# Getting down to the nitty-gritty about noise and it's effect on IQ Locked

Started Apr 15, 2010 | Discussions thread
Re: Total noise power

Joofa wrote:

I'm losing you, but I could be wrong. Just as a thought experiment, say you have some PSD function with 1 unit of some arbitrary resolution. Now take your 2x2 pixel per original pixel increase in resolution, basically you now have four times the pixels, and each pixel has 1/4 the noise power. Each bin of your FFT is now 1/4 the bandwidth, but you also have four times the probability per bin, so you're right back where you started. Hencse, the PSD has not changed. It is a density, not an absolute.

PSD is the Fourier transform of the autocorrelation function. Under the white noise assumption, the autocorrelation for lower MP is N*delta(t) and for higher MP it is N/4*delta(t). Now you can take the Fourier transform and see that the PSDs are different.

I'll try it on my signal analyzer here at work, your assumption still doesn't seem right to me. You are increasing resolution by 4, so you could expect a -6dB change per bin. However, you now have 4 times as many sites to sample and as a whole you would get +6dB in distribution. The net effect is zero. From another view, the probability distribution as a system has not changed just because you slice it up more. This is density.

In fact, do you have any SDF files from something like a 35670A that would back up your argument? Send it to me. I and another here would love to see it.

It also isn't useful for non-random signals, which I'm still not sure is completely the case.

The concept of PSD is perfectly valid for non-random or deterministic signals.

The concept is valid. However, brace yourself for misleading answers. Imagine a pure tone with a signal well above the noise floor. Say your bin bandwidth is 1 unit and the amplitude is 20dB. Now, double the resolution. Since this is a density function, your denominator is units or (units^.5) depending on how you like to view your data. Essentially, increasing resolution makes the amplitude of the tone increase. Let the resolution go to something small, and the tone get huge, but the original signal hasn't changed. So what's the right answer? They're all correct. However, and this happens to me all the time, project specs may be given in terms of PSD and engineers measure signals and report them. Depending on the resolution selected, you can get results that pass or fail. In other words, in the real world, PSD should be limited to random signals.

Joofa

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Dj Joofa

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