# Digital Domain Frequency Transformation MCQ [Free PDF] – Objective Question Answer for Digital Domain Frequency Transformation Quiz

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

As in the analog domain, frequency transformations can be performed on a digital low pass filter to convert it to either a bandpass, band stop, or high pass filter. The transformation involves the replacing of the variable z-1 with 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

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

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. Bandpass
D. All-pass

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)|.ej 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 |ak| to ensure that a stable filter is transformed into another stable filter?

A. < 1
B. =1
C. > 1
D. 0

The value of |ak| < 1 to ensure that a stable filter is transformed into another stable filter to satisfy the condition 1.

6. Which of the following methods are inappropriate to design high pass and many bandpass filters?

A. Impulse invariance
B. Mapping of derivatives
C. Impulse invariance & Mapping of derivatives
D. None of the mentioned

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 bandpass filters due to the aliasing problems.

A. True
B. False

We know that the impulse invariance method and mapping of derivatives are inappropriate to use in the designing of high pass and bandpass filters due to the aliasing problems.

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

Since there is a problem with aliasing in designing high pass and many bandpass filters using impulse invariance and mapping of derivatives, we cannot employ the analog frequency transformation followed by conversion of the result into the 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

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, the 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 the frequency domain?

A. Impulse invariance
B. Mapping of derivatives
C. Bilinear transformation
D. None of the mentioned

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 the frequency domain.

11. Which of the following techniques of designing IIR filters do not involve the conversion of an analog filter into a digital filter?

A. Bilinear transformation
B. Impulse invariance
C. Approximation of derivatives
D. None of the mentioned

Except for the impulse invariance method, the design techniques for IIR filters involve the conversion of an analog filter into a digital filter by some mapping from the s-plane to the z-plane.

12. Using which of the following methods, a digital IIR filter can be directly designed?

D. All of the mentioned

There are several methods for designing digital filters directly. The three techniques are Pade approximation and the least square method, the specifications are given in the time domain and the design is carried out in the time domain. The other one is the least-squares technique in which the design is carried out in the frequency domain.

13. What is the number of parameters that a filter consists of?

A. M+N+1
B. M+N
C. M+N-1
D. M+N-2

The filter has L=M+N+1 parameters, namely, the coefficients {ak} and {bk}, which can be selected to minimize some error criteria.

14. The minimization of ε involves the solution of a set of non-linear equations.

A. True
B. False

In general, h(n) is a non-linear function of the filter parameters and hence the minimization of ε involves the solution of a set of non-linear equations.

15. What should be the upper limit of the solution to match h(n) perfectly to the desired response hd(n)?

A. L
B. L+1
C. L-1
D. L+2

If we select the upper limit as U=L-1, it is possible to match h(n) perfectly to the desired response hd(n) for 0 < n < M+N.

16. For how many values of the impulse response, a perfect match is present between h(n) and hd(n)?

A. L
B. M+N+1
C. 2L-M-N-1
D. All of the mentioned

We obtain a perfect match between h(n) and the desired response hd(n) for the first L values of the impulse response and we also know that L=M+N+1.

17. The degree to which the design technique produces acceptable filter designs depends in part on the number of filter coefficients selected.

A. True
B. False

The degree to which the design technique produces acceptable filter designs depends in part on the number of filter coefficients selected. Since the design method matches hd(n) only up to the number of filter parameters, the more complex the filter, the better the approximation to hd(n).

18. According to this method of design, the filter should have one of the following in large numbers?

A. Only poles
B. Both poles and zeros
C. Only zeros
D. None of the mentioned

The major limitation of the Pade approximation method, namely, the resulting filter must contain a large number of poles and zeros.

19. Which of the following conditions are in the favor of Pade approximation method?

A. Desired system function is rational
B. Prior knowledge of the number of poles and zeros
C. Desired system function is rational & Prior knowledge of the number of poles and zeros
D. None of the mentioned

The Pade approximation method results in a perfect match to Hd(z) when the desired system function is rational and we have prior knowledge of the number of poles and zeros in the system.

20. Which of the following filters will have an impulse response as shown in the below figure?

A. Butterworth filters
B. Type-I Chebyshev filter
C. Type-II Chebyshev filter
D. None of the mentioned

The diagram that is given in the question is the impulse response of the Butterworth filter.

21. For what number of zeros, the approximation is poor?

A. 3
B. 4
C. 5
D. 6

We observe that when the number of zeros is minimum, that is when M=3, the resulting frequency response is a relatively poor approximation to the desired response.

22. Which of the following pairs of M and N will give a perfect match?

A. 3,6
B. 3,4
C. 3,5
D. 4,5

When M is increased from three to four, we obtain a perfect match with the desired Butterworth filter not only for N=4 but for N=5, and in fact, for larger values of N.

23. Which of the following filters will have an impulse response as shown in the below figure?

A. Butterworth filters
B. Type-I Chebyshev filter
C. Type-II Chebyshev filter
D. None of the mentioned

The diagram that is given in the question is the impulse response of the type-II Chebyshev filter.

24. Which of the following filter we use in least-square design methods?

A. All zero
B. All pole
C. Pole-zero
D. Any of the mentioned