This set of Control Systems Multiple Choice Questions & Answers (MCQs) focuses on “Spectrum Analysis of Sampling Process”.

1. A band limited signal with a maximum frequency of 5 KHz to be sampled. According to the sampling theorem, the sampling frequency which is not valid is:

a) 5 KHz

b) 12 KHz

c) 15 KHz

d) 20 KHz

2. Let x(t) be a continuous-time, real valued signal band-limited to F Hz. The Nyquist sampling rate in Hz, For y(t) =x(0.5t) +x(t)-x(2t) is

a) F

b) 2F

c) 4F

d) 8F

3. Statement (I): Aliasing occurs when the sampling frequency is less than twice the maximum frequency in the signal.

Statement (II): Aliasing is a reversible process.

a) Both statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I).

b) Both Statement (I) and Statement (II) are individually true but Statement (II) is not correct explanation of Statement (I)

c) Statement (I) is true but Statement (II) is false

d) Statement (I) is False but Statement (II) is true

4. Increased pulse-width in the flat-top sampling leads to:

a) Attenuation of high frequencies in reproduction

b) Attenuation of low frequencies in reproduction

c) Greater aliasing errors in reproduction

d) No harmful effects in reproduction

5. A signal represented by x(t) =5cos 400πt is sampled at a rate 300 samples/sec. The resulting samples are passed through an ideal low pass filter of cut-off frequency 150 Hz. Which of the following will be contained in the output of the LPF?

a) 100 Hz

b) 100 Hz, 150 Hz

c) 50 Hz, 100 Hz

d) 50 Hz, 100 Hz, 150 Hz

6. An LTI system having transfer function s^{2}+1/s^{2}+2s+1 and input x(t) =sin(t+1) is in steady state. The output is sampled at ws rad/s to obtain the final output {y (k)}. Which of the following is true?

a) Y is zero for all sampling frequencies ws

b) Y is non zero for all sampling frequencies ws

c) Y is non zero for ws>2 but zero for ws<2

d) Y is zero for ws>2 but non zero for ws<2

7. A bandpass sampling extends from 4-6 kHz. What is the smallest sampling frequency required to retain all the information in the signal.

a) 1 kHz

b) 2 kHz

c) 3 kHz

d) 4 kHz

8. A signal m(t) with bandwidth 500 Hz is first multiplied by a signal g(t). The resulting signal is passed through an ideal low pass filter with bandwidth 1 kHz. The output of the low pass filter would be :

a) Impulse

b) m(t)

c) 0

d) m(t)del(t)

9. A digital measuring instrument employs a sampling rate of 100 samples/second. The sampled input x(n) is averaged using the difference equation:

Y (n) =[x (n)+x (n-1)+x(n-2)+x(n-4)/4] For a step input, the maximum time taken for the output to reach the final value after the input transition is

a) 20 ms

b) 40 ms

c) 80 ms

d) ∞

10. The sinusoid x(t) =6cos10πt is sampled at the rate of 15 Hz and applied to ideal rectangular LPF with cut-off frequency of 10 Hz, then the output of filter contains:

a) Only 10π rad/sec component

b) 10π rad/sec component

c) 10π rad/sec and 20π rad/sec components

d) +10π rad/sec and +20π rad/sec components