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:
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