freqz2

R2026b

2-D frequency response

Syntax

[H,fx,fy] = freqz2(h)

[H,fx,fy] = freqz2(h,[nx,ny])

[H,fx,fy] = freqz2(h,[nx,ny],[dx,dy])

H = freqz2(h,fx,fy)

freqz2(___)

Description

[H,fx,fy] = freqz2(h) returns the 64-by-64 frequency response H of the 2-D FIR filter h. h must be in the form of a correlation kernel. freqz2 also returns the frequency vectors fx and fy as normalized frequencies in the range -1.0 to 1.0, where 1.0 corresponds to half the sampling frequency, or π radians.

[H,fx,fy] = freqz2(h,[nx,ny]) returns the ny-by-nx frequency response H of 2-D FIR filter h.

You can also specify nx and ny as two separate arguments: [H,fx,fy] = freqz2(h,nx,ny).

[H,fx,fy] = freqz2(h,[nx,ny],[dx,dy]) uses [dx,dy] to override the intersample spacing in h. You can also specify a scalar to use the same spacing in both the x and y dimensions.

H = freqz2(h,fx,fy) returns the frequency response for the 2-D FIR filter h at the specified frequency values in fx and fy. These frequency values must be in the range -1.0 to 1.0, where 1.0 corresponds to half the sampling frequency, or π radians.

freqz2(___) displays a mesh plot of the 2-D magnitude frequency response when no output arguments are specified.

Examples

View Frequency Response of Filter

This example shows how to create a two-dimensional filter using fwind1 and how to view the filter's frequency response using freqz2.

Create an ideal frequency response.

Hd = zeros(16,16);
Hd(5:12,5:12) = 1;
Hd(7:10,7:10) = 0;

Create a 1-D window. This example uses a Bartlett window of length 16.

w = [0:2:16 16:-2:0]/16;

Create the 16-by-16 filter using fwind1 and the 1-D window. This filter gives the closest match to the ideal frequency response.

h = fwind1(Hd,w);

Display the actual frequency response of the filter.

colormap(parula(64))
freqz2(h,[32 32]);
axis ([-1 1 -1 1 0 1])

Design 2-D FIR Filter Using Frequency Sampling Method

This example shows how to design a 2-D FIR filter using the frequency sampling method on a desired frequency response.

Given a matrix that defines the shape of the frequency response, the frequency sampling method creates a filter in the spatial domain whose frequency response matches the matrix at the sampled frequencies. Frequency sampling places no constraints on the behavior of the frequency response of the filter between the sampled frequencies. Further, frequency sampling might not be able to capture discontinuities in the ideal frequency response. These interpolation errors and discontinuities usually cause ripples in the frequency response of the filter. Ripples are oscillations around a constant value. The frequency response of a practical filter often has ripples, whereas the frequency response of an ideal filter is flat.

Define and visualize the target 2-D frequency response of an 11-by-11 filter.

Hd = zeros(11,11); 
Hd(4:8,4:8) = 1;
[f1,f2] = freqspace(11,"meshgrid");
mesh(f1,f2,Hd)
title("Desired Frequency Response")

Create the filter based on the target frequency response using the fsamp2 function. The fsamp2 function returns the filter h in the spatial domain with a frequency response that passes through the points in the input matrix Hd.

h = fsamp2(Hd);

Plot the frequency response of the filter.

freqz2(h,[32 32])
title("Actual Frequency Response")

Notice the ripples in the actual frequency response compared to the desired frequency response. These ripples are a fundamental problem with the frequency sampling design method that occur wherever there are sharp transitions in the desired response. You can reduce the spatial extent of the ripples by using a larger filter. However, a larger filter does not reduce the height of the ripples, and requires more computation time for filtering. To achieve a smoother approximation of the desired frequency response, consider using the frequency transformation method or the windowing method, instead.

Filter an image using the designed filter, and visualize the results.

inputImage = imread("coins.png");
outputImage = imfilter(inputImage,h);
imshowpair(inputImage,outputImage,"montage")

Input Arguments

h — 2-D FIR filter

numeric matrix

2-D FIR filter in the form of a correlation kernel, specified as a numeric matrix.

nx,ny — Number of points in frequency response

[64 64] (default) | positive integer | 2-element vector

Number of points in the frequency response, specified as a positive integer or a 2-element vector of positive integers of the form [nx ny]. If you specify a positive integer, then freqz2 uses that number of points for both nx and ny.

dx,dy — Sample spacing

0.5 (default) | numeric scalar | 2-element vector

Sample spacing, specified as a numeric scalar or a 2-element numeric vector of the form [dx dy]. dx determines the spacing for the x dimension and dy determines the spacing for the y dimension. If you specify a scalar, then freqz2 uses the value to determine the intersample spacing in both dimensions. The default spacing of 0.5 corresponds to a sampling frequency of 2.0.

Changing dx and dy has the effect of changing the spread of values in fx and fy. For example, setting dx to 0.25 instead of 0.5 causes the values in fx to range from -2.0 to 2.0 instead of -1.0 to 1.0. Setting dy to 1.0 instead of 0.5 causes fy to range from -0.5 to 0.5 instead of -1.0 to 1.0.

fx, fy — Frequency vectors

numeric vectors

Frequency vectors, specified as numeric vectors.

Data Types: double

Output Arguments

H — Frequency response

numeric array

Frequency response, returned as a numeric array.

fx — Frequency vector

vector

Frequency vector, returned as a numeric vector.

Data Types: double

fy — Frequency vector

vector

Frequency vector, returned as a numeric vector.

Version History

Introduced before R2006a