matlab - 有没有一种更简洁的方法来生成正弦波总和？

Question

我编写了一个简单的 matlab/octave 函数来为每个分量创建具有独立振幅、频率和相位的正弦波总和。有没有更简洁的方式来写这个？

## Create a sum of cosines with independent amplitude, frequency and
## phase for each component:
##   samples(t) = SUM(A[i] * sin(2 * pi * F[i] * t + Phi[i])
## Return samples as a column vector.
##
function signal = sum_of_cosines(A = [1.0], 
                                 F = [440], 
                                 Phi = [0.0], 
                                 duration = 1.0, 
                                 sampling_rate = 44100)
  t = (0:1/sampling_rate:(duration-1/sampling_rate));
  n = length(t);
  signal = sum(repmat(A, n, 1) .* cos(2*pi*t' * F + repmat(Phi, n, 1)), 2);
endfunction

特别是，对 repmat() 的调用似乎有点笨拙——是否有一些漂亮的矢量化技术等着我学习？

Answer 1

这是一样的吗？

signal = cos(2*pi*t' * F + repmat(Phi, n, 1)), 2) * A';

然后可能

signal = real(exp(j*2*pi*t'*F) * (A .* exp(j*Phi))');

---

如果你的内存有限，这应该能很好地工作:

e_jtheta = exp(j * 2 * pi * F / sampling_rate);
phasor = A .* exp(j*Phi);
samples = zeros(duration,1);
for k = 1:duration
    samples(k) = real((e_jtheta .^ k) * phasor');
end