how to generate a time series of given autocorrelation

I have a list a randomly generated numbers that follow a certain probability distribution function (PDF). Since they are generated randomly, their sequence does not have any auto-correlation. I am wondering if there is any way to re-order their sequence according to a pre-given autocorrelation? Or more generally, to re-order them according to a given power spectral density?

In short: how to generate a time series given both PDF (amplitude-wise) and PSD (in frequency domain)?

For example, a list of random gaussian numbers is a white noise. I need to keep the signal amplitude and re-order their sequence to approximate the desired autocorrelation or power density spectrum?

[Honglei Chen]

https://www.mathworks.com/matlabcentral/answers/47634-to-generate-a-random-signal-with-the-given-psd

This might be helpful to you. If this does not address your issue, you may want to provide more details.

HTH

[John BG]

if you reorder the points you are going to change the probability distribution properties of the function that you want to catch.

Are you sure the 2 sequences are complete uncorrelated?

John BG

<mailto:[e-mail] [e-mail]>

[Zhang]

I do not totally agree with that. The PDF is about the amplitude distribution, but it does not contain information about how the signals are sequenced. The PSD is about the sequence of the signals, although the amplitudes also affect the PSD. This is the problem I have. So my issue is to generate a random sequence of numbers whose amplitudes should exactly follow a given PDF, with the sequence having the largest correlation with a sequence that has the exact PSD.