Question

please show steps, focus on part b more

1. (23 points) Sampling and Aliasing. (a) Find the Nyquist sampling rate wn for the given x(t). (Recall that the sampling frequency has to be twice larger than the bandwidth of the signal to recover the signal without loss of information.) i. (5 pts) X(t) = sinc(5000) * cos(7t). ii. (5 pts) r(t) = sin(101) cos(106) iii. (5 pts) (t) = sinc(50000) + cos(56) (b) (8 pts) Let r(t) = sinc(t/h), y(t) = cos(21), and z(t) = sinc(5t/). Sketch the Fourier Transform V (jw) for each signal v(t) below. (only need to sketch the shape and mark the x-axis and y-axis where appropriate). Then, determine the appropriate sampling rate w, allowed so that there is no aliasing. P 10 i. v(t) = y(t) + z(t). ii. v(t) = y(t) + z(t). iii. v(t) = *(t) + z(t). iv. v(t) = x(0)z(t).

Answer 1

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