Digital Signal Processing Questions and Answers – Discrete-Time Processing of Continuous Time Signals

This set of Advanced Digital Signal Processing Questions & Answers focuses on “Discrete-Time Processing of Continuous Time Signals”.

1. When the frequency band is selected we can specify the sampling rate and the characteristics of the pre filter, which is also called as __________ filter.
a) Analog filter
b) Anti aliasing filter
c) Analog & Anti aliasing filter
d) None of the mentioned
View Answer

Answer: b
Explanation: Once the desired frequency band is selected we can specify the sampling rate and the characteristics of the pre filter, which is also called an anti aliasing filter. The anti aliasing filter is an analog filter which has a twofold purpose.

2. What are the main characteristics of Anti aliasing filter?
a) Ensures that bandwidth of signal to be sampled is limited to frequency range
b) To limit the additive noise spectrum and other interference, which corrupts the signal
c) All of the mentioned
d) None of the mentioned
View Answer

Answer: c
Explanation: The anti aliasing filter is an analog filter which has a twofold purpose. First, it ensures that the bandwidth of the signal to be sampled is limited to the desired frequency range. Using an antialiasing filter is to limit the additive noise spectrum and other interference, which often corrupts the desired signal. Usually, additive noise is wideband and exceeds the bandwidth of the desired signal.

3. In general, a digital system designer has better control of tolerances in a digital signal processing system than an analog system designer who is designing an equivalent analog system.
a) True
b) False
View Answer

Answer: a
Explanation: Analog signal processing operations cannot be done very precisely either since electronic components in analog systems have tolerances and they introduce noise during their operation. In general, a digital system designer has better control of tolerances in a digital signal processing system than an analog system designer who is designing an equivalent analog system.
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4. The selection of the sampling rate Fs=1/T, where T is the sampling interval, not only determines the highest frequency (Fs/2) that is preserved in the analog signal but also serves as a scale factor that influences the design specifications for digital filters.
a) True
b) False
View Answer

Answer: a
Explanation: Once we have specified the pre filter requirements and have selected the desired sampling rate, we can proceed with the design of the digital signal processing operations to be performed on the discrete-time signal. The selection of the sampling rate Fs=1/T, where T is the sampling interval, not only determines the highest frequency (Fs/2) that is preserved in the analog signal but also serves as a scale factor that influences the design specifications for digital filters and any other discrete-time systems through which the signal is processed.

5. What is the configuration of system for digital processing of an analog signal?
a) Analog signal|| Pre-filter -> D/A Converter -> Digital Processor -> A/D Converter -> Post-filter
b) Analog signal|| Pre-filter -> A/D Converter -> Digital Processor -> D/A Converter -> Post-filter
c) Analog signal|| Post-filter -> D/A Converter -> Digital Processor -> A/D Converter -> Pre-filter
d) None of the mentioned
View Answer

Answer: b
Explanation: The anti-aliasing filter is an analog filter which has a twofold purpose.
Analog signal|| Pre-filter -> A/D Converter -> Digital Processor -> D/A Converter -> Post-filter
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6. In DM, further the two integrators at encode are replaced by one integrator placed before comparator, and then such system is called?
a) System-delta modulation
b) Sigma-delta modulation
c) Source-delta modulation
d) None of the mentioned
View Answer

Answer: b
Explanation: In DM, Furthermore, the two integrators at the encoder can be replaced by a single integrator placed before the comparator. This system is known as sigma-delta modulation (SDM).

7. What is the system function of the integrator that is modeled by the discrete time system?
a) H(z)=\(\frac{z^{-1}}{1-z^{-1}}\)
b) H(z)=\(\frac{z^{-1}}{1+z^{-1}}\)
c) H(z)=\(\frac{z^{z^1}}{1-z^1}\)
d) H(z)=\(\frac{z^{z^1}}{1+z^1}\)
View Answer

Answer: a
Explanation: The integrator is modeled by the discrete time system with system function
H(z)=\(\frac{z^{-1}}{1-z^{-1}}\)
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8. What is the z-transform of sequence {dq(n)} i.e., Dq(z)= ?
a) \(H_s (z)X(z)- H_n (z)E(z)\)
b) \(H_s (z)X(z)+ H_n (z)E(z)\)
c) \(H_s (n)X(z)+ H_n (n)E(z)\)
d) \(H_n (z)X(z)- H_s (z)E(z)\)
View Answer

Answer: b
Explanation: \(D_q (z)=\frac{H(z)}{1+H(z)} X(z)+\frac{1}{1+H(z)} E(z)\)
= \(H_s (z)X(z)+H_n (z)E(z)\).

9.The performance of the SDM system is determined by the noise system function Hn(z), which has a magnitude of?
a) \(|H_n (z)|=2 |sin⁡ \frac{πF}{F_s}|\)
b) \(|H_n (z)|=4 |sin⁡ \frac{πF}{F_s}|\)
c) \(|H_n (z)|=3 |sin⁡ \frac{πF}{F_s}|\)
d) \(|H_n (z)|= |sin⁡ \frac{πF}{F_s}|\)
View Answer

Answer: a
Explanation: The performance of the SDM system is therefore determined by the noise system function H_(n)(z), which has a magnitude frequency response: \(|H_n (z)|=2 |sin⁡ \frac{πF}{F_s}|\).
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10. The in-band quantization noise variance is given as?
a) \(\sigma_n^2=\int_{-B}^B |H_n (F)|^3 S_e (F)dF\)
b) \(\sigma_n^2=\int_{-B}^B |H_n (F)|^2 S_e (F)dF\)
c) \(\sigma_n^2=\int_{-B}^B |H_n (F)|^1 S_e (F)dF\)
d) None
View Answer

Answer: b
Explanation: The in-band quantization noise variance is given as: \(\sigma_n^2=\int_{-B}^B |H_n (F)|^2 S_e (F)dF\) where \(S_e (F)=\frac{\sigma_e^2}{F_(s)}\) is the power spectral density of the quantization noise.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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