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2-D FIR filter using frequency sampling

`h = fsamp2(Hd)`

`h = fsamp2(f1,f2,Hd,[m n])`

designs a two-dimensional FIR filter with frequency response `h`

= fsamp2(`Hd`

)`Hd`

,
and returns the filter coefficients in matrix `h`

. The filter
`h`

has a frequency response that passes through points in
`Hd`

.

`fsamp2`

designs two-dimensional FIR filters based on a desired
two-dimensional frequency response sampled at points on the Cartesian plane.
`Hd`

is a matrix containing the desired frequency response
sampled at equally spaced points between -1.0 and 1.0 along the
*x* and *y* frequency axes, where 1.0
corresponds to half the sampling frequency, or π radians.

$${H}_{d}({f}_{1},{f}_{2})={{H}_{d}({\omega}_{1},{\omega}_{2})|}_{{\omega}_{1}=\pi {f}_{1},{\omega}_{2}=\pi {f}_{1}}$$

For accurate results, use frequency points returned by `freqspace`

to create
`Hd`

.

produces an `h`

= fsamp2(`f1`

,`f2`

,`Hd`

,`[m n]`

)`m`

-by-`n`

FIR filter by matching the
filter response at the points in the vectors `f1`

and
`f2`

. The frequency vectors `f1`

and
`f2`

are in normalized frequency, where 1.0 corresponds to half
the sampling frequency, or π radians. The resulting filter fits the desired response
as closely as possible in the least squares sense. For best results, there must be
at least `m*n`

desired frequency points. `fsamp2`

issues a warning if you specify fewer than `m*n`

points.

`fsamp2`

computes the filter `h`

by taking the
inverse discrete Fourier transform of the desired frequency response. If the desired
frequency response is real and symmetric (zero phase), the resulting filter is also zero
phase.

[1] Lim, Jae S.,
*Two-Dimensional Signal and Image Processing*, Englewood
Cliffs, NJ, Prentice Hall, 1990, pp. 213-217.

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