Re: [Discuss-gnuradio] root_raised_cosine principle

On 09/01/2014 05:01 PM, adream wrote:
> Hi,
> I get the source code of root_raised_cosine function in gr_firdes.cc,
> but I can't understand why it writes in that way, is there any paper can
> give me more details about the principle of root_raised_cosine

Any standard textbook on digital communications will explain this. You
might want to look out for keywords such as pulse shaping and Nyquist
criterion. Have a look at the wiki page for recommended reading.

M

> Thank you
>
> this is the source code of root_raised_cosine
> vector<float> gr_firdes::root_raised_cosine (double gain,
> double sampling_freq,
> double symbol_rate,
> double alpha,
> int ntaps)
> {
> ntaps |= 1; // ensure that ntaps is odd
>
> double spb = sampling_freq/symbol_rate; // samples per bit/symbol
> vector<float> taps(ntaps);
> double scale = 0;
> for(int i=0;i<ntaps;i++)
> {
> double x1,x2,x3,num,den;
> double xindx = i - ntaps/2;
> x1 = M_PI * xindx/spb;
> x2 = 4 * alpha * xindx / spb;
> x3 = x2*x2 - 1;
> if( fabs(x3) >= 0.000001 ) // Avoid Rounding errors...
> {
> if( i != ntaps/2 )
> num = cos((1+alpha)*x1) + sin((1-alpha)*x1)/(4*alpha*xindx/spb);
> else
> num = cos((1+alpha)*x1) + (1-alpha) * M_PI / (4*alpha);
> den = x3 * M_PI;
> }
> else
> {
> if(alpha==1)
> {
> taps[i] = -1;
> continue;
> }
> x3 = (1-alpha)*x1;
> x2 = (1+alpha)*x1;
> num = (sin(x2)*(1+alpha)*M_PI
> - cos(x3)*((1-alpha)*M_PI*spb)/(4*alpha*xindx)
> + sin(x3)*spb*spb/(4*alpha*xindx*xindx));
> den = -32 * M_PI * alpha * alpha * xindx/spb;
> }
> taps[i] = 4 * alpha * num / den;
> scale += taps[i];
> }
>
> for(int i=0;i<ntaps;i++)
> taps[i] = taps[i] * gain / scale;
>
> return taps;
> }
>
>
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