Half and Full Wave rectifying and Fourier Rectifying a sinusoidal provides a way

Question

Half and Full Wave rectifying and Fourier
Rectifying a sinusoidal provides a way to create a dc source. In this problem we consider the Fourier series of the full wave and half wave rectified signals. The full wave rectified signal xf(t) has a period T0 = 1 and its period from 0 to 1is:
x (t) = sin (?t) 0? t ? 1
While the period for the half wave rectifier signal xh(t) is:
x 2 (t) =(sin(?t)) for 0?t?1 and 0 for 1<t?1

Use the even and odd decomposition of x h (t) to obtain its Fourier coefficients. This computation of the Fourier coefficients of x h (t) avoids some difficulties when you attempt to plot its magnitude line spectrum. Use MATLAB and your analytic results here to plot the magnitude line spectrum of the half wave signal and use the dc and 40 harmonics to obtain an approximation of the half wave signal.

Part b:

Explanation / Answer

%full wave rectifier clear all t=0:1/1000:3*pi; for i=1:100 n=i; yp=(2*exp(j*2*n*t))/(pi*(1-4*n^2)*(j*6*n+1)); n=-i; yn=(2*exp(j*2*n*t))/(pi*(1-4*n^2)*(j*6*n+1)); y(i,:)=yp+yn; end yf = 2/pi + sum(y); plot(t,yf, t, (2/pi)*ones(1,length(yf))) axis([0 3*pi 0 1]); Power=0; for n=1:50 Power(n) = abs(2/(pi*(1-4*n^2)*(j*6*n+1))); end TotalPower = 2*sum((Power.^2)); figure; stem( Power(1,1:20));

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