11. Which of the following is the correct relation between ω and Ω?
A. Ω=ωT
B. T=Ωω
C. ω=ΩT
D. None of the mentioned
Answer: C
We know that z=esT
Now substitute s=σ+jΩ and z=r.ejω, which represents ‘z’ in the polar form
On equating both sides, we get
ω=ΩT.
12. When σ<0, then what is the condition on ‘r’?
A. 0<r<1
B. r=1
C. r>1
D. None of the mentioned
Answer: A
We know that z=esT
Now substitute s=σ+jΩ and z=r.ejω, which represents ‘z’ in the polar form
On equating both sides, we get
r=eσT
Thus when σ<0, the value of ‘r’ varies from 0<r<1.
13. When σ>0, then what is the condition on ‘r’?
A. 0<r<1
B. r=1
C. r>1
D. None of the mentioned
Answer: C
We know that z=esT
Now substitute s=σ+jΩ and z=r.ejω, which represents ‘z’ in the polar form
On equating both sides, we get
r=eσT
Thus when σ>0, the value of ‘r’ varies from r>1.
14. What is the period of the scaled spectrum Fs.X(F)?
A. 2Fs
B. Fs/2
C. 4Fs
D. Fs
Answer: D
When a continuous-time signal x(t) with spectrum X(F) is sampled at a rate Fs=1/T samples per second, the spectrum of the sampled signal is a periodic repetition of the scaled spectrum Fs.X(F) with period Fs.
15. In which of the following transformations, poles, and zeros of H(s) are mapped directly into poles and zeros in the z-plane?
A. Impulse invariance
B. Bilinear transformation
C. Approximation of derivatives
D. Matched Z-transform
Answer: D
In this method of transforming an analog filter into an equivalent digital filter is to map the poles and zeros of H(s) directly into poles and zeros in the z-plane.
16. Which of the following is true in matched z-transform?
A. Poles of H(s) are directly mapped to poles in z-plane
B. Zeros of H(s) is directly mapped to poles in z-plane
C. Poles & Zeros of H(s) are directly mapped to poles in z-plane
D. None of the mentioned
Answer: C
In the transformation of the analog filter into the digital filter by matched z-transform method, the poles and zeros of H(s) directly into poles and zeros in the z-plane.
17. In matched z-transform, the poles and zeros of H(s) are directly mapped into poles and zeros in the z-plane.
A. True
B. False
Answer: A
In this method of transforming an analog filter into an equivalent digital filter is to map the poles and zeros of H(s) directly into poles and zeros in the z-plane.
18. The factor of the form (s-A. in H(s) is mapped into which of the following factors in the z-domain?
A. 1-eaTz
B. 1-eaTz-1
C. 1-e-aTz-1
D. 1+eaTz-1
Answer: B
If T is the sampling interval, then each factor of the form (s-A. in H(s) is mapped into the factor (1-eaTz-1) in the z-domain.
19. The factor of the form (s+A. in H(s) is mapped into which of the following factors in the z-domain?
A. 1-eaTz
B. 1-eaTz-1
C. 1-e-aTz-1
D. 1+eaTz-1
Answer: C
If T is the sampling interval, then each factor of the form (s+A. in H(s) is mapped into the factor (1-e-aTz-1) in the z-domain.
20. If the factor of the form (s-A. in H(s) is mapped into 1-eaTz-1 in the z-domain, that kind of transformation is called ______
A. Impulse invariance
B. Bilinear transformation
C. Approximation of derivatives
D. Matched Z-transform
Answer: D
If T is the sampling interval, then each factor of the form (s-A. in H(s) is mapped into the factor (1-eaTz-1) in the z-domain. This mapping is called the matched z-transform.
21. The poles obtained from matched z-transform are identical to poles obtained from which of the following transformations?
A. Bilinear transformation
B. Impulse invariance
C. Approximation of derivatives
D. None of the mentioned
Answer: B
We observe that the poles obtained from the matched z-transform are identical to the poles obtained with the impulse invariance method.
22. The zero positions obtained from matched z-transform and impulse invariance methods are not the same.
A. True
B. False
Answer: A
We observe that the poles obtained from the matched z-transform are identical to the poles obtained with the impulse invariance method. However, the two techniques result in different zero positions.
23. The sampling interval in the matched z-transform must be properly selected to yield the pole and zero locations at the equivalent position in the z-plane.
A. True
B. False
Answer: A
To preserve the frequency response characteristic of the analog filter, the sampling interval in the matched z-transformation must be properly selected to yield the pole and zero locations at the equivalent position in the z-plane.
24. What should be the value of sampling interval T, to avoid aliasing?
A. Zero
B. Sufficiently large
C. Sufficiently small
D. None of the mentioned
Answer: C
Aliasing in this matched z-transformation can be avoided by selecting the sampling interval T sufficiently small.
