Please Show all steps Given the discretetime signal xnsinpin

Please Show all steps:

Given the discrete-time signal x[n]=sin(pin/6). Sketch the magnitude and phase of the DTFT of times[n+12]

Solution

  

subplot(2,1,1);

plot(n, x);

stem([0 150],[0 0.5])

xlabel(‘Frequency – Hz’)

ylabel(‘Amplitude/X1 – V’)

title(\'AMPLITUDE SPECTRUM\');

subplot(2,1,2);

plot(w, X);

stem([0 150],[0 4])

xlabel(‘Frequency – Hz’)

ylabel(‘Phase - rads.’)

title(\'PHASE SPECTRUM\');

w = 0:6:150i;
	n = 0:1:100;
	w0 = 2;
	x = sin (pi*(n+12)/6);
	X = dtft(x, n, w);
	subplot(2,1,1); plot(n, x); stem([0 150],[0 0.5]) xlabel(‘Frequency – Hz’) ylabel(‘Amplitude/X1 – V’) title(\'AMPLITUDE SPECTRUM\');
	subplot(2,1,2); plot(w, X); stem([0 150],[0 4]) xlabel(‘Frequency – Hz’) ylabel(‘Phase - rads.’) title(\'PHASE SPECTRUM\');