Signal Processing MCQ Questions & Answers

31.
The first stage DIT-FFT of a sequence x(n) is given by:

A. \[X\left( k \right) = \left\{ \begin{array}{l} G\left( k \right) + W_N^kH\left( k \right)\,\,\,\,\,0 \le k \le \left( {\frac{N}{2} - 1} \right)\\ G\left( {k + \frac{N}{2}} \right) - W_N^kH\left( {k + \frac{N}{2}} \right)\,\,\,\,\,\frac{N}{2} \le k \le \left( {N - 1} \right) \end{array} \right.\]

B. \[X\left( k \right) = \left\{ \begin{array}{l} G\left( k \right) - W_N^kH\left( k \right)\,\,\,\,\,0 \le k \le \left( {\frac{N}{2} - 1} \right)\\ G\left( {k + \frac{N}{2}} \right) - W_N^kH\left( {k + \frac{N}{2}} \right)\,\,\,\,\,\frac{N}{2} \le k \le \left( {N - 1} \right) \end{array} \right.\]

C. \[X\left( k \right) = \left\{ \begin{array}{l} G\left( k \right) - W_N^kH\left( k \right)\,\,\,\,\,0 \le k \le \left( {\frac{N}{2} - 1} \right)\\ G\left( k \right) + W_N^kH\left( k \right)\,\,\,\,\,\frac{N}{2} \le k \le \left( {N - 1} \right) \end{array} \right.\]

D. \[X\left( k \right) = \left\{ \begin{array}{l} G\left( {k + N} \right) - W_N^kH\left( k \right)\,\,\,\,\,0 \le k \le \left( {\frac{N}{2} - 1} \right)\\ G\left( k \right) + W_N^kH\left( k \right)\,\,\,\,\,\frac{N}{2} \le k \le \left( {N - 1} \right) \end{array} \right.\]

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32.
What is the value of magnitude frequency response of Butterworth low pass filter at Ω = 0 ?

A. 1

B. $$\frac{1}{{\sqrt 2 }}$$

C. 0

D. 2

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33.
The input-output relationship of a causal stable LTI system is given as y[n] = αy[n - 1] + βx[n]
If the impulse response h[n] of this system satisfies the condition $$\sum\limits_{n = 0}^\infty {h\left[ n \right] = 2,} $$ the relationship between α and β is

A. $$\alpha = 1 - \frac{\beta }{2}$$

B. $$\alpha = 1 + \frac{\beta }{2}$$

C. α = 2β

D. α = -2β

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34.
The linear time invariant system h(t) = (e^-4t + e^4t).u(t) is . . . . . . . . and . . . . . . . .

A. Causal, Unstable

B. Noncausal, Unstable

C. Causal, Stable

D. Noncausal, Stable

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35.
The unit sample response of a discrete system is 1, $$\frac{1}{2},\,\frac{1}{4},$$ 0, 0, 0 . . . For an input sequence 1, 0, 1, 0, 0, 0 . . ., what is the output sequence?

A. $$1,\,\frac{1}{2},\,\frac{1}{4},\,\frac{1}{2},\,\frac{1}{4},\,0,\,0\,...$$

B. $$1,0,\,\frac{1}{4},\,0,\,0\,...$$

C. $$2,\,\frac{1}{2},\,\frac{5}{4},\,0,\,0\,...$$

D. $$1,\,\frac{1}{2},\,\frac{5}{4},\,\frac{1}{2},\,\frac{1}{4},\,0,\,0\,...$$

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36.
The output w[n] of the system shown in figure is \[\xrightarrow{{x\left[ n \right]}}\boxed{y\left[ n \right] = \sum\limits_{ - \infty }^n {x\left[ k \right]} }\xrightarrow{{y\left[ n \right]}}\boxed{w\left[ n \right] = y\left[ n \right] - y\left[ {n - 1} \right]}\xrightarrow{{w\left[ n \right]}}\]

A. x[n]

B. x[n - 1]

C. x[n] - x[n - 1]

D. \[\frac{1}{2}\] (x[n - 1]) + x[n]

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37.
A matched filter having a frequency response $$H\left( f \right) = \frac{{1 - {e^{ - j2\pi fT}}}}{{j2\pi f}}$$ matches to:

A. \[s\left( t \right) = \left\{ \begin{array}{l} 1,\,\,\,\,0 \le t \le T\\ 0,\,\,\,\,{\rm{otherwise}} \end{array} \right.\]

B. \[s\left( t \right) = \left\{ \begin{array}{l} - 1,\,\,\,\,0 \le t \le T\\ \,\,\,0,\,\,\,\,{\rm{otherwise}} \end{array} \right.\]

C. \[s\left( t \right) = \left\{ \begin{array}{l} 1 - \frac{t}{T},\,\,\,\,0 \le t \le T\\ \,\,\,\,\,0,\,\,\,\,{\rm{otherwise}} \end{array} \right.\]

D. \[s\left( t \right) = \left\{ \begin{array}{l} - 1 + \frac{t}{T},\,\,\,\,0 \le t \le T\\ \,\,\,\,\,0,\,\,\,\,{\rm{otherwise}} \end{array} \right.\]

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38.
Auto-correlation function R_x(τ) of a stationary process X(t) is

A. a deterministic function with maximum value at τ = 0

B. a deterministic function which is periodic

C. a stationary random process

D. a periodic stationary process

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39.
What is the ROC for the given signal?
$${x_1}\left[ n \right] = {\left( {\frac{1}{2}} \right)^n}u\left[ {n - 3} \right]$$

A. $$\left| z \right| > \frac{1}{2}$$

B. $$\left| z \right| < \frac{1}{2}$$

C. $$\left| z \right| < \frac{1}{3}$$

D. $$\left| z \right| > \frac{1}{3}$$

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40.
If the step response of a causal, linear time-invariant system is a(t), then the response of the system to a general input x(t) would be

A. $$\int\limits_{{0^ + }}^t {\frac{{da\left( \tau \right)}}{{d\tau }}x\left( {t - \tau } \right)d\tau } $$

B. $$a\left( 0 \right)x\left( t \right) + \int\limits_{{0^ + }}^t {\frac{{da\left( \tau \right)}}{{d\tau }}x\left( {t - \tau } \right)d\tau } $$

C. $$x\left( 0 \right)a\left( t \right) + \int\limits_{{0^ + }}^t {x\left( \tau \right)a\left( {t - \tau } \right)d\tau } $$

D. $$x\left( 0 \right)a\left( t \right) + \int\limits_{{0^ + }}^t {\frac{{da\left( \tau \right)}}{{d\tau }}x\left( {t - \tau } \right)d\tau } $$

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Signal Processing MCQ Questions & Answers | ECE

31. The first stage DIT-FFT of a sequence x(n) is given by:

Answer & Solution

32. What is the value of magnitude frequency response of Butterworth low pass filter at Ω = 0 ?

Answer & Solution

33. The input-output relationship of a causal stable LTI system is given as y[n] = αy[n - 1] + βx[n] If the impulse response h[n] of this system satisfies the condition $$\sum\limits_{n = 0}^\infty {h\left[ n \right] = 2,} $$ the relationship between α and β is

Answer & Solution

34. The linear time invariant system h(t) = (e-4t + e4t).u(t) is . . . . . . . . and . . . . . . . .

Answer & Solution

35. The unit sample response of a discrete system is 1, $$\frac{1}{2},\,\frac{1}{4},$$ 0, 0, 0 . . . For an input sequence 1, 0, 1, 0, 0, 0 . . ., what is the output sequence?

Answer & Solution

Answer & Solution

37. A matched filter having a frequency response $$H\left( f \right) = \frac{{1 - {e^{ - j2\pi fT}}}}{{j2\pi f}}$$ matches to:

Answer & Solution

38. Auto-correlation function Rx(τ) of a stationary process X(t) is

Answer & Solution

39. What is the ROC for the given signal? $${x_1}\left[ n \right] = {\left( {\frac{1}{2}} \right)^n}u\left[ {n - 3} \right]$$

Answer & Solution

40. If the step response of a causal, linear time-invariant system is a(t), then the response of the system to a general input x(t) would be

Answer & Solution

Read More Section(Signal Processing)

31.
The first stage DIT-FFT of a sequence x(n) is given by:

32.
What is the value of magnitude frequency response of Butterworth low pass filter at Ω = 0 ?

33.
The input-output relationship of a causal stable LTI system is given as y[n] = αy[n - 1] + βx[n]
If the impulse response h[n] of this system satisfies the condition $$\sum\limits_{n = 0}^\infty {h\left[ n \right] = 2,} $$ the relationship between α and β is

34.
The linear time invariant system h(t) = (e^-4t + e^4t).u(t) is . . . . . . . . and . . . . . . . .

35.
The unit sample response of a discrete system is 1, $$\frac{1}{2},\,\frac{1}{4},$$ 0, 0, 0 . . . For an input sequence 1, 0, 1, 0, 0, 0 . . ., what is the output sequence?

37.
A matched filter having a frequency response $$H\left( f \right) = \frac{{1 - {e^{ - j2\pi fT}}}}{{j2\pi f}}$$ matches to:

38.
Auto-correlation function R_x(τ) of a stationary process X(t) is

39.
What is the ROC for the given signal?
$${x_1}\left[ n \right] = {\left( {\frac{1}{2}} \right)^n}u\left[ {n - 3} \right]$$

40.
If the step response of a causal, linear time-invariant system is a(t), then the response of the system to a general input x(t) would be