fwind1

2-D FIR filter using 1-D window method

Syntax

h = fwind1(Hd,win)

h = fwind1(Hd,win1,win2)

h = fwind1(f1,f2,Hd,___)

Description

The fwind1 function designs 2-D FIR filters using the window method. fwind1 uses a 1-D window specification to design a 2-D FIR filter based on the desired frequency response. fwind1 works with 1-D windows only. Use fwind2 to work with 2-D windows.

You can apply the 2-D FIR filter to images by using the filter2 function.

example

h = fwind1(Hd,win) creates a 2-D FIR filter h based on the desired frequency response Hd. fwind1 uses the 1-D window win to form an approximately circularly symmetric 2-D window using Huang's method.

h = fwind1(Hd,win1,win2) uses two 1-D windows, win1 and win2, to create a separable 2-D window.

h = fwind1(f1,f2,Hd,___) enables you to specify the desired frequency response Hd at arbitrary frequencies f1 and f2 along the x- and y-axes.

Examples

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Create 2-D FIR Filter using 1-D Window Method

Open Live Script

This example shows how to design an approximately circularly symmetric two-dimensional bandpass filter using a 1-D window method.

Create the frequency range vectors f1 and f2 using freqspace. These vectors have length 21.

[f1,f2] = freqspace(21,'meshgrid');

Compute the distance of each position from the center frequency.

r = sqrt(f1.^2 + f2.^2);

Create a matrix Hd that contains the desired bandpass response. In this example, the desired passband is between 0.1 and 0.5 (normalized frequency, where 1.0 corresponds to half the sampling frequency, or $π$ radians).

Hd = ones(21); 
Hd((r<0.1)|(r>0.5)) = 0;

Display the ideal bandpass response.

colormap(parula(64))
mesh(f1,f2,Hd)

Design the 1-D window. This example uses a Hamming window of length 21.

win = 0.54 - 0.46*cos(2*pi*(0:20)/20);

Plot the 1-D window.

figure
plot(linspace(-1,1,21),win);

Using the 1-D window, design the filter that best produces this frequency response

h = fwind1(Hd,win);

Display the actual frequency response of this filter.

freqz2(h)

Input Arguments

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`Hd` — Desired frequency response
numeric matrix

Desired frequency response, specified as a numeric matrix. Hd is sampled at equally spaced points between -1.0 and 1.0 (in normalized frequency, where 1.0 corresponds to half the sampling frequency, or π radians) along the x and y frequency axes. For accurate results, create Hd by using the freqspace function.

`win` — 1-D window
numeric matrix

1-D window, specified as a numeric matrix. You can specify win using windows from Signal Processing Toolbox™ software, such as hamming (Signal Processing Toolbox), hann (Signal Processing Toolbox), bartlett (Signal Processing Toolbox), blackman (Signal Processing Toolbox), kaiser (Signal Processing Toolbox), or chebwin (Signal Processing Toolbox).