low_pass_filter.m

matlab环境下的低通滤波设计及实现

%Create a signal
t = [0:0.001:1];
sub_t = 100;
signal=cos(2*pi*50*t);%+2*sin(2*pi*120*t);
figure;
subplot(2,1,1);
plot(t(1:sub_t),signal(1:sub_t),'g'),title('ORIGINAL SIGNAL'),xlabel('time (s)');

%Add noise to the signal
randn('state',0);
sign_and_noise = signal + 0.5*randn(size(t));
hold on;subplot(2,1,1);
plot(t(1:sub_t),sign_and_noise(1:sub_t),'b'), title('SIGNAL');xlabel('time (s)');
legend('original','disturbed');

N=2048;
SIG= abs(fft(signal,N));
SIG = fftshift(SIG);
F = [-N/2:N/2-1]/N;
figure;
subplot(3,1,1);
plot(F,SIG),title('ORIGINAL SIGNAL IN FREQUENCY DOMAIN');
xlabel('freq');ylabel('magnitude (dB)');

SIG_NOISE= abs(fft(sign_and_noise,N));
SIG_NOISE = fftshift(SIG_NOISE);
subplot(3,1,2);
plot(F,SIG_NOISE);title('DISTURBED SIGNAL IN FREQUENCY DOMAIN');
xlabel('freq');ylabel('magnitude (dB)');


%Create An Ideal LowPass
f = [0:length(t)-1]/length(t);
low_pass = rectpuls(f, 0.15);
subplot(3,1,3);
plot(f, low_pass);title('LOW PASS FILTER');
xlabel('freq');ylabel('magnitude (dB)');


lp_t = fftshift(real(ifft(low_pass)));
figure
plot(lp_t);

%Convolution in time domain
res = conv(sign_and_noise, real(ifft(low_pass)));
figure(1);
subplot(2,1,2);
plot(t(1:sub_t), res(1:sub_t),'k');

%Product in frequency domain
res_freq = fft(sign_and_noise) .* (low_pass);
res_time = real(ifft(res_freq));
hold on, subplot(2,1,2);
plot(t(1:sub_t), res_time(1:sub_t),'r'),title('RECONSTRUCTED SIGNAL');xlabel('time (s)');
hold on, subplot(2,1,2);
plot(t(1:sub_t), signal(1:sub_t),'b-.');
legend('convolution in t','product in f','original');