Generating artificial (synthetic) time series for spectral analysis

Hello, I am attempting to create a synthetic time series to perform spectral analysis (FFT and Lomb-Scargle) on. Ideally, this time series will have three frequencies in it plus noise. I can generate an artificial time series using rand function, but I do not know how to incorporate specific frequencies and noise (this seems like a different process than rand. Any help would be greatly appreciated!

Answer 1

[Stephan]

See this example:

https://de.mathworks.com/help/matlab/ref/fft.html?searchHighlight=fft&s_tid=doc_srchtitle#buuutyt-9

Best regards

Stephan