--- a/fourier/firwin.m +++ b/fourier/firwin.m @@ -3,90 +3,91 @@ % Usage: g=firwin(name,M); % g=firwin(name,M,...); % -% FIRWIN(name,M) will return a FIR window of length M of type name. -% -% All windows are symmetric, they are zero delay and zero phase -% filters. They can be used for the Wilson and WMDCT transform, except when noted otherwise. +% `firwin(name,M)` will return an FIR window of length *M* of type *name*. +% +% All windows are symmetric and generate zero delay and zero phase +% filters. They can be used for the Wilson and WMDCT transform, except +% when noted otherwise. % % In the following PSL means "Peak Sidelobe level", and the main lobe % width is measured in normalized frequencies. % -% If a window g forms a "partition of unity" (PU) it means specifically -% that -% -%C g+fftshift(g)==ones(L,1); -% -% A perfect PU can only be formed if the window length is even, but -% some windows may work for odd lengths anyway. +% If a window *g* forms a "partition of unity" (PU) it means specifically +% that:: +% +% g+fftshift(g)==ones(L,1); +% +% A PU can only be formed if the window length is even, but some windows +% may work for odd lengths anyway. % % If a window is the square root of a window that forms a PU, the window % will generate a tight Gabor frame / orthonormal Wilson/WMDCT basis if -% the number of channels is less than M. +% the number of channels is less than *M*. % % The windows available are: % -%- hann - von Hann window. Forms a PU. The Hann window has a -% mainlobe with of 8/M, a PSL of -31.5 dB and decay rate -% of 18 dB/Octave. -% -%- sine - Sine window. This is the square root of the Hanning -% window. The sine window has a mainlobe width of 8/M, -% a PSL of -22.3 dB and decay rate of 12 dB/Octave. -% Aliases: 'cosine', 'sqrthann' -% -%- rect - (Almost) rectangular window. The rectangular window has a -% mainlobe width of 4/M, a PSL of -13.3 dB and decay -% rate of 6 dB/Octave. Forms a PU. Alias: 'square' -% -%- sqrtrect - Square root of the rectangular window. -% -%- tria - (Almost) triangular window. Forms a PU. Alias: 'bartlett' -% -%- sqrttria - Square root of the triangular window. -% -%- hamming - Hamming window. Forms a PU that sums to 1.08 instead -% of 1.0 as usual. The Hamming window has a -% mainlobe width of 8/M, a PSL of -42.7 dB and decay -% rate of 6 dB/Octave. This window should not be used for -% a Wilson basis, as a reconstruction window cannot be -% found by WILDUAL. -% -%- blackman - Blackman window. The Hamming window has a -% mainlobe width of 12/M, a PSL of -58.1 dB and decay -% rate of 18 dB/Octave. -% -%- blackman2 - Alternate Blackman window. This window has a -% mainlobe width of 12/M, a PSL of -68.24 dB and decay -% rate of 6 dB/Octave. -% -%- nuttall - Nuttall window. The Nuttall window has a -% mainlobe width of 16/M, a PSL of -93.32 dB and decay -% rate of 18 dB/Octave. -% -%- itersine - Iterated sine window. Generates an orthonormal -% Wilson/WMDCT basis. This window is described in -% Wesfreid and Wickerhauser (1993) and is used in the -% ogg sound codec. Alias: 'ogg' +% 'hann' von Hann window. Forms a PU. The Hann window has a +% mainlobe with of 8/M, a PSL of -31.5 dB and decay rate +% of 18 dB/Octave. +% +% 'sine' Sine window. This is the square root of the Hanning +% window. The sine window has a mainlobe width of 8/M, +% a PSL of -22.3 dB and decay rate of 12 dB/Octave. +% Aliases: `'cosine'`, `'sqrthann'` +% +% 'rect' (Almost) rectangular window. The rectangular window has a +% mainlobe width of 4/M, a PSL of -13.3 dB and decay +% rate of 6 dB/Octave. Forms a PU. Alias: `'square'` +% +% 'sqrtrect' Square root of the rectangular window. +% +% 'tria' (Almost) triangular window. Forms a PU. Alias: `'bartlett'` +% +% 'sqrttria' Square root of the triangular window. +% +% 'hamming' Hamming window. Forms a PU that sums to 1.08 instead +% of 1.0 as usual. The Hamming window has a +% mainlobe width of 8/M, a PSL of -42.7 dB and decay +% rate of 6 dB/Octave. This window should not be used for +% a Wilson basis, as a reconstruction window cannot be +% found by WILDUAL. +% +% 'blackman' Blackman window. The Hamming window has a +% mainlobe width of 12/M, a PSL of -58.1 dB and decay +% rate of 18 dB/Octave. +% +% 'blackman2' Alternate Blackman window. This window has a +% mainlobe width of 12/M, a PSL of -68.24 dB and decay +% rate of 6 dB/Octave. +% +% 'nuttall' Nuttall window. The Nuttall window has a +% mainlobe width of 16/M, a PSL of -93.32 dB and decay +% rate of 18 dB/Octave. +% +% 'itersine' Iterated sine window. Generates an orthonormal +% Wilson/WMDCT basis. This window is described in +% Wesfreid and Wickerhauser (1993) and is used in the +% ogg sound codec. Alias: `'ogg'` % % FIRWIN understands the following flags at the end of the list of input % parameters: % -%- 'wp' - Output is whole point even. This is the default. -% -%- 'hp' - Output is half point even, as most Matlab filter +% 'wp' Output is whole point even. This is the default. +% +% 'hp' Output is half point even, as most Matlab filter % routines. % -%- 'taper',t - Extend the window by a flat section in the middle. The +% 'taper',t Extend the window by a flat section in the middle. The % argument t is the ratio of the rising and falling % parts as compared to the total length of the % window. The default value of 1 means no % tapering. Accepted values lie in the range from 0 to 1. % -% Additionally, FIRWIN accepts flags to normalize the output. Please see -% the help of NORMALIZE. Default is to use 'peak' normalization, which is -% useful for using the output for windowing in the time-domain. For -% filtering in the time-domain, a normalization of '1' or 'area' is -% preferable. +% Additionally, `firwin` accepts flags to normalize the output. Please see +% the help of |normalize|_. Default is to use `'peak'` normalization, +% which is useful for using the output from `firwin` for windowing in the +% time-domain. For filtering in the time-domain, a normalization of `'1'` +% or `'area'` is preferable. % % See also: pgauss, pbspline, firkaiser, normalize % @@ -260,4 +261,3 @@ g=normalize(g,flags.norm); -%OLDFORMAT