Digital Signal Processing interview questions

1. 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
2. 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
3. C.N-point frequency representation of a finite sequence with bin spacing fs/N, itself periodic in N and computable by fast algorithms
4. 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

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1. A.Quantisation noise
2. B.Circular convolution
3. C.Discrete Fourier transform
4. D.Limit cycles

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1. 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
2. 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
3. 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
4. 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

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1. 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
2. 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
3. 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
4. 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

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1. A.FFT complexity
2. B.Quantisation noise
3. C.Limit cycles
4. D.Decimation

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1. 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
2. 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
3. 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
4. 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

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1. 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
2. B.N-point frequency representation of a finite sequence with bin spacing fs/N, itself periodic in N and computable by fast algorithms
3. 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
4. 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

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1. A.FIR versus IIR filters
2. B.Quantisation noise
3. C.FFT complexity
4. D.Window functions

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1. 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
2. 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
3. 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
4. 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

Answer + AI explanation with Pro

1. 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
2. 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
3. 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
4. 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

Answer + AI explanation with Pro

1. A.FFT complexity
2. B.Window functions
3. C.Quantisation noise
4. D.Circular convolution

Answer + AI explanation with Pro

1. 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
2. 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
3. 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
4. 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

Answer + AI explanation with Pro

1. 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
2. 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
3. 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
4. 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

Answer + AI explanation with Pro

1. A.Quantisation noise
2. B.Decimation
3. C.Discrete Fourier transform
4. D.Bilinear transform

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1. 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
2. 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
3. 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
4. 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

Answer + AI explanation with Pro

1. 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
2. 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
3. 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
4. D.N-point frequency representation of a finite sequence with bin spacing fs/N, itself periodic in N and computable by fast algorithms

Answer + AI explanation with Pro

1. A.Window functions
2. B.FIR versus IIR filters
3. C.Discrete Fourier transform
4. D.Limit cycles

Answer + AI explanation with Pro

1. 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
2. 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
3. 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
4. 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

Answer + AI explanation with Pro

1. 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
2. B.N-point frequency representation of a finite sequence with bin spacing fs/N, itself periodic in N and computable by fast algorithms
3. 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
4. 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

Answer + AI explanation with Pro

1. A.Quantisation noise
2. B.Decimation
3. C.Window functions
4. D.Circular convolution

Answer + AI explanation with Pro

1. 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
2. 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
3. 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
4. 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

Answer + AI explanation with Pro

1. 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
2. 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
3. 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
4. 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

Answer + AI explanation with Pro

1. A.Quantisation noise
2. B.FIR versus IIR filters
3. C.Circular convolution
4. D.Decimation

Answer + AI explanation with Pro

1. 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
2. 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
3. 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
4. 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

Answer + AI explanation with Pro

1. 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
2. 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
3. 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
4. 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

Answer + AI explanation with Pro

1. A.Decimation
2. B.Quantisation noise
3. C.Limit cycles
4. D.Discrete Fourier transform

Answer + AI explanation with Pro

1. 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
2. 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
3. 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
4. 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

Answer + AI explanation with Pro