Quiz 2 INEL 4301

HL.m

function y = HL(x)

x2 = x(x >= -60 & x <= 60);
y(find(x >= -60 & x <= 60))= exp(-1i *((2*pi)/30 * x2));

y(find(x > 60 | x < -60)) = 0;
end

quiz2.m

%INEL 4095 - Signals and Systems
%CAUSAL FIRST ORDER RC-FILTER 
%Ideal Low-pass filter versus RC-filter
%Prof. Domingo Rodriguez - Spring 2012
%
close all;
%PARAMETER SETTINGS**************************************
Fs=1000;					%Sampling Frequency
Ts=1/Fs;						%Sampling Period or Sampling Time
N=300;						%Length of each discrete signal or vector
V=N*Ts;						%Time duration (in seconds) for each signal
fm=60;						%Cuttoff frequency
Wn=2*fm/Fs;					%Normalized frequency
M=300;       				%Length of the impulse response signal
R=10000;						%Value of Resistor
C=1/(2*pi*fm*R);			%Value of Capacitor
a=1/(R*C);					%Time Constant Parameter
h0=a;							%Initial Condition Parameter
t=0:Ts:V-Ts;				%General time axis
th=0:Ts:M*Ts-Ts; 			%Time axis for plotting impulse response signal
f=-Fs/2:Fs/M:Fs/2-Fs/M;	%Frequency axis
%********************************************************
%RC-FILLTER 
hRC=h0*exp(-a*th);		%RC-Filter impulse response function
hmax=max(hRC);				%Maximum value of impulse response function
hRC=(hRC/hmax);			%Normalized impulse response function
fhRC=fft(hRC);				%Fourier Transform of impulse response function
sfhRC=fftshift(fhRC);	%Frequency shift for two sided spectrum plot
asfhRC=abs(sfhRC);		%Absolute value calculation
Hmax=max(asfhRC);			%Maximum value of frequency response function
asfhRC=(asfhRC/Hmax);	%Normilized frequency response function
%
%********************************************************
%MATLAB FIR1 FILTER
Wn=(2*fm)/Fs;				%Normilized cut-off frequency for ideal filter
h=fir1(N-1,Wn);			%Impulse response function of ideal filter
fh=fft(h);					%Fourier transform of impulse response function
sfh=fftshift(fh);			%Frequency shift for two sided spectrum plot
msfh=abs(sfh);				%Absolute value calculation
%
%********************************************************
%PLOTS
%********************************************************
plot(f,asfhRC,f,msfh,'r') 	%Plots of RC and Ideal filters
grid
xlabel('Frequency in Hz.')	%Horizontal axis
ylabel('Magnitude')			%Vertical axis
title('HL(f) and HRC(f)')	%Title of plot

% Quiz
% HL = exp(-1i *((2*pi)/30 * f));
% mHL = abs(HL);
% aHL = angle(HL);
% plot(f, mHL)
% grid
% xlabel('Frequency in Hz.')	%Horizontal axis
% ylabel('Magnitude')			%Vertical axis
% title('HL(f)')	%Title of plot
% 
% figure
% plot(f, aHL)
% grid
% xlabel('Frequency in Hz.')	%Horizontal axis
% ylabel('Phase')			%Vertical axis
% title('HL(f)')	%Title of plot

%%%%%%%%%%%% Exercise A
% Fs = 480;
% N = 100;
% Ts = 1/Fs;
% V = N*Ts;
% t=0:Ts:V-Ts;
% finc = Fs/N
% f = -Fs/2:finc:Fs/2-finc;
figure 
plot(f, abs(HL(f)))
grid
xlabel('Frequency in Hz.')	%Horizontal axis
ylabel('Magnitude')			%Vertical axis
title('HL(f)')	%Title of plot

figure
plot(f, angle(HL(f)))
grid
xlabel('Frequency in Hz.')	%Horizontal axis
ylabel('Phase')			%Vertical axis
title('HL(f)')	%Title of plot

%%%%%%%%%%%% Exercise B
hl = ifft(HL(f));
%hl = 120*sinc(120*(t-1/30));
plot(t, hl)
grid
xlabel('Time in s')	%Horizontal axis
ylabel('Magnitude')			%Vertical axis
title('hl(t)')	%Title of plot

figure
plot(t, angle(hl))
grid
xlabel('Time in s')	%Horizontal axis
ylabel('Phase')			%Vertical axis
title('hl(t)')	%Title of plot


%%%%%%%%%%%% Exercise C
x = cos(2*pi*30*t) + cos(2*pi*45*t) + cos(2*pi*120*t);
% x = cos(2*pi*30*t) + cos(2*pi*30*t);
y = conv(x, hl, 'same');
%y = 2*cos(2*pi*30*t)* HL(30)+ 2*cos(2*pi*45*t)*HL(45) + 2*cos(2*pi*120*t)*HL(120);
% y = cos(2*pi*120*t)*HL(120);

figure
plot(t, y)
grid
xlabel('Time in s')	%Horizontal axis
ylabel('Magnitude')			%Vertical axis
title('y(t)')	%Title of plot

Y = fft(y);
figure
plot(f, abs(Y))
grid
xlabel('Frequency in Hz.')	%Horizontal axis
ylabel('Magnitude')			%Vertical axis
title('Y(f)')	%Title of plot

%%%$%%%%%%%%%%%%%%%%%%%%
% fh = -100:100-1;
% plot(fh, abs(HL(fh)))
% grid
% xlabel('Frequency in Hz.')	%Horizontal axis
% ylabel('Magnitude')			%Vertical axis
% title('HL(f)')	%Title of plot
% 
% figure
% plot(fh, angle(HL(fh)))
% grid
% xlabel('Frequency in Hz.')	%Horizontal axis
% ylabel('Phase')			%Vertical axis
% title('HL(f)')	%Title of plot

% % Inverse
% hl = ifft(Hl);
% 
% plot(fh, abs(hl))
% grid
% xlabel('Time in s')	%Horizontal axis
% ylabel('Magnitude')			%Vertical axis
% title('hl(t)')	%Title of plot
% 
% figure
% plot(fh, angle(hl))
% grid
% xlabel('Time in s')	%Horizontal axis
% ylabel('Phase')			%Vertical axis
% title('hl(t)')	%Title of plot