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

1. What is the passband edge frequency of an analog low pass normalized filter?

Let H(s) denote the transfer function of a low pass analog filter with a passband edge frequency ΩP equal to 1 rad/sec. This filter is known as the analog low pass normalized prototype.

2. If H(s) is the transfer function of an analog low pass normalized filter and Ωu is the desired passband edge frequency of the new low pass filter, then which of the following transformation has to be performed?

A. s → s/Ωu
B. s → s.Ωu
C. s → Ωu/s
D. none of the mentioned

If Ωu is the desired passband edge frequency of the new low pass filter, then the transfer function of this new low pass filter is obtained by using the transformation s → s/Ωu.

3. Which of the following is a low pass-to-high pass transformation?

A. s → s / Ωu
B. s → Ωu / s
C. s → Ωu.s
D. none of the mentioned

The low pass-to-high pass transformation is simply achieved by replacing s by 1/s. If the desired high pass filter has the passband edge frequency Ωu, then the transformation is
s → Ωu / s.

4. Which of the following is the backward design equation for a low pass-to-low pass transformation?

A. $$\Omega_S=\frac{\Omega_S}{\Omega_u}$$

B. $$\Omega_S=\frac{\Omega_u}{\Omega’_S}$$

C. $$\Omega’_S=\frac{\Omega_S}{\Omega_u}$$

D. $$\Omega_S=\frac{\Omega’_S}{\Omega_u}$$

If Ωu is the desired passband edge frequency of the new low pass filter, then the transfer function of this new low pass filter is obtained by using the transformation s → s/Ωu. If ΩS and Ω’S are the stopband frequencies of prototype and transformed filters respectively, then the backward design equation is given by
$$\Omega_S=\frac{\Omega’_S}{\Omega_u}$$.

5. Which of the following is a low pass-to-band pass transformation?

A. s→$$\frac{s^2+Ω_u Ω_l}{s(Ω_u+Ω_l)}$$
B. s→$$\frac{s^2-Ω_u Ω_l}{s(Ω_u-Ω_l)}$$
C. s→$$\frac{s^2+Ω_u Ω_l}{s(Ω_u-Ω_l)}$$
D. s→$$\frac{s^2-Ω_u Ω_l}{s(Ω_u+Ω_l)}$$

If Ωu and Ωl are the upper and lower cutoff pass band frequencies of the desired bandpass filter, then the transformation to be performed on the normalized low pass filter is

s→$$\frac{s^2+Ω_u Ω_l}{s(Ω_u-Ω_l)}$$

6. Which of the following is the backward design equation for a low pass-to-high pass transformation?

A. $$\Omega_S=\frac{\Omega_S}{\Omega_u}$$

B. $$\Omega_S=\frac{\Omega_u}{\Omega’_S}$$

C. $$\Omega’_S=\frac{\Omega_S}{\Omega_u}$$

D. $$\Omega_S=\frac{\Omega’_S}{\Omega_u}$$

If Ωu is the desired passband edge frequency of the new high pass filter, then the transfer function of this new high pass filter is obtained by using the transformation s → Ωu /s. If ΩS and Ω’S are the stopband frequencies of prototype and transformed filters respectively, then the backward design equation is given by

$$\Omega_S=\frac{\Omega_u}{\Omega’_S}$$.

7. Which of the following is a low pass-to-band stop transformation?

A. s→$$\frac{s(Ω_u-Ω_l)}{s^2+Ω_u Ω_l}$$

B. s→$$\frac{s(Ω_u+Ω_l)}{s^2+Ω_u Ω_l}$$

C. s→$$\frac{s(Ω_u-Ω_l)}{s^2-Ω_u Ω_l}$$

D. none of the mentioned

If Ωu and Ωl are the upper and lower cutoff pass band frequencies of the desired band stop filter, then the transformation to be performed on the normalized low pass filter is

s→$$\frac{s(Ω_u-Ω_l)}{s^2-Ω_u Ω_l}$$

8. If A=$$\frac{-Ω_1^2+Ω_u Ω_l}{Ω_1 (Ω_u-Ω_l)}$$ and B=$$\frac{Ω_2^2-Ω_u Ω_l}{Ω_2 (Ω_u-Ω_l)}$$, then which of the following is the backward design equation for a low pass-to-band pass transformation?

A. ΩS=|B|
B. ΩS=|A|
C. ΩS=Max{|A|,|B|}
D. ΩS=Min{|A|,|B|}

If Ωu and Ωl are the upper and lower cutoff pass band frequencies of the desired bandpass filter and Ω1 and Ω2 are the lower and upper cutoff stopband frequencies of the desired bandpass filter, then the backward design equation is

ΩS=Min{|A|,|B|}
where,

A=$$\frac{-Ω_1^2+Ω_u Ω_l}{Ω_1 (Ω_u-Ω_l)}$$ and B=$$\frac{Ω_2^2-Ω_u Ω_l}{Ω_2 (Ω_u-Ω_l)}$$.

9. If A=$$\frac{Ω_1 (Ω_u-Ω_l)}{-Ω_1^2+Ω_u Ω_l}$$ and B=$$\frac{Ω_2 (Ω_u-Ω_l)}{Ω_2^2-Ω_u Ω_l}$$, then which of the following is the backward design equation for a low pass-to-band stop transformation?

A. ΩS=Max{|A|,|B|}
B. ΩS=Min{|A|,|B|}
C. ΩS=|B|
D. ΩS=|A|

If Ωu and Ωl are the upper and lower cutoff pass band frequencies of the desired band stop filter and Ω1 and Ω2 are the lower and upper cutoff stopband frequencies of the desired band stop filter, then the backward design equation is
ΩS=Min{|A|,|B|}
where, A=$$\frac{Ω_1 (Ω_u-Ω_l)}{-Ω_1^2+Ω_u Ω_l}$$ and B=$$\frac{Ω_2 (Ω_u-Ω_l)}{Ω_2^2-Ω_u Ω_l}$$.

10. Which of the following is a low pass-to-high pass transformation?

A. s → s / Ωu
B. s → Ωu/s
C. s → Ωu.s
D. none of the mentioned

The low pass-to-high pass transformation is simply achieved by replacing s with 1/s. If the desired high pass filter has the passband edge frequency Ωu, then the transformation is
s → Ωu/s.

11. Which of the following operation has to be performed to increase the sampling rate by an integer factor I?

A. Interpolating I+1 new samples
B. Interpolating I-1 new samples
C. Extrapolating I+1 new samples
D. Extrapolating I-1 new samples

An increase in the sampling rate by an integer factor of I can be accomplished by interpolating I-1 new samples between successive values of the signal.

12. In one of the interpolation processes, we can preserve the spectral shape of the signal sequence x(n).

A. True
B. False

The interpolation process can be accomplished in a variety of ways. Among them, there is a process that preserves the spectral shape of the signal sequence x(n).

13. If v(m) denotes a sequence with a rate Fy=I.Fx which is obtained from x(n), then which of the following is the correct definition for v(m)?

A.x(mI), m=0,±I,±2I…. 0, otherwise
B. x(mI), m=0,±I,±2I…. x(m/I), otherwise
C. x(m/I), m=0,±I,±2I….
0, otherwise
D. None of the mentioned

If v(m) denote a sequence with a rate Fy=I.Fx which is obtained from x(n) by adding I-1 zeros between successive values of x(n). Thus
v(m)= x(m/I), m=0,±I,±2I….
0, otherwise.

14. If X(z) is the z-transform of x(n), then what is the z-transform of interpolated signal v(m)?

A. X(zI)
B. X(z+I)
C. X(z/I)
D. X(zI)

By taking the z-transform of the signal v(m), we get
V(z)=(sum_{m=-∞}^∞ v(m)z^{-m})
=(sum_{m=-∞}^∞ x(m)z^{-mI})
= X(z-I)

15. If x(m) and v(m) are the original and interpolated signals and ωy denotes the frequency variable relative to the new sampling rate, then V(ωy)= X(ωyI).

A. True
B. False

The spectrum of v(m) is obtained by evaluating V(z) = X(zI) on the unit circle. Thus V(ωy)= X(ωyI), where ωy denotes the frequency variable relative to the new sampling rate.

16. What is the relationship between ωx and ωy?

A. ωy= ωx.I
B. ωy= ωx/I
C. ωy= ωx+I
D. None of the mentioned

We know that the relationship between sampling rates is Fy=IFx and hence the frequency variables ωx and ωy are related according to the formula
ωy= ωx/I.

17. The following sampling rate conversion technique is an interpolation by a factor I.

A. True
B. False

From the diagram, the values are interpolated between two successive values of x(n), thus it is called as sampling rate conversion using interpolation by a factor I.

18. The following sampling rate conversion technique is an interpolation by a factor I.

A. True
B. False

The sampling rate conversion technique given in the diagram is decimation by a factor D.

19. Which of the following is true about the interpolated signal whose spectrum is V(ωy)?

A. (I-1)-fold non-periodic
B. (I-1)-fold periodic repetition
C. I-fold non periodic
D. I-fold periodic repetition

We observe that the sampling rate increase, obtained by the addition of I-1 zero samples between successive values of x(n), results in a signal whose spectrum is an I-fold periodic repetition of the input signal spectrum.

20. C=I is the desired normalization factor.

A. True
B. False

The amplitude of the sampling rate converted signal should be multiplied by a factor C, whose value when equal to I is called the desired normalization factor W.

21. Sampling rate conversion by the rational factor I/D is accomplished by what connection of interpolator and decimator?

A. Parallel
C. Convolution
D. None of the mentioned

A sampling rate conversion by the rational factor I/D is accomplished by cascading an interpolator with a decimator.

22. Which of the following has to be performed in sampling rate conversion by rational factor?

A. Interpolation
B. Decimation
C. Either interpolation or decimation
D. None of the mentioned

We emphasize that the importance of performing the interpolation first and decimation second is to preserve the desired spectral characteristics of x(n).

23. Which of the following operation is performed by the blocks given in the figure below?

A. Sampling rate conversion by a factor I
B. Sampling rate conversion by a factor D
C. Sampling rate conversion by a factor D/I
D. Sampling rate conversion by a factor I/D

In the diagram given, an interpolator is in a cascade with a decimator which together performs the action of sampling rate conversion by a factor I/D.

24. The Nth root of unity WN is given as ______

A. ej2πN
B. e-j2πN
C. e-j2π/N
D. ej2π/N

X(k)=$$\sum_{n=0}^{N-1} x(n)e^{-j2πkn/N}=\sum_{n=0}^{N-1} x(n) W_N^{kn}$$