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# solved21 - S 21.1(P 4.4(i H(z = 1 z^-1*z^-2 z^-3(ii...

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S 21.1 (P 4.4) ______________ (i) H(z) = 1 - z^(-1} - *z^(-2) + z^(-3) (ii) H(exp(j*omega)) = 1 - exp(-j*omega) - exp(-j*2*omega) + exp(-j*3*omega) = exp(-j*3*omega/2). .. *(exp(j*3*omega/2) - exp(j*omega/2) - exp(-j*omega/2) + exp(-j*3*omega/2)) = exp(-j*3*omega/2)*(2*cos(3*omega/2)-2*cos(omega/2)) Thus |H(exp(j*omega)| = |2*cos(3*omega/2)-2*cos(omega/2)| and |H(exp(j*omega)|^2 = (2*cos(3*omega/2)-2*cos(omega/2))^2 (Note: An alternative expression for |H(exp(j*omega)|^2 is found by expanding H(exp(j*omega))*H(exp(-j*omega)) ) To plot |H(exp(j*omega)|: h = [1 -1 -1 1]; f = (0:511)/512; % 512 points chosen (arbitrarily) H = fft(h,512); plot(f,abs(H)), title('Amplitude Response'), xlabel('\Omega/2\pi') (iii) x[n] = 1 = exp(j*0*n) y[n] = H(exp(j*0)*x[n] = 0 x[n] = (-1)^n = exp(j*pi*n) y[n] = H(exp(j*pi))*x[n] = 0 x[n] = exp(j*pi*n/4) y[n] = H(exp(j*pi/4))*x[n] = (1 - exp(-j*pi/4) - exp(-j*2*pi/4) + exp(-j*3*pi/4))*x[n] = (-sqrt(2)+1+j)*exp(j*pi*n/4) x[n] = cos(pi*n/4+q) y[n] = |H(exp(j*pi/4))| * cos((pi*n/4) + q + angle(H(exp(j*pi/4)))

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solved21 - S 21.1(P 4.4(i H(z = 1 z^-1*z^-2 z^-3(ii...

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