Matlab信号展开

将a的每个元素重复 N 个，[ 1 3 4 5 7] ---> [ 1 1 1 1 3 3 3 3 4 4 4 4 5 5 5 5 7 7 7 7 ]

N = 10;
a = [ 1 3 4 5 7];
%欲将a的每个元素重复 N 个
% 1、先将a整形为每个元素后加 N-1 个0
%       例如：c=[1 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 ...]
% 2、再将c与b卷积 conv(c,b)，取结果的前 N*M 个
b = ones(1,N);
% 1、
M = length(a);
c = zeros(N,M);
c(1,:) = a;
c = reshape(c,1,N*M);
% 2、
out = conv(c,b);
out = out(1:N*M);

等价于

out = rectpulse([1 3 5 ],10);
% out = [1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 5 ]

rectpulse(a,N);

---

理想低通滤波器

$$ H(f)=\{^{1, \quad |f| \leq 5/(2T_s)}_{0,  \quad others} $$

$$ H(f)=\begin{cases} 1 & |f| \leq 5/(2T_s) \\ 0 & others  \end{cases} $$

则 h(t)=5*sinc(5*t/Ts)