Raised Cosine Filters
A raised cosine filter is a low-pass filter which is commonly used for pulse shaping in
data transmission systems (e.g. modems).
The frequency response |H(f)| of a perfect raised cosine filter
is symmetrical about 0 Hz, and is divided into three parts
(just like Gallia):
it is flat (constant) in the pass-band;
it sinks in a graceful cosine curve to zero
through the transition region; and it is zero outside the pass-band.
The response of a real filter is an approximation to this behaviour.
The equations which defined the filter contain a parameter ``beta'',
which is known as the roll-off factor or the excess bandwidth.
``beta'' lies between 0 and 1.
I'd like to show you the equations which define the frequency-domain and time-domain response, but
HTML is not up to it. If you can view PostScript, you can see the equations here,
or consult Proakis.
The filter is designed as a finite-impulse-response (FIR) filter. You specify the length of the impulse
response; that is equal to the number (n, say) of x coefficients in the ``C'' code.
The filter will have:
Here we go:
- n - 1 zeros, and
- n - 1 poles at z = 0, just for causality.
Tony Fisher /