%% L09_Recursion
%% ==============
%% Script to illustrate Recursive (IIR) filter implementation.
%% See Lecture09
%%
%% Created  : 15 Aug 2005
%% Modified : 15 Aug 2005
%%
%% Copyright (c) 2005 Salman Durrani .
%% ------------------------------------------------------------

clc
clear all

%% Sampling frequency
Fs = 500;

%% Time vector of 0.5second
t = 0:1/Fs:0.5;

%% Create a sine wave of 10 Hz corrupted by sine wave of 100 Hz
x = sin(2*pi*t*10) +sin(2*pi*t*100);
L=length(x);

%% Recursive/IIR filter (low pass) fc = 0.05*Fs/2 = 12.5 Hz 
a0=0.15;
b1=0.85;
y(1)=0;

for k=2:L
    y(k)=a0*x(k)+b1*y(k-1);
end

%% Generate the plot, title and labels.
figure
plot(t,sin(2*pi*t*10),'b');
hold on
plot(t,sin(2*pi*t*100),'g')
xlabel('Time (s)');
ylabel('Amplitude')
legend('10 Hz','100 Hz')
axis([0 0.5 -2 2])

figure
plot(t,x,'k');
hold on
plot(t,y,'r','Linewidth',2)
xlabel('Time (s)');
ylabel('Amplitude')
legend('Filter Input','Filter Output')
axis([0 0.5 -2 2])

figure
plot(t,sin(2*pi*t*10),'b');
hold on
plot(t,y,'r','Linewidth',2)
xlabel('Time (s)');
ylabel('Amplitude')
legend('10 Hz','Filter Output')
axis([0 0.5 -2 2])

%% Normalised Frequency Response
figure
num=[a0];
den=[1 -b1];
freqz(num,den)

%% Scaled Frequency Response of Filter using knowledge of sampling
%% frequency
figure
num=[a0];
den=[1 -b1];
freqz(num,den,512,Fs)