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I have noise measurements for a circuit, in units of noise power (measured in Watts against a known load), per frequency bin. For simulation purposes, I wish to synthesize noise with the same spectral shape.

I believe I can model my noise as Gaussian, but it isn't white. How can I synthesize such noise?

My guess is that I can synthesize WGN using MATLAB's wgn function, and then filter it. However, I'm not sure how to create the filter. Additionally, my signal is single ended so I guess I should add some offset to account for it. Any suggestions?

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