This is no straight forward method for filter random signal to get the desire PSD.  What worked for me is the following:

1. Apply FFT to Hanning Window

2. Compute the magnitude and phase of FFT'ed data

3. Find the Dominant Frequency of the Hanning Window Filtered FFT

4. Apply Butterworth Filter to the data

5. Apply High-pass filter at Hz using 4-pole Butterworth forward and backward

6. Apply low-pass filter at Hz using 4-pole Butterworth forward and backward

7. Apply FFT to the Hanning Window & Butterworth filtered data

I use this approach for vibration data, which requires some trial and error.

Dear 

you can use wavelet transform for noise removal using wavelet thresholding. you may refer following paper:

http://www.ingentaconnect.com/content/asp/jmihi/2015/00000005/00000002/art00034?token=0047194a81dfb98b87e2a46762c6b665d76703f255349445f2a673f582f47e85b6b790b

If you take samples of the signal and reorder them, PDF will not change, whereas PSD will be completely different. So, you can generate signal with right PDF and then use reordering of the samples in order to obtain necessary PSD.

Dear Friends, maybe my question wasn't precise enough. Anyway thanks for answers and I will add some information what I have done in this subject. My intention was to involve filtering of noise into signal generator used for fatigue tests of mechanical structures. In my case the basic information about loading is the shape of PSD function. So the problem was in setting the filter parameters for filtering the noise to desired PSD. Finally I took another way to obtain the signal - it is an algorithm based on IFFT and amplitudes from PSD. Works well :-)