【MATLAB】图像处理相关函数lpfilter、dftuv函数

function [H, D] = lpfilter(type, M, N, D0, n)
% LPFILTER Computes frequency domain lowpass filters
%   H = LPFILTER(TYPE, M, N, D0, n) creates the transfer function of a
%   lowpass filter, H, of the specified TYPE and size (M-by-N). To view the
%   filter as an image or mesh plot, it should be centered using H =
%   fftshift(H)
%   Valid value for TYPE, D0, and n are:
%   'ideal' Ideal lowpass filter with cutoff frequency D0. n need not be
%           supplied. D0 must be positive.
%   'btw'   Butterworth lowpass filter of order n, and cutoff D0. The
%           default value for n is 1.0. D0 must be positive.
%   'gaussian'Gaussian lowpass filter with cutoff (standard deviation) D0.
%           n need not be supplied. D0 must be positive.
%
% 得到指定类型的低通滤波器

% Use function dftuv to set up the meshgrid arrays needed for computing the
% required distances.
[U, V] = dftuv(M, N);
% Compute the distances D(U, V)
D = sqrt(U.^2 + V.^2);
% Begin filter computations
switch type
    case 'ideal'
        H = double(D <= D0);
    case 'btw'
        if nargin == 4
            n =1;
        end
        H = 1 ./ (1 + (D ./ D0) .^ (2 * n));
    case 'gaussian'
        H = exp(-(D .^ 2) ./ (2 * (D0 ^ 2)));
    otherwise
        error('Unkown filter type.')
end

        

function [U, V] = dftuv(M, N)
% DFTUV Computes meshgrid frequency matrices.
% [U, V] = DFTUV(M, N) computes meshgrid frequency matrices U and V. U and
% V are useful for computing frequency-domain filter functions that can be
% used with DFTFILT. U and V are both M-by-N.
% more details to see the textbook Page 93
%
% [U，V] = DFTUV（M，N）计算网格频率矩阵U和V。 U和V对于计算可与DFTFILT一起使用的
% 频域滤波器函数很有用。 U和V都是M-by-N。更多细节见冈萨雷斯教材93页

% Set up range of variables.
% 设置变量范围
u = 0 : (M - 1);
v = 0 : (N - 1);

% Compute the indices for use in meshgrid.
% 计算网格的索引，即将网络的原点转移到左上角，因为FFT计算时变换的原点在左上角。
idx = find(u > M / 2);
u(idx) = u(idx) - M;
idy = find(v - N / 2);
v(idy) = v(idy) - N;

% Compute the meshgrid arrays.
% 计算网格矩阵
[V, U] = meshgrid(v, u);