<div dir="ltr"><h1><font color="#000000" size="2" style="font-weight:normal" face="arial, helvetica, sans-serif">Firstly, white noise means only that the power spectral density is flat, or equivalently, that the autocorrelation function is zero everywhere except at lag zero.</font></h1><h1><font color="#000000" size="2" style="font-weight:normal" face="arial, helvetica, sans-serif">One can generate Gaussian noise with an arbitrary power spectral density by filtering white Gaussian noise with a suitable filter. The output of the filter is the convolution of the impulse response of the filter with the autocorrelation function of white noise, which gives us the impulse response of the filter. So, from the convolution theorem and the definition of the PSD, the PSD of the output is the squared magnitude of the frequency response of filter.</font></h1><h1><font size="2" style="font-weight:normal" face="arial, helvetica, sans-serif">An alternative method for synthesizing Gaussian noise with an arbitrary power spectral density is to generate tones with unity amplitude and random phase, where the probability of picking any particular tone frequency is proportional to the height of the PSD.<br></font></h1><h1><font size="2" style="font-weight:normal" face="arial, helvetica, sans-serif">The filter method tends to be more computationally efficient.</font><br></h1><div>Dr. Phillip M. Feldman</div><h1 style="color:rgb(0,0,0);font-family:"Times New Roman""><b style="font-size:medium">Suzen, Mehmet</b><span style="font-weight:normal;font-size:medium"> </span><a href="mailto:scipy-dev%40python.org?Subject=Re%3A%20%5BSciPy-Dev%5D%201/f%20noise%20generation&In-Reply-To=%3CCAPtbhHwp3dq6jiWEDhAbVn45ruUXKW%3D0%2BoD1PKvnHVdKjaw7GA%40mail.gmail.com%3E" title="[SciPy-Dev] 1/f noise generation" style="font-weight:normal;font-size:medium">msuzen at gmail.com </a><br></h1><i style="color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium">Tue Aug 8 08:15:33 EDT 2017</i><span style="color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium"></span><p style="color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium"></p><ul style="color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium"><li>Previous message (by thread): <a href="https://mail.python.org/pipermail/scipy-dev/2017-August/022035.html">[SciPy-Dev] 1/f noise generation</a></li><li><b>Messages sorted by:</b> <a href="https://mail.python.org/pipermail/scipy-dev/2017-August/date.html#22036">[ date ]</a> <a href="https://mail.python.org/pipermail/scipy-dev/2017-August/thread.html#22036">[ thread ]</a> <a href="https://mail.python.org/pipermail/scipy-dev/2017-August/subject.html#22036">[ subject ]</a> <a href="https://mail.python.org/pipermail/scipy-dev/2017-August/author.html#22036">[ author ]</a></li></ul><hr style="color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium"><pre style="white-space:pre-wrap;color:rgb(0,0,0)">On 8 August 2017 at 12:58, Neal Becker <<a href="https://mail.python.org/mailman/listinfo/scipy-dev">ndbecker2 at gmail.com</a>> wrote:
><i> I think you mean non-white, not nongaussian
</i>
Excellent point. white noise means constant PSD, not only Gaussian.</pre></div>