Using Lowpass filter to filter DC component from BPSK signal

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Hi guys!
I have a code matlab for BPSK demodulation. And I have problem with filtering DC component from BPSK signal. My process is
BPSK_sig*carrier=1/2*(1+cos(2wt)) and I want to use LPF to get DC component which recover to original signal

What should I do? Thanks alot!
And here is my matlab code
Code: 
%MATLAB Script for a Binary PSK with two Phases
  
% Clear all variables and close all figures
clear all;
close all;
  
bit_stream = [1,0,1,0,1,0,1,0];
 
% Enter the two Phase shifts - in Radians
% Phase for 0 bit
P1 = 0;
  
% Phase for 1 bit
P2 = pi;
  
% Frequency of Modulating Signal
f = 2; %f --> time period
  
% Sampling rate of sine wave - This will define the resoultion
fs = 100;
  
% Time for one bit
t = 0: 1/fs : 1;
  
% This time variable is just for plot
time = [];
  
PSK_signal = [];
Digital_signal = [];
carrier_signal = [];
  
for ii = 1: 1: length(bit_stream)
  
% The Original Digital Signal
    if bit_stream(ii)==0
        bit0 = zeros(1,length(t));
        Digital_signal = [Digital_signal bit0];
    end
 
    if bit_stream(ii)==1
        bit1 = ones(1,length(t));
        Digital_signal = [Digital_signal bit1];
    end
  
% The FSK Signal
    if bit_stream(ii)==0
        PSK_signal = [PSK_signal cos(2*pi*f*t + P2)];
    end
    if bit_stream(ii)==1
        PSK_signal = [PSK_signal cos(2*pi*f*t + P1)];
    end
  
% Generating carrier wave
carrier_signal = [carrier_signal (cos(2*pi*f*t))];
  
time = [time t];
t = t + 1;
  
end
  
% Plot the Original Digital Signal
subplot(4,1,1);
plot(time,Digital_signal,'r','LineWidth',2);
xlabel('Time (bit period)');
ylabel('Amplitude');
title('Original Digital Signal');
axis([0 time(end) -0.5 1.5]);
grid on;
  
% Plot the carrier Signal
subplot(4,1,2);
plot(time,carrier_signal,'g','LineWidth',2);
xlabel('Time (bit period)');
ylabel('Amplitude');
title('carrier Signal');
axis([0 time(end) -1.5 1.5]);
grid on;
  
% Plot the PSK Signal
subplot(4,1,3);
plot(time,PSK_signal,'LineWidth',2);
xlabel('Time (bit period)');
ylabel('Amplitude');
title('PSK Signal with two Phase Shifts');
axis([0 time(end) -1.5 1.5]);
grid on;

% Plot the Demodulation BPSK Signal
de_PSK_signal=PSK_signal.*carrier_signal;
subplot(4,1,4);
plot(time,de_PSK_signal,'LineWidth',2);
xlabel('Time (bit period)');
ylabel('Amplitude');
title('Demodulation BPSK Signal');
axis([0 time(end) -1.5 1.5]);
grid on;
 

I love the output of your code - it looks really neat

If you've got the signal processing toolbox handy, you can use:

Code Python - [expand]
1

Hd = design(fdesign.lowpass('N,Fc', 40, f, fs));


...which builds an FIR lowpass filter with 40 taps with a corner frequency f (your signalling rate) at sampling rate fs.
You can view the resultant filter with:

Code Python - [expand]
1

fvtool(Hd)


...and apply it to your data (and plot it) via:

Code Python - [expand]
1

subplot(4,1,4); plot(time, filtfilt(Hd.Numerator, 1, de_PSK_signal),'LineWidth',2);


Note that I've used filtfilt(..), which is a non-causal zero-phase filter, which makes everything line up and look nice in time domain plots such as yours. Compare the result with a (causal) filter implementation such as:

Code Python - [expand]
1

subplot(4,1,4); plot(time, filter(Hd, de_PSK_signal),'LineWidth',2);


As you probably already know, you can read all about these functions with the online help: doc filtfilt ... for example.
Cheers
 
Thanks you very much! Could you please tell me the meaning of N, FC, 40. Why do you choose 40? I tried some other numbers and still get the result. One more question: How could I recover the original signal from LPF signal because original signal is square wave
 

The syntax "N, Fc" tells MATLAB you're going to specify the filter by the number of taps and it's corner frequency. (There's a multitude of ways you can specify a filter response, and this is one of the simplest).

N is the number of taps comprising your FIR filter. The greater the number of taps, the more "ideal" the filter response - i.e. the more closely it approaches a low-pass brick wall. Generally, the more the better, although the practical constraints are the corresponding increases in the required computation and delay through the filter. I chose 40, because execution time/causality wasn't important... and the result looked pretty

Fc is the corner frequency of the lowpass response - i.e. the frequency corresponding to the -3dB point of the amplitude rolloff. You want this point to be high enough to pass your modulated data, but low enough to reject your carrier frequency component - it's often a tradeoff. (The number of taps of the filter also plays a part here - both decreasing Fc and/or increasing N will reduce the residual carrier ripple, with their own unique performance consequences/penalties).

To recover the input square wave you need to threshold the filtered data, or use some sort of majority voting system etc etc. Optimal data recovery is a whole field in itself, but simple thresholding will work well here - something along the lines of:

if (filteredValue > threshold)
dataOut = 1;
else
dataOut = 0;
end
 
Thanks alot thylacine1975. I presented about this point yesterdat to my teacher and he said:"Using LPF to filter DC component is theoretical way but the BER is high. Try use intergral function in matlab". But when I try to use integral function for de_PSK_signal, matlab warnning "First input argument must be a function
handle." Is de_PSK_signal is not function?
 

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