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Frequency sampling-based FIR filter design

`b = fir2(n,f,m)`

`b = fir2(n,f,m,npt,lap)`

`b = fir2(___,window)`

returns
an `b`

= fir2(`n`

,`f,m`

)`n`

th-order FIR filter with frequency-magnitude
characteristics specified in the vectors `f`

and `m`

.
The function linearly interpolates the desired frequency response
onto a dense grid and then uses the inverse Fourier transform and
a Hamming window to obtain the filter coefficients.

`fir2`

uses frequency sampling to design filters.
The function interpolates the desired frequency response linearly
onto a dense, evenly spaced grid of length `npt`

. `fir2`

also
sets up regions of `lap`

points around repeated
values of `f`

to provide steep but smooth transitions.
To obtain the filter coefficients, the function applies an inverse
fast Fourier transform to the grid and multiplies by `window`

.

[1] Mitra, Sanjit K. *Digital Signal Processing:
A Computer Based Approach*. New York: McGraw-Hill, 1998.

[2] Jackson, L. B. *Digital Filters and Signal
Processing*. 3rd Ed. Boston: Kluwer Academic Publishers,
1996.