1. A real-valued signal x(t) is known to be uniquely determined by its samples when the sampling frequency is ws = 1000n . For what values of w is X(w) guaranteed to be zero?

It is desired to sample and quantize the x(t)=sin(1000pit) sign. Since the sampling period is given as Ts=0.2*1000 and tau=0.1*1000 a) Plot the sign x(t) and the sampled sign xö(t), specifying values ​​over a period. b) Draw the sign Xö(f) by specifying the values.

Determine the input signal form of x1(n) x1(n) = {-4,1,0,2,-3,-1}

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Consider the DT signal x[n] shown in the plot below. You can assume that x[n] = 0 for all values of n not shown in the plot. er A -3 -2 -1 \x[n] 3 4 5 >n (a) Is X(e) purely even, odd or neither? Solve this part without computing the DTFT. (b) Is X (e) real, imaginary or neither? Solve this part without computing the DTFT. (c) Now derive the DTFT X(e¹¹). (Do verify that the expression you obtain satisfies the answers you have for Parts a and b).

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