Digital Domain Frequency Transformations

Digital Communications Systems

This set of Basic Digital Signal Processing Questions & Answers focuses on “Frequency Transformations in the Digital Domain”.

1. The frequency transformation in the digital domain involves replacing the variable z-1 by a rational function g(z-1).
a) True
b) False

2. The mapping z-1 → g(z-1) must map inside the unit circle in the z-plane into __________
a) Outside the unit circle
b) On the unit circle
c) Inside the unit circle
d) None of the mentioned

3. The unit circle must be mapped outside the unit circle.
a) True
b) False

4. The mapping z-1 → g(z-1) must be __________
a) Low pass
b) High pass
c) Band pass
d) All-pass

5. What should be the value of |ak| to ensure that a stable filter is transformed into another stable filter?
a) < 1
b) =1
c) > 1
d) 0
.

6. Which of the following methods are inappropriate to design high pass and many band pass filters?
a) Impulse invariance
b) Mapping of derivatives
c) Impulse invariance & Mapping of derivatives
d) None of the mentioned

7. The impulse invariance method and mapping of derivatives are inappropriate to use in the designing of high pass and band pass filters due to aliasing problem.
a) True
b) False

8. We can employ the analog frequency transformation followed by conversion of the result into the digital domain by use of impulse invariance and mapping the derivatives.
a) True
b) False

9. It is better to perform the mapping from an analog low pass filter into a digital low pass filter by either of these mappings and then perform the frequency transformation in the digital domain.
a) True
b) False

10. In which of the following transformations, it doesn’t matter whether the frequency transformation is performed in the analog domain or in frequency domain?
a) Impulse invariance
b) Mapping of derivatives
c) Bilinear transformation
d) None of the mentioned

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