freqspace

Frequency spacing for frequency response

Syntax

[f1,f2] = freqspace(n)

[f1,f2] = freqspace([m n])

[x,y] = freqspace(___,'meshgrid')

f = freqspace(N)

f = freqspace(N,'whole')

Description

[f1,f2] = freqspace(n) returns the two-dimensional frequency vectors f1 and f2 for an n-by-n matrix.

freqspace returns the implied frequency range for equally spaced frequency responses. freqspace is useful when creating desired frequency responses for various one- and two-dimensional applications.

[f1,f2] = freqspace([m n]) returns the two-dimensional frequency vectors f1 and f2 for an m-by-n matrix.

[x,y] = freqspace(___,'meshgrid') is equivalent to

[f1,f2] = freqspace(...);
[x,y] = meshgrid(f1,f2);

f = freqspace(N) returns the one-dimensional frequency vector f assuming N evenly spaced points around the unit circle.

f = freqspace(N,'whole') returns N evenly spaced points around the whole unit circle. In this case, f is 0:2/N:2*(N-1)/N.

Examples

Create Matrix of Desired Passband Response Using Frequency Vectors

Create a matrix Hd that contains the desired bandpass response for an approximately symmetric, two-dimensional bandpass filter with passband between 0.1 and 0.5 (normalized frequency, where 1.0 corresponds to half the sampling frequency, or π radians.) Use freqspace to create the frequency vectors f1 and f2.

[f1,f2] = freqspace(21,'meshgrid');
Hd = ones(21); 
r = sqrt(f1.^2 + f2.^2);
Hd((r<0.1)|(r>0.5)) = 0;
colormap(jet(64))
mesh(f1,f2,Hd)

Input Arguments

n — Length of frequency vectors

numeric scalar

Length of the frequency vectors, specified as a positive numeric scalar.

Data Types: single | double

[m n] — Length of each frequency vector

two-element vector of positive numeric values

Length of each frequency vector, specified as a two-element vector of the form [m n].

Data Types: single | double

N — Number of points around the unit circle

numeric scalar

Number of points around the unit circle, specified as a positive numeric scalar.

Data Types: single | double

Output Arguments

f1 — 2-D frequency vector

numeric vector

2-D frequency vector, returned as a numeric vector.

For n odd, both f1 and f2 are [-n+1:2:n-1]/n.

For n even, both f1 and f2 are [-n:2:n-2]/n.

f2 — 2-D frequency vector

numeric vector

2-D frequency vector, returned as a numeric vector. f2 has the same odd and even behavior as f1.

x — X-coordinates over grid

numeric matrix

X-coordinates over a grid, returned as a numeric matrix.

y — Y-coordinates over grid

numeric matrix

Y-coordinates over a grid, returned as a numeric matrix.

f — 1-D frequency vector of points around the unit circle

numeric vector

1-D frequency vector of points around the unit circle, returned as a numeric vector of N evenly spaced points.

• For N even or odd, f is (0:2/N:1).

• For N even, freqspace returns (N+2)/2 points.

• For N odd, freqspace returns (N+1)/2 points.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

The freqspace function supports GPU array input with these usage notes and limitations:

• To run this function on a GPU and obtain a gpuArray output, use any of the following syntaxes:

  [f1,f2] = gpuArray.freqspace(n)
  [f1,f2] = gpuArray.freqspace([m n])
  [x,y] = gpuArray.freqspace(___,'meshgrid')
  f = gpuArray.freqspace(N)
  f = gpuArray.freqspace(N,'whole')

• Alternatively, you can specify n, m, or N as a gpuArray.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced before R2006a