Question

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Let x(t) be a signal with Nyquist rate coo-Nyquist rate is the frequency which, under the sampling theorem, must be exceeded by the sampling frequency. Determine the Nyquist rate for each of the following signals: a) x(t) x(t-3) b) x(3t 2) c) dxO d) x(t)cos(3t) e) x2(t) f x(t).x(t) dt

Answer 1

Given x(t) signal Nyquist rate w_0. a) x(t) + x(t - 3) x(w_0) + e^-3jw times [w_0] No change in Nyquist rate so that why Nyquist rate = w_0 b) x (3t + 2) x(3(t + 2/3) 1/3 e^2/3 j times times [w/3] w_1/3 rightarrow w_0 rightarrow w_1 rightarrow 3 w_0 So, Nyquist rate is 3W_0 \r\n No change in Nyquist rate same w_0 x(t) cos (3t) x(t) [1/2 (e^j3t + e^-jt)] 1/2 [X (w_1 - 3) + x (w_1 + 3)] w_1 - 3 = w_0 rightarrow w_1 = w_0 + 3 Nyquist rate w_1 + 3 = w_0 rightarrow w_1 = w_0 - I is the Nyquist rate a) x^2 (t) x[u_0] times [w_0] So Nyquist rate become 2w. f) x(t) * x(t) x() times [w] So, no change in Nyquist rate, same w_0