Use the power spectral density P n4f generate stochastic processes s mT having this energy distribution where T is the sampling

Question

Use the power spectral density P n4f generate stochastic processes s mT having this energy distribution where T is the sampling period and M the desired number of signal samples in time This is easily done through the following equation s m 7 2 df P n cos 2 n df m T p n 0 Where s m T The stochastic process df frequency resolution fs N P n the PSD mT the amount of time covered for m samples Random phase from U 0 2 where each is drawn from U 0 2 The square root is necessary to transform from power to voltage The factor of one half takes into consideration that power spectra of real signals are symmetric in frequency and only positive frequencies are used in this formulation Multiplication by the sampling period Tscales the power to the correct level Keep in mind that computers don t know absolute time and frequency Therefore example P naf is the nth PSD value in a vector Like the cosine about is the mth element of a vector of length M Labeling frequency axes and time axes requires your consideration and DSP expertise The amplitude of synthesized signals may differ from original ones provided but their characteristics should look the same Provide plots of the signals that you synthesize Comment on their similarity or difference from the provided signals Provide your source code

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