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# Signals & Systems : Nuclear Quiz 2

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Question 1

Find the Fourier transform of the signal x(t) =

Question 2

The Nyquist sampling rate for the following signal will be

x(t) = sinc (106t) sinc2 (105t)

Question 3

Let , find the Fourier Transform of .

Question 4

The minimum amplitude of cross correlated sequence of x(n)=(2,6,0,2) and h(n)=(4,0,5) is

Question 5

A casual LTI system is described by the difference equation 3y[n] = αy [n-2] – 3x[n] + βx [n-2]. The system is stable only if

Question 6

Two discrete-time signals x[n] and h[n] are both non-zero for n = 0, 1, 2 and are zero otherwise. It is given that X[0] = 1, x[1] =2, x[2]=1,h[0]=1. Let y[n] be the linear convolution od x[n] and h[n]. Given y[1]=3 and y[2]=4, the value of the expression (10y[3]+y[4]) is_____.

Question 7

Check the stability of the system h (n) = 0.5n u (-n) + 0.125n u (n)

Question 8

Consider two signal x [n] = {1,2,4} and h [n] = {1,1,1,1,1}.

The convolution y[n] = x[n] * h[n] is

Question 9

Let x(n) = (0.5)n u(n). The DTFT of x(n) is

Question 10

The impulse response h[n] of a linear time-invariant system is given by h[n] = u[n + 3] + u [n – 2] – 2u[n – 7], where u[n] is the unit step sequence. The above system is
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