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I am trying to pass a BPSK signal through a root-raised cosine filter in Octave. To do this, I convolve the signal with the impulse response of an RRC filter, defined as follows (source):

RRC impulse response

The BPSK signal has a symbol rate of $$\frac{1}{T_s} =10 \text{ Mbps}$$. Would this not result in a massive value for pretty much the entire impulse response, since every case involves a multiplication by $\frac{1}{T_s}$? This is the impulse response I get with my implementation in Octave.

enter image description here

I used the same method as in the accepted answer to this question, using $D=10$, $F_s=200 \text{ MHz}$, and $\beta=0.3$. This is the relative shape one would expect an RRC impulse response to have, but it peaks at about $1.1 \times 10^7$ because of the high symbol rate. Obviously, when I convolve my data signal with this impulse response the filtered signal has a massive magnitude which I don't want. I didn't include my code because I'm more interested in correcting my understanding of the RRC filter. With the given impulse response, how can this filter work for high symbol rates?

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After generating the pulse, you need to scale it to give it the energy you wish. Starting from the pulse RRC, find its energy E = sum(RRC.*RRC). Then, RRC ./ sqrt(E) has energy equal to one. Finally, multiply by the square root of the desired energy.

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