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# firrcos

Raised cosine FIR filter design

## Syntax

b = firrcos(n,Fc,df)
b = firrcos(n,Fc,df,Fs)
b = firrcos(n,Fc,df,Fs,'bandwidth')
b = firrcos(n,Fc,df,Fs,'type')
b = firrcos(...,'type',delay)
b = firrcos(...,'type',delay,window)
b = firrcos(n,Fc,r,Fs,'rolloff')
b = firrcos(...,'rolloff','type')
[b,a] = firrcos(...)

## Description

b = firrcos(n,Fc,df) uses a default sampling frequency of Fs = 2.

b = firrcos(n,Fc,df,Fs) or, equivalently,

b = firrcos(n,Fc,df,Fs,'bandwidth') returns an order n lowpass linear-phase FIR filter with a raised cosine transition band. The order n must be even. The filter has cutoff frequency Fc, transition bandwidth df, and sampling frequency Fs, all in hertz. df must be small enough so that Fc ± df/2 is between 0 and Fs/2. The coefficients in b are normalized so that the nominal passband gain is always equal to 1.

b = firrcos(n,Fc,df,Fs,'type') designs either a normal raised cosine filter or a square root raised cosine filter according to how you specify the string 'type'. Specify 'type' as:

• 'normal', for a regular raised cosine filter. This is the default, and is also in effect when the 'type' argument is left empty, [], or unspecified.

• 'sqrt', for a square root raised cosine filter.

b = firrcos(...,'type',delay) specifies an integer delay in the range [0,n+1]. The default is n/2 for all n.

b = firrcos(...,'type',delay,window) applies a length n+1 window to the designed filter to reduce the ripple in the frequency response. window must be a length n+1 column vector. If no window is specified, a rectangular (rectwin) window is used. Care must be exercised when using a window with a delay other than the default.

b = firrcos(n,Fc,r,Fs,'rolloff') interprets the third argument, r, as the rolloff factor instead of the transition bandwidth, df. r must be in the range [0,1].

b = firrcos(...,'rolloff','type') specifies the type of raised cosine filter.

[b,a] = firrcos(...) always returns a = 1.

## Examples

Design an order 20 raised cosine FIR filter with cutoff frequency 0.25 of the Nyquist frequency and a transition bandwidth of 0.25:

```h = firrcos(20,0.25,0.25);
freqz(h,1)
```