Digital Signal Processing Questions and Answers – Matched Z Transformation

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This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Matched Z Transformation”.

1. 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
View Answer

Answer: d
Explanation: In this method of transforming 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.
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2. 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) are 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
View Answer

Answer: c
Explanation: In the transformation of analog filter into digital filter by matched z-transform method, the poles and zeros of H(s) directly into poles and zeros in the z-plane.

3. In matched z-transform, the poles and zeros of H(s) are directly mapped into poles and zeros in z-plane.
a) True
b) False
View Answer

Answer: a
Explanation: In this method of transforming 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.

4. The factor of the form (s-a) in H(s) is mapped into which of the following factors in z-domain?
a) 1-eaTz
b) 1-eaTz-1
c) 1-e-aTz-1
d) 1+eaTz-1
View Answer

Answer: b
Explanation: 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.

5. The factor of the form (s+a) in H(s) is mapped into which of the following factors in z-domain?
a) 1-eaTz
b) 1-eaTz-1
c) 1-e-aTz-1
d) 1+eaTz-1
View Answer

Answer: c
Explanation: 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.
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6. If the factor of the form (s-a) in H(s) is mapped into 1-eaTz-1 in the z-domain, the that kind of transformation is called as ______________
a) Impulse invariance
b) Bilinear transformation
c) Approximation of derivatives
d) Matched Z-transform
View Answer

Answer: d
Explanation: 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.

7. 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
View Answer

Answer: b
Explanation: We observe that the poles obtained from the matched z-transform are identical to the poles obtained with the impulse invariance method.

8. The zero positions obtained from matched z-transform and impulse invariance method are not same.
a) True
b) False
View Answer

Answer: a
Explanation: 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.

9. 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
View Answer

Answer: a
Explanation: 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.

10. What should be value of sampling interval T, to avoid aliasing?
a) Zero
b) Sufficiently large
c) Sufficiently small
d) None of the mentioned
View Answer

Answer: c
Explanation: Aliasing in this matched z-transformation can be avoided by selecting the sampling interval T sufficiently small.
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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn