# Signal Spectrum Shaping

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.

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.