Note: This page has been translated by MathWorks. Please click here

To view all translated materials including this page, select Japan from the country navigator on the bottom of this page.

To view all translated materials including this page, select Japan from the country navigator on the bottom of this page.

2-D FIR filter using 2-D window method

`h = fwind2(Hd,win)`

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

produces the two-dimensional FIR filter `h`

= fwind2(`Hd`

,`win`

)`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`

.

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.

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

to create `Hd`

.

lets you specify the desired frequency response `h`

= fwind2(`f1`

,`f2`

,`Hd`

,`win`

)`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`

.

`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.

Was this topic helpful?