# Root Raised Cosine Filtering

The PSK31 Standard uses Root Raised Cosine Filters as a matched filter. Our PSK31 signal is convolved by the Root Raised Cosine waveform to mimimize Inter-Symbol Interference. For this project we can easily compute the RRC filter and then convolve it with our output stream. For the computation of the RRC we need a couple of constants specific to the PSK31 standard.

``````beta: we will use 0.5 as a damping factor
T: We will use half of the symbol duration so 0.032/2=0.016
SAMPLE_RATE: 48000.0
ts: In our case we will use the audio standard of 1/48kHz``````

With these constants above we can compute a Root Raised Cosine filter with the following code. Note, the `sinc` function is needed to create the Root Raised Cosine Filter.

The creation of the array will look as follows:

``````int lenRC = 0; // will be 9217 for this case
float *rrc = RootRaisedCosineFilter(0.5,0.032/2,1.0/SAMPLE_RATE,&lenRC);``````

Now, let’s see inside this function to find out how the Root Raised Cosine Filter `rrc[]` is computed.

File: rootcosinefilt.c

``````float sinc(float x)
{
return x == 0.0 ? 1.0 : sin(M_PI*x)/M_PI/x;
}

float* RootRaisedCosineFilter(float beta, float T, float ts, unsigned long* lenRC)
{
float t;
const int Nsymb = 12;
const float samp_per_symb = T/ts;
unsigned long N = (unsigned long) Nsymb*samp_per_symb+1;
(*lenRC) = N;
float *rc = (float *) calloc(N,sizeof(N));

float max = 0.0;
float shift = -Nsymb*T/2.0;
for(int i=0;i<N;i++)
{
t = shift+ts*((float) i);

if(fabs(t) == T/2.0/beta)
{
rc[i] = M_PI*sinc(1.0/2.0/beta)/Nsymb/T/2.0;
continue;
}
float tv = t/T;
float tvb = beta*tv;
float t1 = sinc(tv)/T;
float t2 = cos(M_PI*tvb);
float t3 = 1-pow(2.0*tvb,2);
rc[i] = t1*t2/t3;
if(rc[i]>max)
{
max = rc[i];
}
}
for(int i=0;i<N;i++) rc[i] /= max;
return rc;
}``````