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## Raised Cosine Filter vs Root Raised Cosine Filter-difference between Raised Cosine and Root Raised Cosine Filters

This page on Raised Cosine Filter filter vs Root Raised Cosine Filter describes difference between Raised Cosine Filter and Root Raised Cosine Filter. It covers impulse response functions and plots.

As we know filters are used to remove unwanted frequency components from the signal. As we know digital data bits will look like as square wave in time domain, it will consist of more harmonic components. Due to this RF specification such as adjacent channel leakage ratio will not meet the requirement of the standard. Hence the said filters are needed in order to process basaband digital data informations before being coupled with RF part (i.e. RF Transceiver).

Using these filters, shape of the data bits will become smooth and hence harmonic contents will reduce to great extent.

### Raised Cosine Filter

The equation-1 is used to realise impulse response of raised cosine filter. The same have been plotted which is shown in figure-1. As shown ideal raised cosine filter response will have unity gain at lower frequencies. It will have total attenuation at higher frequencies. The frequency response follows raised cosine function in the middle part.

The width of middle part is determined by Alpha. Alpha is a rool off factor which has value in the range from 0 to 1. Pass band of filter is defined by points between 50% of signal attenuation.

There are different typesof filters such as IIR filter, Analog filter and FIR filter. FIR filters are easy to implement and best to use. Refer FIR filter vs IIR filter for difference between FIR and IIR filters. The equation-2 helps to realise Raised Cosine FIR filter impulse response.

Higher order of filters will realize better raised cosine shape, but this results into longer delay.

### Root Raised Cosine Filter

The equation-3 is used to realise impulse response of root raised cosine filter. The frequency response has been plotted and shown in following figure-2.

As shown the response is almost same as figure-1. But it will have more steeper response in the middle and it follows square root of the function mentioned in equation-1.

Equation-4 is used to realise root raised cosine FIR filter frequency response. While using root raised cosine filter, one part is used at transmitter side and the similar part is also used at the receiver side.

### MATLAB Functions

Following MATLAB function returns co-efficients (b) for above said filter types.
b = rcosdesign(beta,span,sps,shape)
Shape = 'sqrt' ➨ returns coefficients as per square-root raised cosine FIR filter.
Shape = 'normal' ➨ returns coefficients as per raised cosine FIR filter.