%Problem 3.32;
%Demonstration of validite Rayleigh model for the case ofs hort term
%fading; 

clear all; close all;
t=[1:2000]/1000; %time scale;
S=exp(-16*(t-1).^2); Sbp=real(S.*exp(i*2*pi*25*t)); %real envelope and bandpass signal;
Fi=pi*(unidrnd(20,20,1000)-1)/10; CA=sum(exp(i*Fi)); %1000 samples of resultant complex amplitudes;
SRE=abs(CA(1:7))'*S; %exemplary resulting envelopes;
subplot(311); plot(t,SRE);  xlabel('t/T'); ylabel('Res. envelope'); ylim([-0.5 10]); grid; %plotting them;
subplot(312); hist(abs(CA),[1:40]);  xlabel('res. amp.'); ylabel('1000xPr'); xlim([0,20]); %plotting histogram of resulting amplitudes;
x=[0:1:40]; y=raylpdf(x,sqrt(20)); %forming Rayleigh PDF;
subplot(313); plot(x,y); xlabel('resultant amplitude'); ylabel('pdf'); xlim([0,20]); %plotting Rayleigh PDF;