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2-D FIR filter using 2-D window method

`h = fwind2(Hd, win)`

h = fwind2(f1, f2, Hd, win)

Use `fwind2`

to design two-dimensional FIR
filters using the window method. `fwind2`

uses a
two-dimensional window specification to design a two-dimensional FIR
filter based on the desired frequency response `Hd`

. `fwind2`

works
with two-dimensional windows; use `fwind1`

to work
with one-dimensional windows.

`h = fwind2(Hd, win)`

produces
the two-dimensional FIR filter `h`

using an inverse
Fourier transform of the desired frequency response `Hd`

and
multiplication by the window `win`

. `Hd`

is
a matrix containing the desired frequency response at equally spaced
points in the Cartesian plane. `fwind2`

returns `h`

as
a computational molecule, which is the appropriate form to use with `filter2`

. `h`

is
the same size as `win`

.

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

to
create `Hd`

. (See the entry for `freqspace`

for
more information.)

`h = fwind2(f1, f2, Hd, win)`

lets
you specify the desired frequency response `Hd`

at
arbitrary frequencies (`f1`

and `f2`

)
along the *x-* and *y*-axes.
The frequency vectors `f1`

and `f2`

should
be in the range -1.0 to 1.0, where 1.0 corresponds to half the sampling
frequency, or π radians. `h`

is the same size
as `win`

.

The input matrix `Hd`

can be of class `double`

or
of any integer class. All other inputs to `fwind2`

must
be of class `double`

. All outputs are of class `double`

.

`fwind2`

computes `h`

using
an inverse Fourier transform and multiplication by the two-dimensional
window `win`

.

$${h}_{d}({n}_{1},{n}_{2})=\frac{1}{{\left(2\pi \right)}^{2}}{\displaystyle {\int}_{-\pi}^{\pi}{\displaystyle {\int}_{-\pi}^{\pi}{H}_{d}({\omega}_{1},{\omega}_{2}){e}^{j{\omega}_{1}{n}_{1}}{e}^{j{\omega}_{2}{n}_{2}}d{\omega}_{1}d{\omega}_{2}}}$$

$$h({n}_{1},{n}_{2})={h}_{d}({n}_{1},{n}_{2})w({n}_{1},{n}_{2})$$

[1] Lim, Jae S., *Two-Dimensional
Signal and Image Processing*, Englewood Cliffs, NJ, Prentice
Hall, 1990, pp. 202-213.

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