Re: [Discuss-gnuradio] root_raised_cosine principle

[Martin Braun]

Please stick to the list.

On 09/01/2014 05:35 PM, adream wrote:
> Thanks for your reply
> May be I should make my question more specifically,
> 
> den = -32 * M_PI * alpha * alpha * xindx/spb;
> 
> I can't understand well why there is "-32"

That I don't know. Of course, it's just a gain change, so it won't
affect the spectral shape.
Perhaps Tom can weigh in here.

M
> 
> thank you
> 
> 
> 2014-09-01 23:18 GMT+08:00 Martin Braun <address@hidden
> <mailto:address@hidden>>:
> 
>     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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