%% Frequency Response Descriptions for LTI Systems
%
% Copyright Barry Van Veen 2014

%% Set up workspace

clear
close all
set(0,'defaultaxesfontsize',22);
set(0,'defaulttextfontsize',22);
linwidth = 2;

% Use freqz to convert the coefficients of the difference equation into
% samples of the frequency response

%% System 1: 6 point averaging

B = [ 1 1 1 1 1 1]/6;
A = 1;

[H,om] = freqz(B,A);

figure(1)

subplot(2,1,1)
hp = plot(om,abs(H));
set(hp,'LineWidth',linwidth);
title('6 pt Avg: Magnitude Response')
xlabel('Frequency (rads)')
ylabel('Gain')
xlim([0,pi])

subplot(2,1,2)
hp = plot(om,unwrap(angle(H)));
set(hp,'LineWidth',linwidth);
title('6 pt Avg: Phase Response')
xlabel('Frequency (rads)')
ylabel('Phase (rads)')
xlim([0,pi])

h = get(0,'CurrentFigure');
set(h,'Position',[0,0,1000,600])

%% System 2: 6 point difference

B = [1 -1 1 -1 1 -1]/6;
A = 1;

[H,om] = freqz(B,A);

figure(2)

subplot(2,1,1)
hp = plot(om,abs(H));
set(hp,'LineWidth',linwidth);
title('6 pt Diff: Magnitude Response')
xlabel('Frequency (rads)')
ylabel('Gain')
xlim([0,pi])

subplot(2,1,2)
hp = plot(om,unwrap(angle(H)));
set(hp,'LineWidth',linwidth);
title('6 pt Diff: Phase Response')
xlabel('Frequency (rads)')
ylabel('Phase (rads)')
xlim([0,pi])

h = get(0,'CurrentFigure');
set(h,'Position',[0,0,1000,600])

%% System 3: First-order recursive system y[n] = 0.95y[n-1] + 0.05x[n]

B = 0.05;
A = [1 -0.95];

[H,om] = freqz(B,A);

figure(3)

subplot(2,1,1)
hp = plot(om,abs(H));
set(hp,'LineWidth',linwidth);
title('Recursive Low Pass: Magnitude Response')
xlabel('Frequency (rads)')
ylabel('Gain')
xlim([0,pi])

subplot(2,1,2)
hp = plot(om,unwrap(angle(H)));
set(hp,'LineWidth',linwidth);
title('Recursive Low Pass: Phase Response')
xlabel('Frequency (rads)')
ylabel('Phase (rads)')
xlim([0,pi])

h = get(0,'CurrentFigure');
set(h,'Position',[0,0,1000,600])

%% System 4: First-order recursive system y[n] = -0.95y[n-1] + 0.05x[n]

B = 0.05;
A = [1 0.95];

[H,om] = freqz(B,A);

figure(4)

subplot(2,1,1)
hp = plot(om,abs(H));
set(hp,'LineWidth',linwidth);
title('Recursive High Pass: Magnitude Response')
xlabel('Frequency (rads)')
ylabel('Gain')
xlim([0,pi])

subplot(2,1,2)
hp = plot(om,unwrap(angle(H)));
set(hp,'LineWidth',linwidth);
title('Recursive High Pass: Phase Response')
xlabel('Frequency (rads)')
ylabel('Phase (rads)')
xlim([0,pi])

h = get(0,'CurrentFigure');
set(h,'Position',[0,0,1000,600])