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Raised Cosine Filters

Raised Cosine Filters exist primarily to shape pulses for use in communications systems.  (Excellent background information on this subject may be found in Ken Gentile's article,  0402Gentile50.pdf, published by RF Design in April, 2002).

The ideal Raised Cosine Filter frequency response consists of unity gain at low frequencies, a raised cosine function in the middle, and total attenuation at high frequencies.  The width of the middle frequencies is defined by the roll-off factor Alpha, (0<Alpha<=1).  In FilterSolutions, the passband frequency is defined as the 50% signal attenuation point.  The group delay must remain constant at least out to 15 to 20 dB of attenuation.

When the passband frequency of a Raised Cosine Filter is set to half the data rate, then the impulse response, (Nyquist's first criteria), is satisfied. The impulse response is zero for T = NTs, where N is an integer, and T is the data period. FilterSolutions enables the synthesis of analog, IIR and FIR Raised Cosine Filters. (FIR filters are the most accurate). However, if it is not possible to use an FIR filter, analog filters may approximate the Raised Cosine response.

The higher the order of the filter, the greater the Raised Cosine approximation.  High order Raised Cosine filters also produce longer time delays.  The lower Alpha values use less bandwidth, however, they also produce more Inter-Symbol Interference, (ISI), due to the combination of element value errors and design imperfections.