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

Answer: A

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. \(σ_d^2=3σ_x^2 [1-γ_{xx} (1)]\)

Answer: B

\(σ_d^2=E[d^2 (n)] = E{[x(n)- x(n-1)]^2}\)

= \(E [x^2 (n)]-2E{x(n)x(n-1)}+E[x^2 (n-1)]\)

= \(2σ_x^2 [1+γ_{xx} (1)]\).

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. \(σ_d^2=2σ_x^2 [1+a^2]\)

Answer: C

An even better approach is to quantize the difference, d(n) = x(n)–ax(n-1), where a is a parameter selected to minimize the variance in d(n).

Therefore \(σ_d^2=σ_x^2 [1-a^2]\) .

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. \({γ_{xx} (1)}{σ_d^2}\)

Answer: A

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)

Answer: C

In the equation d(n) = x(n)–ax(n-1), the quantity ax(n-1) is called a First-order predictor of x(n).

6. The differential predictive signal quantizer system is known as?

A. DCPM
B. DMPC
C. DPCM
D. None of the mentioned

Answer: C

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

Answer: A

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 ).

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

Answer: D

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. \(\hat{x}(n)=\sum_{k=0}^pa_k x(n-k)\)

Answer: B

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 \(\hat{x}(n)=\sum_{k=1}^pa_k x(n-k)\).

10. The simplest form of differential predictive quantization is called?
A. AM
B. BM
C. DM
D. None of the mentioned

Answer: C

The simplest form of differential predictive quantization is called delta modulation (DM).