Using Lowpass filter to filter DC component from BPSK signal

[sadsorry]

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

%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;

 

[thylacine1975]

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

 

[sadsorry]

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

 

[thylacine1975]

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

 

[sadsorry]

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?