# SRRC filter — filter span tradeoffs

I am simulating (in Matlab) the transmit portion of a comm system. I generate random data, then I want to modulate it to BPSK, pulse shape the data, and then potentially shift it up in frequency by a carrier. My question is regarding the pulse shaping portion.

Atleast in matlab, to generate the root raised cosine filter using the rcosdesign function, you need to know the roll-off factor ($\beta$) , as well as the samples-per-symbol ($sps$) and the filter span ($span$). The samples per symbol will be dictated by the sampling frequency $f_s$ as well as the desired length of the generated signal with a certain datarate $R$. For example, if I have a BPSK signal with a sampling frequency of 8192 Hz, and I want to generate 1 second of data at a datarate of 256 Hz, then

$$sps = f_s/R$$

Now we've established 2 of the inputs to creating the filter are set, the rolloff factor $\beta$ and the samples per symbol, $sps$. Now, my understanding is that the filter span is kind of arbitrary. I know that a longer filter span creates a longer group delay, but what are the other tradeoffs to having a longer filter span versus shorter?

• Lengthening the span of the filter drives down the stop-band. – John Jan 10 '14 at 19:45