clear all
close all
clc

Fs = 1000;            % Sampling frequency
T = 1/Fs;             % Sampling period
L = 128;             % Length of signal
t = (0:L-1)*T;        % Time vector
S = sin(2*pi*10*t) + sin(2*pi*20*t) + sin(2*pi*40*t) + sin(2*pi*80*t);
X = S + 2*randn(size(t));
plot(1000*t(1:50),X(1:50))
title('Signal Corrupted with Zero-Mean Random Noise')
xlabel('t (milliseconds)')
ylabel('X(t)')
Y = fft(X);
P2 = abs(Y/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);
f = Fs*(0:(L/2))/L;
plot(f,P1)
title('Single-Sided Amplitude Spectrum of X(t)')
xlabel('f (Hz)')
ylabel('|P1(f)|')
Y = fft(S);
P2 = abs(Y/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);

plot(f,P1)
title('Single-Sided Amplitude Spectrum of S(t)')
xlabel('f (Hz)')
ylabel('|P1(f)|')
N = 2048; fpr=100; fx1=10; fx2=20; fx3=40;fx4=80;
nx = 0:N-1; dt = 1/fpr; t = dt*nx;
x1 = cos(2*pi*fx1*t);
x2 = cos(2*pi*fx2*t);
x3 = cos(2*pi*fx3*t);
x4 = cos(2*pi*fx4*t);
x = x1 + x2 + x3 + x4;
M = 7; fg = 20;
h = fir1(M-1,2*fg/fpr);
subplot(311); stem(f,'filled'); grid;
title('Sygnał filtrowany');
subplot(312); stem(Y,'filled'); grid;
title('Odp impulsowa filtru FIR');
subplot(313)
splot = conv(S,h,'same');
plot(splot)