# How to properly filter a BPSK demodulated signal?

I am new to this field and yesterday I began a project for BPSK modulation. So this is what i did:

$\ x(t) = 0$ or$\ 1$ binary data

$\ Fs = 15$ sampling frequency kHz

$\ Fc = 10$ carrier frequency kHz

# BPSK modulation

$\ BPSK(t) = A.sin(2.\pi.Fc.t + \pi.x(t) )$ # BPSK demodulation

$\ S(t) = BPSK(t) . (Ac.sin(2.\pi.Fc.t))$ # low pass filter

void lowPassFrequency(float input[], float fs, float output[], int points)
{
float  CUTOFF = 2 * Fc;
float RC = 1.0/(CUTOFF*2*M_PI);
float dt = 1.0/fs;
float alpha = dt/(RC+dt);
output = input;

for(int i = 1; i < points; ++i)
{
output[i] = output[i-1] + (alpha*(input[i] - output[i-1]));
}
} it seems to me that the filtering part is not as it should be ... it supposed to be smoothed so i can get values like -1 and 1 ... Any ideas please?

• I'd say your filter doesn't have enough out-of-band rejection.
– MBaz
Apr 25, 2018 at 14:03

You must use a sampling frequency of at least the Nyquist rate, which is greater than 15 kHz in this case. It should be greater than $2(f_c + W/2) = 2 (10~\text{kHz} + W/2)$, being $W$ the signal's bandwidth.