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DFT末尾补零和内部插值效果

已有 914 次阅读| 2011-12-15 18:23 |个人分类:数字信号处理

DFT末尾补零效果

原来x(n)的DFT为X(k)，在末尾补零rN个后成为y(n)，则

Y(k) = X(k/r)，在中间相当于插值，在频域插值。

然后，末尾补零x(n)的Z变换和DTFT是不会改变的仍为X(z), X(exp(jw))

% padding zero in the end, check effect to Xk

clc; clear;

f1=2.67;

f2=3.75;

f3=6.75;

fs=20;

N = 16;

n = 0:N-1;

x = sin(2*pi*f1*n/fs) + sin(2*pi*f2*n/fs) + sin(2*pi*f3*n/fs);

X = fft(x, N);

X = abs(X);

k = fs/N * (0:N-1); %fs/N是频域分辨率

stem(k, X(1:N), 'o', 'r'); hold on

% padding with rN zeros

r = 2;

x(N+1:r*N) = 0;

X = fft(x, r*N);

X = abs(X);

k = fs/(r*N) * (0:r*N-1);

stem(k, X(1:r*N), '*'); hold on

% padding with rN zeros

r = 4;

x(N+1:r*N) = 0;

X = fft(x, r*N);

X = abs(X);

k = fs/(r*N) * (0:r*N-1);

stem(k, X(1:r*N), '>', 'y');

序列插值之后变化

序列插值之后变化

% Interpolation 0, DFT effect
clc; clear;
f1=2.67;
f2=3.75;
fs=20;
N = 16;
n = 0:N-1;
x = sin(2*pi*f1*n/fs) + sin(2*pi*f2*n/fs);

X = fft(x, N);
X = abs(X);
k = fs/N * (0:N-1);     %fs/N是频域分辨率
subplot(2,1,1); stem(k, X(1:N), 'o', 'r');

% 内插0，两个数之间插入1个0
xi = zeros(1, 2*N);
for i = 1:2:2*N
    xi(i) = x((i+1)/2);
end
X = fft(xi, 2*N);
X = abs(X);
k = fs/(2*N) * (0:2*N-1);     %fs/N是频域分辨率
subplot(2,1,2);stem(k, X(1:2*N), 'o', 'r'); title('内插1个0后频谱');

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