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It's all about vectorization. N = 8; K = 10; k = 1:K; % row vector f = k * 100; % row vector alpha = k / 10; % row vector a = k / 10; % row vector phi = k * pi; % row vector deltat = 1; n = (0:N-1)'; % column vector b = (1:N)'; % column vector x = sum(a.*exp(1j*phi).*exp((-alpha+1j*2*pi*f)*deltat.*n)+b, 2);...


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For what values of the model parameters, does it generate a real signal? That's probably not possible. Roughly speaking, your frequencies are all positive and a real signal must have a conjugate symmetric spectrum, i.e. equal amount of positive and negative frequencies. If you make the sum run from $-K$ to $+K$ and set $a_k = a_{-k}, \alpha_k = \alpha_{-k}, ...


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There are two interpretations of this problem. One is that only real voltages and currents can exist in the real world. Complex signals exist to simplify calculations, and in the DSP realm, where computers can easily handle complex numbers. The other interpretation is that a complex signal is just two real signals, one of which is labeled "imaginary&...


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