Communications Toolbox

Designing Raised Cosine Filters

The rcosine function designs (but does not apply) filters of these types:

• Finite impulse response (FIR) raised cosine filter
• Infinite impulse response (IIR) raised cosine filter
• FIR square-root raised cosine filter
• IIR square-root raised cosine filter

The function returns the transfer function as output. To learn about applying raised cosine filters, see Filtering with Raised Cosine Filters.

Sampling Rates

The rcosine function assumes that you want to apply the filter to a digital signal whose sampling rate is Fd. The function also requires you to provide the filter's sampling rate, Fs. The ratio of Fs to Fd must be an integer.

Example Designing a Square-Root Raised Cosine Filter

For example, the command below designs a square-root raised cosine FIR filter with a sampling rate of 2, for use with a digital signal whose sampling rate is 1.

• num = rcosine(1,2,'fir/sqrt')
  
  num =
  
    Columns 1 through 7 
  
      0.0021   -0.0106    0.0300   -0.0531   -0.0750    0.4092    0.8037
  
    Columns 8 through 13 
  
      0.4092   -0.0750   -0.0531    0.0300   -0.0106    0.0021
  

Here, the vector num contains the coefficients of the filter, in ascending order of powers of z^-1.

Other Options in Filter Design

You can also control the filter design by specifying the rolloff factor, group delay, and (for IIR filters) tolerance index explicitly, instead of having rcosine use its default values. The reference entry for rcosine explains these parameters. The group delay is also mentioned above in Noncausality and the Group Delay Parameter.

Filtering with Raised Cosine Filters

Selected Bibliography for Special Filters