Re: [Discuss-gnuradio] root_raised_cosine principle

[Martin Braun]

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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