信息处理 - 重叠保存方法零填充fft吉布现象 - 吾爱随笔录

我在频域做重叠保存方法。我使用频率采样方法将汉克尔函数制作为数字滤波器（制作任意幅度的相位滤波器）。我做ifft和零填充fft

我听说如果过滤器是非因果的，则零填充 fft 会出现吉布现象。我的过滤器有同样的问题。我正在做移位 FIR 滤波器来制作因果滤波器，但问题没有解决....请帮帮我



    clear all;
    close all;

    %% parameter
    
    fs = 2000;
    ts = 1/fs;
    c = 340;
    R = 1;
    
    %% hankel filter     
    Lp = 50;
    N = 2*Lp+1;                     %filter length
    resol = 0:N-1;                  % frequency resolution
    f = resol/N*fs;
    k = 2*pi*f/c;
    M=5;
    R = 2;
    nu = 2;                   %hankel order
    
    
    % frequency sampling method

    right = besselh(nu,k(1:(N-1)/2 +1)*R); %Hankel function 0~pi
    right(1:5) = 0;                     %eliminate infinite part
    left = fliplr(right);              
    left = conj(left);                  
    left(end) = [];
    
    H = [right left];               % symmetric freuqnecy response
    h = ifft(H);                % impulse response   
    
    nn = 80;                        %shift index 
    h1 = [h(nn : end) h(1:nn-1)];   % shift impulse response to make causal filter
    H1 = fft(h1,2*N);               %zero padding fft

    
    subplot(2,1,1)
    plot(h1)
    subplot(2,1,2)
    plot(abs(H1))

clear; close all; %% parameter fs = 2000; ts = 1/fs; c = 340; %% hankel filter Lp = 50; N = 2*Lp+1; % filter length NN = 2^nextpow2(N * 100); % NN >> N resol = 0:NN-1; % frequency resolution f = resol/NN*fs/2; % you miss /2 here k = 2*pi*f/c; M = 5; R = 2; nu = 2; %hankel order % window method right = besselh(nu,k(1:(NN-1)/2 +1)*R); %Hankel function 0~pi right(1:200) = 1; %eliminate infinite part left = fliplr(right); left = conj(left); left(end) = []; H = [right left]; % symmetric freuqnecy response h = ifft(H); % impulse response h1 = ifftshift(h); % shift impulse response to make causal filter win = hann(N).'; h2 = h1(NN/2-N/2:NN/2+N/2-1) .* win; % windowed impulse response H2 = fft(h2,2*N); %zero padding fft figure; subplot(2,1,1) plot(h2) subplot(2,1,2) plot(abs(H2))