term means: "sustained low-level oscillations in fixed-point recursive filters caused by rounding or overflow in the feedback path even when the input is zero"?
A.Limit cycles — sample-rate reduction by integer M that must be preceded by a low-pass filter with cutoff π/M to prevent aliasing of the discarded band
B.Limit cycles — tapers applied to a truncated impulse response or data record; rectangular gives −13 dB sidelobes, Hamming about −43 dB at the price of a wider main lobe
C.Limit cycles — sustained low-level oscillations in fixed-point recursive filters caused by rounding or overflow in the feedback path even when the input is zero
D.Limit cycles — mapping s = (2/T)(1 − z⁻¹)/(1 + z⁻¹) from analog to digital filter that preserves stability but warps frequency, corrected by pre-warping the critical frequencies
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