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I am looking for methods/algorithms for signal spectrum shaping. Let's say we have a white Gaussian noise and want to have a desired power-spectral density. The first solution that comes to mind is filtering. I was wondering if there are any other techinques.

I appreciate any hints.

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but... "shaping the spectrum" is exactly the definition of a filter. I think you can justifiably call everything that shapes a spectrum a filter, so no, nothing but filtering shapes a spectrum.

Note that just because that's the most commonly analyzed case, filters are more than just linear filters.

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Let us assume that your desired spectrum can be expressed as analytical or numerically and it is denoted as $H(f)$. First, you should take the inverse Fourier Transform of $H(f)$ in order to obtain the impulse response $h(t)$ (You can do this numerically or analytically as well.). Then, apply convolution on your signal by utilizing $h(t)$. Recall that $h(t)$ may result in an infinite impulse response in length. In such a case, (if you are planning to implement an FIR filter) try to express your $h(t)$ as long as possible to present the desired spectrum shaping operation.

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