# 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

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.

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

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

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

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

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.

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

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

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

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

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