1. The basic task of the A/D converter is to convert a discrete set of digital code words into a continuous range of input amplitudes.
A. True
B. False
Answer: B
The basic task of the A/D converter is to convert a continuous range of input amplitude into a discrete set of digital code words. This conversion involves the processes of Quantization and Coding.
2. What is the type of quantizer, if a Zero is assigned a quantization level?
A. Midrise type
B. Mid tread type
C. Mistreat type
D. None of the mentioned
Answer: B
If a zero is assigned a quantization level, the quantizer is of the mid-treat type.
3. What is the type of quantizer, if a Zero is assigned a decision level?
A. Midrise type
B. Mid tread type
C. Mistreat type
D. None of the mentioned
Answer: A
If a zero is assigned a decision level, the quantizer is of the midrise type.
4. What is the term used to describe the range of an A/D converter for bipolar signals?
A. Full scale
B. FSR
C. Full-scale region
D. FS
Answer: B
The term Full-scale range (FSR) is used to describe the range of an A/D converter for bipolar signals (i.e., signals with both positive and negative amplitudes).
5. What is the term used to describe the range of an A/D converter for uni-polar signals?
A. Full scale
B. FSR
C. Full-scale region
D. FSS
Answer: A
The term Full scale (FS) is used for unipolar signals.
6. What is the fixed range of the quantization error eq(n)?
A. \(\frac{\Delta}{6}\) < e<sub>q</sub>(n) ≤ \(\frac{\Delta}{6}\)
B. \(\frac{\Delta}{4}\) < e<sub>q</sub>(n) ≤ \(\frac{\Delta}{4}\)
C. \(\frac{\Delta}{2}\) < e<sub>q</sub>(n) ≤ \(\frac{\Delta}{2}\)
D. \(\frac{\Delta}{16}\) < e<sub>q</sub>(n) ≤ \(\frac{\Delta}{16}\)
Answer: C
The quantization error eq(n) is always in the range \(\frac{\Delta}{2}\) < eq(n) \(\frac{\Delta}{2}\), where Δ is quantizer step size.
7. If the dynamic range of the signal is smaller than the range of the quantizer, the samples that exceed the quantizer are clipped, resulting in a large quantization error.
A. True
B. False
Answer: B
If the dynamic range of the signal, defined as Xmax-xmin, is larger than the range of the quantizer, the samples that exceed the quantizer range are clipped, resulting in a large (greater than Δ2 quantization error.
8. What is the relation defined by the operation of quantizer?
A. xq(n) ≡ Q[x(n)] = \(\hat{x}_k\)
B. xq(n) = Q[x(n)] = \(\hat{x}_k\), if x(n) ∈ Ik
C. xq(k) ≡ Q[x(k)] =\(\hat{x}_k\)
D. none of the mentioned
Answer: B
The possible outputs of the quantizer (i.e., the quantization levels) are denoted as (hat{x}_1, hat{x}_2,…hat{x}_L). The operation of the quantizer is defined by the relation, xq(n) ≡ Q[x(n)]= (hat{x}_k), if x(n) ∈ Ik.
9. What is the step size or the resolution of an A/D converter?
A. Δ = (R)/2(b+1)
B. Δ = (R)/2(b-1)
C. Δ = (R)/3(b+1)
D. Δ = (R)/2
Answer: A
The coding process in an A/D converter assigns a unique binary number to each quantization level.
If we have L levels, we need at least L different binary numbers. With a word length of b + 1 bits, we can represent 2b+1 distinct binary numbers. Hence we should have 2(b+1) > L or, equivalently, b + 1 > log2 L.
Then the step size or the resolution of the A/D converter is given by
Δ = (R)/2(b+1), where R is the range of the quantizer.
10. In the practical A/D converters, if the first transition may not occur at exactly + 1/2 LSB, then such kind of error is known as ____________
A. Scale-factor error
B. Offset error
C. Linearity error
D. All of the mentioned
Answer: B
We note that practical A/D converters may have offset error (the first transition may not occur at exactly + 1/2 LSB.
11. In the practical A/D converters, if the difference between the values at which the first transition and the last transition occur is not equal to FS – 2LSB, then such error is known as _________
A. Scale-factor error
B. Offset error
C. Linearity error
D. All of the mentioned
Answer: A
We note that practical A/D converters scale-factor (or gain) error (the difference between the values at which the first transition and the last transition occur is not equal to FS — 2LSB.
12. In the practical A/D converters, if the differences between transition values are not all equal or uniformly changing, then such error is known as?
A. Scale-factor error
B. Offset error
C. Linearity error
D. All of the mentioned
Answer: C
We note that practical A/D converters have linearity error (the differences between transition values are not all equal or uniformly changing).
11. 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.
12. 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
\(σ_d^2=E[d^2 (n)] = E{[x(n)- x(n-1)]^2}\)
= \(E [x^2 (n)]-2E{x(n)x(n-1)}+E[x^2 (n-1)]\)
= \(2σ_x^2 [1+γ_{xx} (1)]\).
13. 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 \(σ_d^2=σ_x^2 [1-a^2]\) .
14. 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 \({γ_{xx} (1)}{γ_{xx} (0)} = {γ_{xx} (1)}{σ_x^2}\).
15. 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).
16. 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).
17. 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 ).
18. 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 ).
19. 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 \(\hat{x}(n)=\sum_{k=1}^pa_k x(n-k)\).
20. 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).
21. What is the abbreviation of DM?
A. Diameter Modulation
B. Distance Modulation
C. Delta Modulation
D. None of the mentioned
Answer: C
The simplest form of differential predictive quantization is called delta modulation (DM).
