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Considering broad range of spectrum analysers such as this one or this one.

Are they just showing the FFT of a voltage signal?

Here someone explaining the difference between the two and mentions:

Although engineers are tempted to use FFTs (fast Fourier transforms) for spectrum analysis, they should really be using (PSDs) power spectral densities. The reason is that PSDs are normalized to the frequency bin width preventing the duration of the data set (and corresponding frequency step) from changing the amplitude of the result. FFTs don't do this!

I'm asking because engineers either look at FFT of a sampled signal or PSD of it using tools like MATLAB, Pythons ect. and I still don't get when to use what.

1-) Basically considering the real-time spectrum analysers I've linked at the very beginning of the question, it seems to me they plot the FFT of the voltage signal(?) And if PSD is superior to FFT in terms of observing noise components why don't spectrum analysers show PSD of the signal instead?

2-) Can you give two signal measurement scenarios where the sampled data is better analysed using FFT or PSD? Its like a question: "Well I have now sampled the voltage signal for 100ms and what spectrum I better use PSD or FFT?". I can assume the signal can be many things such as stationary, noise, pulse ect. Is there a intuition which line to go for? I know its a broad topic a but an example would be great to grasp some insight.

(My assumptions and information might be wrong in the question, but trying to clarify things)

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  • \$\begingroup\$ About differences: spectrum analyzer versus FFT or PSD methods...with a carefully-built spectrum analyzer, you have more assurance that the displayed result has been bandwidth-limited. For example, when measuring noise, a FFT or PSD might include noise around harmonics of sampling frequency (folded back) whereas SA doesn't fold. \$\endgroup\$
    – glen_geek
    Feb 18 at 1:50
  • \$\begingroup\$ @glen_geek thank you for the comment. But how can I know what method this one use?: wiki.analog.com/university/tools/m2k/scopy/spectrumanalyzer Can I count it like a real spectrum analyser or is it just taking FFT? \$\endgroup\$
    – cm64
    Feb 18 at 15:52
  • \$\begingroup\$ here is the schematic of it(ADALM2000): wiki.analog.com/_media/university/tools/m2k/devs/… \$\endgroup\$
    – cm64
    Feb 18 at 15:53
  • \$\begingroup\$ Data sheet for AD9963 states: ADCs support IF sampling frequencies up to 140 MHz, making them suitable for undersampling receivers. Since analog input bandwidth exceeds sampling rate, you're not protected from aliases folding back. You'd want to add analog low-pass filter ahead of this ADC if you desire spectrum analyzer-like response. OR be prepared to identify aliases in the FFT spectrum. Aliased noise is mighty difficult to identify once it is digitized. \$\endgroup\$
    – glen_geek
    Feb 18 at 17:44

1 Answer 1

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Are they just showing the FFT of a voltage signal?

Generally speaking, no, although some modern spectrum analyzers can speed up spectrum acquisition by stepping the local oscillator (LO) and using a good ADC to capture the downconverted band-limited view of the signal around the LO frequency, then taking the FFT of that, and using it to reconstruct the traditional view of the spectrum.

At their simplest, spectrum analyzers apply a filter with an adjustable center frequency and bandwidth to the signal, and measure the amplitude of the signal output from the filter. The filter's center frequency is swept across the frequency range of interest.

The "stepped FFT" analyzers emulate this behavior by default, i.e. the FFT is just an implementation detail that speeds up the spectrum acquisition, but doesn't change how the signal actually looks when displayed.

they plot the FFT of the voltage signal

Not really. A classical spectrum analyzer display is IIRC easiest described as the magnitude (or magnitude squared) of frequency-domain convolution* of the filter response with the Fourier transform of the the signal. The bandwidth, and sometimes also Q, of the filter can be adjusted.

*As opposed to time-domain convolution.

Although engineers are tempted to use FFTs (fast Fourier transforms) for spectrum analysis, they should really be using (PSDs) power spectral densities.

The FFT and PSD are just different scalings of the same transformation. PSD presentation makes it easier to reason quantitatively and compare different PSDs. With a raw FFT, the parameters of the FFT affect the presentation.

Whether you're computing the raw FFT or a PSD, you take the FFT of the signal first.

The PSD is the squared magnitude of the FFT divided by the number of FFT bins, i.e. $$P(f)=\frac{1}{N}{\left|\mathscr{F}[x(f)]\right|}^2.$$

For details, see https://dsp.stackexchange.com/a/24815/8388

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