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Low frequencies Vector Network Analyzer, arduino based.
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nihtila:
I am not a mathematician and do not understand DCT or those formulas really, but I think the point was that why do you calculate FFT when you are only after one frequency which you know (or are you, you do sweep right?). FFT calculates correlation for all frequencies between zero and Nyquist frequency, and although it is efficient computation, it is probably better just calculate correlation for that one frequency you are interested in. It does not change your processing gain if you do not change the length of your signal.

Of course if you have the computation power it probably does not matter. Or this comment may not even be relevant as I do not know exactly how you compute the impedance.

But your project looks cool! Really looking forward to more information.
MasterT:

--- Quote from: nihtila on September 21, 2018, 05:59:03 pm ---I am not a mathematician and do not understand DCT or those formulas really, but I think the point was that why do you calculate FFT when you are only after one frequency which you know (or are you, you do sweep right?). FFT calculates correlation for all frequencies between zero and Nyquist frequency, and although it is efficient computation, it is probably better just calculate correlation for that one frequency you are interested in. It does not change your processing gain if you do not change the length of your signal.

Of course if you have the computation power it probably does not matter. Or this comment may not even be relevant as I do not know exactly how you compute the impedance.

But your project looks cool! Really looking forward to more information.

--- End quote ---

The question I see, why someone would calculate all those 1023 bins if results trashed except only one bin that is goes into arctangent formula for phase extraction? Seems like a nonsense.

Lets me be more specific for this project, so it would be easy for me to explain. I have 250 kHz (putting aside aliasing for now) band splitted into 1024 stripes 244 Hz wide each.  My signal is falling into 125 kHz, bin = 512.

 The problem is that ADC data (and any data) hold not only pure signal, but a noise as well. And all these noise present in each stripes, more or less equally (gaussian somekind off).  Noise level is expressed in Volt / sqrt(Hz), so wide bandwidth - higher noise level.  For person who works with RF it's not a news, wider bandwidth - is always band things, and must be avoided.
I already gave a hardware example with MUX (or mixers). So, if I use a hardware phase discriminator, all 250 kHz wide band with all noise present in it goes into output. The only way to stop it, it's a preselector - or filter.

Now, if I do run  a FFT,  its sorting out everything - useful signal , noise - whatever. FFT is a separator, refinery machine, it would filter out /extract noise for example 128 kHz  out of bin of interest 512, 125 kHz.  Same apply to all 1023 bins, they are all cross-referenced with each other. Noise that presents in each stripe is  extracted from 125k, doing so FFT is "cleaning up" "refines" "polishing" my the only one bin of interest. So at the end, even most results are trashed, but it's doesn't matter since each result is already Accounted and extracted from bin 512.  Numerical data in bin 512 becomes sqrt(1023) time LESS noisy. Because an FFT magically pumped out any dust that otherways will go directly into output, into arctangent formula and generate a phase error.
nihtila:
I'm not sure what you mean by "cross-referencing" between bins. Isn't FFT effectively just a bank of narrow bandpass filters?

Try to generate 125kHz digital reference signal (sine) of the same length as your FFT, and use the same windowing. Correlate that with your wideband signal. You will get one number. If I am not completely wrong, that is the same number as your FFT gives for that bin.
ogden:

--- Quote from: MasterT on September 21, 2018, 02:51:10 pm ---
--- Quote from: ogden on September 21, 2018, 01:57:58 pm ---I would use DCT instead of FFT.

--- End quote ---
Manny people don't understand the absolute supremacy of the FFT on any other method of data processing. The question of "why using FFT instead of DCT?" is the same as "why to sample data by ADC and than process in DSP core, if we can drive a couple of MUXes by quadrature shifted clock?"  Because FFT provides processing gain, increasing SNR ratio by >30 dB(!).

--- End quote ---

Well, I have to admit two things: 1) I was wrong suggesting DCT (discrete cosine transfer) when actually I had DFT (discrete fourier transfer) in mind 2) you are mistaken about "FFT supremacy on any other method of data processing".

Why? - Check datasheet of AD5933, chip you are referring to. It does not do FFT but DFT instead.
oPossum:

--- Quote from: ogden on September 21, 2018, 08:20:43 pm ---It does not do FFT but DFT instead.

--- End quote ---

FFT is just a fast way to do a DFT.
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