How to find the filter coefficients for a DVBS2 shaping SRRC?

Question

in the DVBS2 Standard the SRRC filter is defined as

How can i find the filter's time domain coefficients for implementation? The Inverse Fourier transform of this is not clear to me.

Answer 1

For DVBS2 signal you can use RRC match filter before timing recovery. For match filter, you can use this expression:

For example for n_ISI = 32 and Roll of factor = 0.25 with any sample per symbol you can use this Matlab code:

SPS = 4; %for example
n_ISI=32;
rolloff = 0.25;    
n       = linspace(-n_ISI/2,n_ISI/2,n_ISI*SPS+1) ;

rrcFilt = zeros(size(n)) ;

for iter = 1:length(n)
    if n(iter) == 0
        rrcFilt(iter) = 1 - rolloff + 4*rolloff/pi ;
        
    elseif abs(n(iter)) == 1/4/rolloff
        rrcFilt(iter) = rolloff/sqrt(2)*((1+2/pi)*sin(pi/4/rolloff)+(1-2/pi)*cos(pi/4/rolloff)) ;
        
    else
        rrcFilt(iter) = (4*rolloff/pi)/(1-(4*rolloff*n(iter)).^2) * (cos((1+rolloff)*pi*n(iter)) + sin((1-rolloff)*pi*n(iter))/(4*rolloff*n(iter))) ;
    end
end

But if you want to use SRRC, there are two ways: 1. You can use its frequency representation form if you use filtering in the frequency domain. And for implementation, you can use the expression that you've noted. 2. For time-domain filtering, you should define the FIR filter with its time representation sequence. The time representation of such SRRC pulses is shown to adopt the following form: