Root raised cosine pulse

B=0.5;      %Beta value
Ts = 0.01;  %Sampling interval
N=2000;     %Number of samples 
t=-20:Ts:(N-1)*Ts;
%Formula
pt_RootRaisedCosine = ((sin(pi*t.*(1-B)) + 4*B*t.*cos(pi*t*(1+B))) ./ (pi*t.*(1-(4*B*t).^2)));
plot(pt_RootRaisedCosine);  

Hello,

I am trying to plot root raised cosine pulse for Beta equal to 0.5. But the issue in graph is, there is a little space. I am unable to figure out. Can someone help!

Answer 1

[Walter Roberson]

t.*(1-(4*B*t).^2) is 0 at indices 1951 2001 2051 . For one of those it is because t == 0, and for the other two it is because 4*B*t == 1 so the 1 minus equals 0.

[Image Analyst]

And pt_RootRaisedCosine is a NaN (not a number) at those locations. When there is a nan in the array, the plotting routine does not put a marker there, or connect the valid points on either side of the nan with a line.

Besides the denominator being 0, the numerator is also zero. So while a zero in the denominator normally gives inf (infinity) as a result, 0/0 is undefined - it's neither 0 nor infinity - so that's why it's a nan rather than inf. And therefore does not plot that point.

B=0.5; % Beta value
t=0;
numerator = sin(pi*t.*(1-B)) + 4*B*t.*cos(pi*t*(1+B)) % It's 0.
denominator = pi*t.*(1-(4*B*t).^2)                    % It's 0.
pt_RootRaisedCosine = numerator ./ denominator % It's NaN
0/0   % It's NaN
5/0   % It's Inf

[Sara Nasir]

t = [-N*T:Ts:N*T] + 10^(-8); % in order to avoid division by zero problems at t=0.

This is what i did to not get that space

[Walter Roberson]

inf points are also not plotted, though.