I am not good at math, nevertheless, there’s a practical question.
If I have some magnitude points of the frequency responce, and I can sacrifice the phase data, assuming it’s all zeros, can I use inverse DCT instead of iDFT when calculating FIR coefficients?

I am trying to create a state space system for modeling the problem of binary phase shift keying (0/1) when the transmitter is moving at a constant velocity towards the receiver. The state space system takes the form: