Digital Signal Processing Questions and Answers – Oversampling A/D Converters

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Oversampling A/D Converters”.

1. For a given number of bits, the power of quantization noise is proportional to the variance of the signal to be quantized.
a) True
b) False
View Answer

Answer: a
Explanation: The dynamic range of the signal, which is proportional to its standard deviation σx, should match the range R of the quantizer, it follows that ∆ is proportional to σx. Hence for a given number of bits, the power of the quantization noise is proportional to the variance of the signal to be quantized.

2. What is the variance of the difference between two successive signal samples, d(n) = x(n) – x(n-1)?
a) \(σ_d^2=2σ_x^2 [1+γ_{xx} (1)]\)
b) \(σ_d^2=2σ_x^2 [1-γ_{xx} (1)]\)
c) \(σ_d^2=4σ_x^2 [1-γ_{xx} (1)]\)
d) \(σ_d^2=3σ_x^2 [1-γ_{xx} (1)]\)
View Answer

Answer: b
Explanation: \(σ_d^2=E[d^2 (n)] = E{[x(n)- x(n-1)]^2}\)
= \(E [x^2 (n)]-2E{x(n)x(n-1)}+E[x^2 (n-1)]\)
= \(2σ_x^2 [1+γ_{xx} (1)]\).

3. What is the variance of the difference between two successive signal samples, d(n) = x(n)–ax(n-1)?
a) \(σ_d^2=2σ_x^2 [1-a^2]\)
b) \(σ_d^2=σ_x^2 [1+a^2]\)
c) \(σ_d^2=σ_x^2 [1-a^2]\)
d) \(σ_d^2=2σ_x^2 [1+a^2]\)
View Answer

Answer: c
Explanation: An even better approach is to quantize the difference, d(n) = x(n)–ax(n-1), w here a is a parameter selected to minimize the variance in d(n). Therefore \(σ_d^2=σ_x^2 [1-a^2]\) .
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4. If the difference d(n) = x(n)–ax(n-1), then what is the optimum choice for a = ?
a) \({γ_{xx} (1)}{σ_x^2}\)
b) \({γ_{xx} (0)}{σ_x^2}\)
c) \({γ_{xx} (0)}{σ_d^2}\)
d) \({γ_{xx} (1)}{σ_d^2}\)
View Answer

Answer: a
Explanation: An even better approach is to quantize the difference, d(n) = x(n)–ax(n-1), w here a is a parameter selected to minimize the variance in d(n). This leads to the result that the optimum choice of a is \({γ_{xx} (1)}{γ_{xx} (0)} = {γ_{xx} (1)}{σ_x^2}\).

5. What is the quantity ax(n-1) is called?
a) Second-order predictor of x(n)
b) Zero-order predictor of x(n)
c) First-order predictor of x(n)
d) Third-order predictor of x(n)
View Answer

Answer: c
Explanation: In the equation d(n) = x(n)–ax(n-1), the quantity ax(n-1) is called a First-order predictor of x(n).
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6. The differential predictive signal quantizer system is known as?
a) DCPM
b) DMPC
c) DPCM
d) None of the mentioned
View Answer

Answer: c
Explanation: A differential predictive signal quantizer system. This system is used in speech encoding and transmission over telephone channels and is known as differential pulse code modulation (DPCM).

7. What is the expansion of DPCM?
a) Differential Pulse Code Modulation
b) Differential Plus Code Modulation
c) Different Pulse Code Modulation
d) None of the mentioned
View Answer

Answer: a
Explanation: A differential predictive signal quantizer system. This system is used in speech encoding and transmission over telephone channels and is known as differential pulse code modulation (DPCM ).
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8. What are the main uses of DPCM?
a) Speech Decoding and Transmission over mobiles
b) Speech Encoding and Transmission over mobiles
c) Speech Decoding and Transmission over telephone channels
d) Speech Encoding and Transmission over telephone channels
View Answer

Answer: d
Explanation: A differential predictive signal quantizer system. This system is used in speech encoding and transmission over telephone channels and is known as differential pulse code modulation (DPCM ).

9. To reduce the dynamic range of the difference signal d(n) = x(n) – \(\hat{x}(n)\), thus a predictor of order p has the form?
a) \(\hat{x}(n)=\sum_{k=1}^pa_k x(n+k)\)
b) \(\hat{x}(n)=\sum_{k=1}^pa_k x(n-k)\)
c) \(\hat{x}(n)=\sum_{k=0}^pa_k x(n+k)\)
d) \(\hat{x}(n)=\sum_{k=0}^pa_k x(n-k)\)
View Answer

Answer: b
Explanation: The goal of the predictor is to provide an estimate \(\hat{x}(n)\) of x(n) from a linear combination of past values of x(n), so as to reduce the dynamic range of the difference signal d(n) = x(n)-\(\hat{x}(n)\). Thus a predictor of order p has the form \(\hat{x}(n)=\sum_{k=1}^pa_k x(n-k)\).
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10. The simplest form of differential predictive quantization is called?
a) AM
b) BM
c) DM
d) None of the mentioned
View Answer

Answer: c
Explanation: The simplest form of differential predictive quantization is called delta modulation (DM).

11. What is the abbreviation of DM?
a) Diameter Modulation
b) Distance Modulation
c) Delta Modulation
d) None of the mentioned
View Answer

Answer: c
Explanation: The simplest form of differential predictive quantization is called delta modulation (DM).

12. In DM, the quantizer is a simple ________ bit and ______ level quantizer.
a) 2-bit, one-level
b) 1-bit, two-level
c) 2-bit, two level
d) 1-bit, one level
View Answer

Answer: b
Explanation: The simplest form of differential predictive quantization is called delta modulation (DM). In DM, the quantizer is a simple 1-bit (two-level) quantizer.

13. In DM, What is the order of predictor is used?
a) Zero-order predictor
b) Second-order predictor
c) First-order predictor
d) Third-order predictor
View Answer

Answer: c
Explanation: In DM, the quantizer is a simple 1-bit (two-level) quantizer and the predictor is a first-order predictor.

14. In the equation xq(n)=axq(n-1)+dq(n), if a = 1 then integrator is called?
a) Leaky integrator
b) Ideal integrator
c) Ideal accumulator
d) Both Ideal integrator & accumulator
View Answer

Answer: d
Explanation: In the equation xq(n)=axq(n-1)+dq(n), if a = 1, we have an ideal accumulator (integrator).

15. In the equation xq(n)=axq(n-1)+dq(n), if a < 1 then integrator is called?
a) Leaky integrator
b) Ideal integrator
c) Ideal accumulator
d) Both Ideal integrator & accumulator
View Answer

Answer: a
Explanation: In the equation xq(n)=axq(n-1)+ dq(n), a < 1 results in a ”leaky integrator”.

Sanfoundry Global Education & Learning Series – Digital Signal Processing.

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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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