firls
Least-squares linear-phase FIR filter design
Description
Examples
Input Arguments
Output Arguments
More About
Algorithms
firls
designs a linear-phase FIR filter that minimizes the weighted integrated squared error between an ideal piecewise linear function and the magnitude response of the filter over a set of desired frequency bands.
Reference[2]describes the theoretical approach behindfirls
. The function solves a system of linear equations involving an inner product matrix of roughly the sizen\2
using the MATLAB®\
operator.
These are type I (n
is odd) and type II (n
is even) linear-phase filters. Vectorsf
anda
specify the frequency-amplitude characteristics of the filter:
f
is a vector of pairs of frequency points, specified in the range 0 to 1, where 1 corresponds to the Nyquist frequency. The frequencies must be in increasing order. Duplicate frequency points are allowed.a
is a vector containing the desired amplitudes at the points specified inf
.The desired amplitude function at frequencies between pairs of points (f(k),f(k+1)) forkodd is the line segment connecting the points (f(k),a(k)) and (f(k+1),a(k+1)).
The desired amplitude function at frequencies between pairs of points (f(k),f(k+1)) forkeven is unspecified. These are transition ("don’t care") regions.
f
anda
are the same length. This length must be an even number.
This figure illustrates the relationship between thef
anda
vectors in defining a desired amplitude response.
This function designs type I, II, III, and IV linear-phase filters. Type I and II are the default filters when n is even and odd, respectively, while the'hilbert'
and'differentiator'
flags produce type III (n is even) and IV (n is odd) filters. The various filter types have different symmetries and constraints on their frequency responses (see[1]for details).
Linear Phase Filter Type | Filter Order | 对称系数 | Response H(f), f = 0 | Response H(f), f = 1 (Nyquist) |
---|---|---|---|---|
Type I |
Even |
No restriction |
No restriction |
|
Type II |
Odd |
No restriction |
H(1) = 0 | |
Type III |
Even |
H(0) = 0 |
H(1) = 0 |
|
Type IV |
Odd |
H(0) = 0 |
No restriction |
References
[1] Oppenheim, Alan V., Ronald W. Schafer, and John R. Buck.Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice Hall, 1999.
[2] Parks, Thomas W., and C. Sidney Burrus.Digital Filter Design. Hoboken, NJ: John Wiley & Sons, 1987, pp. 54–83.
Extended Capabilities
Version History
Introduced before R2006a