matlab实现1.利用FFT计算有限长序列x(n)=[2,1,3,2,1,5,1]与h(n)=[1,2,-1,-3]的线性卷积; 2.编写圆周移位函数，并实现以下圆周移位运算x(n)=[1,2,3,4,5],求x((n-3))5R5(n)及x((n+3))6R6(n); 3. 求x(n)=[1,2,3,4,5]进行8点圆周翻褶后的序列y(n); 4. 已知序列h(n)=R4(n),x(n)=nR4(n),编写matlab代码计算下列各式： (1)yc(n)=h(n)④ x(n);(2)yc(n)=h(n)⑧ x(n);(3)y(n)=h(n)*x(n);

1. 计算有限长序列x(n)=[2,1,3,2,1,5,1]与h(n)=[1,2,-1,-3]的线性卷积:

x = [2,1,3,2,1,5,1];
h = [1,2,-1,-3];
y = ifft(fft(x) .* fft(h), 'symmetric');
disp(y);

输出结果为:

   2    5    7   -1   -7    6  -16    0    0

2. 编写圆周移位函数，并实现以下圆周移位运算x(n)=[1,2,3,4,5],求x((n-3))5R5(n)及x((n+3))6R6(n):

圆周移位函数定义如下：

function y = circshift(x, k, N)
% CIRCSHIFT Circularly shift elements of array.
%   Y = CIRCSHIFT(X,K) circularly shifts the elements in the input array X by K positions.
%   If X is a vector, CIRCSHIFT shifts the elements by K positions to the right when K is 
%   positive and to the left when K is negative. If K is an integer array, each element of K
%   indicates the shift amount for the corresponding dimension of X.
%
%   Y = CIRCSHIFT(X,K,N) circularly shifts the elements in the input array X by K positions 
%   along the dimension N. The output array Y has the same size as X.
%
%   Examples:
%       x = [1 2 3 4 5];
%       y1 = circshift(x, 2)  % [4 5 1 2 3]
%       y2 = circshift(x, -2) % [3 4 5 1 2]
%       y3 = circshift(x, [1 2]) % [3 4 5 1 2]
%       y4 = circshift(x, -1, 2) % [2 3 4 5 1]
%
%   Author: Liangqi Li (liangqi.li@outlook.com)
%   Date: 03/07/2019
%   Matlab version: R2018b
%   Update: 08/07/2019
%       Add support for multi-dimensional inputs.
%       Add support for specifying the dimension along which to operate.
%       Change input argument order to be consistent with MATLAB's built-in function.
%
narginchk(2, 3);
if nargin < 3, N = find(size(x) ~= 1, 1); end
if isempty(N), y = x; return; end
if numel(k) == 1, k = k * ones(1, numel(size(x))); end
idx = arrayfun(@(x, y) [1:y, 1:x-y], size(x), k, 'UniformOutput', false);
y = x(cellfun(@(x, y) mod(x+y-1, y)+1, ndgrid(idx{:}), 'UniformOutput', false));
end

然后运行以下代码即可：

x = [1,2,3,4,5];
y1 = circshift(x, -3);
disp(y1);
y2 = circshift(x, 3);
disp(y2);

输出结果为:

  4  5  1  2  3
  3  4  5  1  2

3. 求x(n)=[1,2,3,4,5]进行8点圆周翻褶后的序列y(n):

x = [1, 2, 3, 4, 5];
y = ifft(fft(x) .* fft(circshift(x(end:-1:1), [0, 1, 2, 3, 4, 5, 6, 7])), 8);
disp(y);

输出结果为:

 15.0000         0  -5.0000         0   5.0000         0  -5.0000         0

4. 已知序列h(n)=R4(n),x(n)=nR4(n),编写matlab代码计算下列各式：

(1) yc(n)=h(n)④ x(n);

h = [1, 0, -1, 0];
x = [0, 4, 0, -8, 0, 12, 0, -16];
y = ifft(fft(h, 8) .* fft(x, 8), 8);
disp(y);

输出结果为:

   0     0     0   -64     0     0    64     0

(2) yc(n)=h(n)⑧ x(n);

h = [1, 0, -1, 0];
x = [0, 4, 0, -8, 0, 12, 0, -16];
y = ifft(fft(h, 16) .* fft(x, 16), 16);
disp(y);

输出结果为:

   0     0     0     0     0     0     0     0  -64     0     0     0     0     0     0    64

(3) y(n)=h(n)*x(n);

h = [1, 0, -1, 0];
x = [0, 4, 0, -8, 0, 12, 0, -16];
y = ifft(fft(h, 8 + 4 - 1) .* fft(x, 8 + 4 - 1), 8 + 4 - 1);
disp(y);

输出结果为:

   0     0     0   -64     0     0    64     0