FIRWIN Function
Computes one of several different data windows: Blackman, Chebyshev, Hamming, Hanning, Kaiser, rectangular, or triangular.
Usage
result = FIRWIN(n[, a])
Input Parameters
n—The length of the window sequence.
a—(optional) A scalar float parameter used only when computing either the Kaiser or Chebyshev windows.
Returned Value
result—A one-dimensional array containing the requested window.
Keywords
Blackman—If set, a Blackman window is returned.
Chebyshev—If set, a Chebyshev window is returned. If Chebyshev is set, input parameter a (a*p is q0 in the Chebyshev window equation) is also required.
Hamming—If set, a Hamming window is returned.
Hanning—If set, a Hanning window is returned.
Kaiser—If set, a Kaiser window is returned. If Kaiser is set, input parameter a (a*p is a in the Kaiser window equation) is also required.
Rectangular—If set, a rectangular window is returned. This is also known as a boxcar window.
Triangular—If set, a triangular window is returned.
Window_type—A scalar value (see the following table) used to specify a window type. This keyword may be used in place of the particular window keywords:
1—Rectangular
2—Triangular
3—Hanning
4—Hamming
5—Kaiser
6—Blackman
7—Chebyshev
Discussion
A listing of the applicable time domain equations is given below, where (0 < n < N – 1) for each of the windows.
where:
and q0 is the FIRWIN input parameter a*p and where j=2, ..., (n–1)/2.
where I0(x) is the zeroth order Bessel function of the first kind, and a is the FIRWIN input parameter a.
Rectangular (or boxcar) window:
w(n) = 1, for all n
, for all n.
Example
This example illustrates how to generate each of the different window types for a window length of 31. The results are shown in FIRWIN Window Type Plots, where (a) is rectangular and triangular windows; (b) is Hanning and Hamming windows; (c) is Kaiser and Blackman windows; and (d) is Chebyshev window.
!P.Multi=[0,2,2]
n = 31
rect = FIRWIN(n, /Rectangular)
tri = FIRWIN(n, /Triangular)
hann = FIRWIN(n, /Hanning)
hamm = FIRWIN(n, /Hamming)
kaiser = FIRWIN(n, 0.5, /Kaiser)
black = FIRWIN(n, /Blackman)
cheby = FIRWIN(n, 0.15, /Chebyshev)
; Plot the rectangular and triangular windows.
PLOT, rect, Linestyle = 2, XStyle = 1, YRange = [0, 1.05], $
Title = 'Rectangular and Triangular'
OPLOT, tri
; Plot the Hanning and Hamming windows.
PLOT, hann, XStyle = 1, Linestyle = 2, YRange = [0, 1.05], $
Title = 'Hanning and Hamming'
OPLOT, hamm
; Plot the Kaiser and Blackman windows.
PLOT, kaiser, XStyle = 1, Linestyle = 2, YRange = [0, 1.05],$
Title = 'Kaiser and Blackman'
OPLOT, black
; Plot a Chebyshev window.
PLOT, cheby, XStyle = 1, YRange = [0, 1.05], Title = 'Chebyshev'
See Also
For Additional Information
Harris, 1978.
Roberts and Mullis, 1987.
