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

View Answer

Explanation: As in the analog domain, frequency transformations can be performed on a digital low pass filter to convert it to either a band pass, band stop or high pass filter. The transformation involves the replacing of the variable z

^{-1}by a rational function g(z

^{-1}).

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

View Answer

Explanation: The map z

^{-1}→ g(z

^{-1}) must map inside the unit circle in the z-plane into itself to apply digital frequency transformation.

3. The unit circle must be mapped outside the unit circle.

a) True

b) False

View Answer

Explanation: For the map z

^{-1}→ g(z

^{-1}) to be a valid digital frequency transformation, then the unit circle also must be mapped inside the unit circle.

4. The mapping z^{-1} → g(z^{-1}) must be __________

a) Low pass

b) High pass

c) Band pass

d) All-pass

View Answer

Explanation: We know that the unit circle must be mapped inside the unit circle.

Thus it implies that for r=1, e

^{-jω}= g(e

^{-jω})=|g(ω)|.e

^{j arg [ g(ω) ]}

It is clear that we must have |g(ω)|=1 for all ω. That is, the mapping is all-pass.

5. What should be the value of |a_{k}| to ensure that a stable filter is transformed into another stable filter?

a) < 1

b) =1

c) > 1

d) 0

View Answer

Explanation: The value of |a

_{k}| < 1 to ensure that a stable filter is transformed into another stable filter to satisfy the condition to satisfy the condition 1.

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

View Answer

Explanation: We know that the impulse invariance method and mapping of derivatives are inappropriate to use in the designing of high pass and band pass filters.

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

View Answer

Explanation: We know that 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.

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

View Answer

Explanation: Since there is a problem of aliasing in designing high pass and many band pass filters using impulse invariance and mapping of derivatives, we cannot employ the analog frequency transformation followed by conversion of the result into digital domain by use of these two mappings.

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

View Answer

Explanation: 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 because by this kind of frequency transformation, problem of aliasing is avoided.

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

View Answer

Explanation: In the case of bilinear transformation, where aliasing is not a problem, it does not matter whether the frequency transformation is performed in the analog domain or in frequency domain.

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