Communications Toolbox

rcosiir

Design a raised cosine IIR filter

Syntax

• [num,den] = rcosiir(R,T_delay,rate,T,tol);
  [num,den] = rcosiir(R,T_delay,rate,T,tol,filter_type);
  rcosiir(...);
  rcosiir(...,colr);
  [num,den,sample_time] = rcosiir(...);
  

Optional Inputs

Input	Default Value
T_delay	3
rate	5
T	1
tol	0.01

Description

The rcosiir function designs the same filters that the rcosine function designs when the latter's type_flag argument includes 'iir'. However, rcosine is somewhat easier to use.

The time response of the raised cosine filter has the form

[num,den] = rcosiir(R,T_delay,rate,T,tol) designs an IIR approximation of an FIR raised cosine filter, and returns the numerator and denominator of the IIR filter. The filter's rolloff factor is R, where . T is the symbol period in seconds. The filter's group delay is T_delay symbol periods. rate is the number of sample points in each interval of duration T. rate must be greater than 1. The input sample rate is T samples per second, while the output sample rate is T*rate samples per second. If tol is an integer greater than 1, then it becomes the order of the IIR filter; if tol is less than 1, then it indicates the relative tolerance for rcosiir to use when selecting the order based on the singular values.

The arguments T_delay, rate, T, and tol are optional inputs whose default values are 3, 5, 1, and 0.01, respectively.

[num,den] = rcosiir(R,T_delay,rate,T,tol,filter_type) designs a square-root raised cosine filter if filter_type is 'sqrt'. If filter_type is 'normal' then this syntax is the same as the previous one.

rcosiir(...) plots the time and frequency responses of the raised cosine filter.

rcosiir(...,colr) uses the string colr to determine the plotting color. The choices for colr are the same as those listed for the plot function.

[num,den,sample_time] = rcosiir(...) returns the transfer function and the sample time of the IIR filter.

Examples

The script below compares different values of T_delay.

• rcosiir(0,10);
  subplot(211); hold on;
  subplot(212); hold on;
  col = ['r-';'g-';'b-';'m-';'c-';'w-'];
  R = [8,6,4,3,2,1];
  for ii = R
     rcosiir(0,ii,[],[],[],[],col(find(R==ii),:));
  end;
  

This example shows how the filter's frequency response more closely approximates that of the ideal raised cosine filter as T_delay increases.

See Also

rcosfir, rcosflt, rcosine, rcosdemo, grpdelay

References

Kailath, Thomas, Linear Systems, Englewood Cliffs, N.J., Prentice-Hall, 1980.

Korn, Israel, Digital Communications, New York, Van Nostrand Reinhold, 1985.

rcosflt

rcosine