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.
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.
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.
