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'll try it on my signal analyzer here at work, your assumption still doesn't seem right to me.

Hi,

You don't need a signal analyzer for this. It is simple math that can be checked by hand. May be I am wrong, but still you should be able to verify it by hand.

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.

Ok. We're looking at different domains. You're reducing the focus to one pixel alone, and I'm looking at the entire system of smaller pixels. I'm not sure which one is right, but from your perspective of the pixel, then yes, I agree with you.

I was taking along theoretical ensemble statistics of white noise at a given pixel and its associated PSD so regardless of frequency it should not dip/rise and have a flat line.

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.

The area under a PSD should give the variance of noise on a given pixel. Right? However, in our example the smaller pixel had N/4 noise power and the bigger pixel had N, based upon Poisson statistics. If the PSDs are identical everywhere in the normalized [-1/2,1/2] frequency range then they will produce the same number and will be contrary to the fact that we have different variances on the smaller and bigger pixels as mentioned before.

Joofa wrote

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. ... In other words, in the real world, PSD should be limited to random signals.

Again, PSD is perfectly applicable for a non-random/deterministic signal. Please see the following link where it says that it applies to deterministic signals:
http://en.wikipedia.org/wiki/Spectral_density

The concept of PSD for a random signal is an extension of the notion of PSDs for non-random/deterministic signals. There are more complications in the convergence of PSDs for random signals, though.

Yes, it applies to any integrable and square integrable signal. If I recall, we're working in a Hilbert Space here. What is not shown in your reference is the discretized frequency domain from the FFT. The more resolution you select, the more normalization comes out, making random noise stay the same, but tonal values go up.

Joofa

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Dj Joofa

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