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Design >> Analog Design >> How to understand negative frequency?
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Message started by Frank_Heart on Nov 20^th, 2017, 2:31pm

Title: How to understand negative frequency?
Post by Frank_Heart on Nov 20^th, 2017, 2:31pm

Hi, All,

If we have a 1st Order RC filter, we know the total thermal noise at output is KT/C, spreading from 0 to inf.

While for a uniform quantifier with LSB= VLSB, we will say the total quantification noise is VLSB*VLSB/12, spreading from -0.5*FS to 0.5*FS.

Then how to understand this negative frequency from 0.5*Fs to 0?

Is it because quantification noise is not a "physical" noise, which is from mathematics definition? Only sampling system will 'create' negative half on the spectrum?

Sometimes it is really annoying, as in some simulator, the plotted FFT will only show the positive part, and with the number doubled (I think spectre is in this way?). While in some simulator, they didn't.

Any thoughts on this?

Thanks
Frank

Title: Re: How to understand negative frequency?
Post by Horror Vacui on Nov 21^st, 2017, 2:07pm

The quantization noise is white, because the probably of any voltage btw -LSB/2 and LSB/2 is the same. The quantization noise is generated for every digitization, i.e. the input value is frozen at that instance of acquisition, but it has some deviation from the quantized voltage levels. It has no time or frequency domain behaviour, because it does not exist in time or frequency domain.

Title: Re: How to understand negative frequency?
Post by Berti-2 on Nov 28^th, 2017, 4:21am

I disagree: Strictly speaking, quantization noise is definitely not white and not even random, but fully deterministic.
Nevertheless it is often modeled as an adaptive white noise source because this gives a good approximation if the input signal is busy enough.
I therefore consider it important to be aware that the white noise assumption is just a model, which for most situation is reasonable accurate.

If you have a real signal, the spectrum is always symmetric around DC. So it is sufficient to only consider the positive part. For a complex signal, the spectrum is not necessarily symmetric and you should consider both negative and positive frequencies. In your examples, the spectrum will be symmetric and it doesn't matter whether you consider double- or single-sided spectra (as long the factor 2 is properly considered).