How the spectrum analyser works

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picoperson
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Joined: Thu Sep 09, 2021 7:44 am

How the spectrum analyser works

Post by picoperson »

I'm using a Picoscope 4262 with Picoscope 7.0.80.9088 on an iMac. I'm measuring audio frequency noise in an instrument amplifer, down to Johnson noise. It's giving me some lovely results!

And a bit of confusion. I have the scope set to 2 ms/div, sample rate 5 Msamples/s, it tells me in the timebase panel. So I have loads of samples coming in. If I zoom in to a 100 us window within that trace, i can see lots of high freqency content, typically 500 kHz, bigger than the LF noise I am trying to measure, despite having the 200 kHz BW limiter turned on. Oh well, that's life. I can smooth out that HF content in the scope trace by turning on the digital filter in the Y axis panel, and that neatly cuts out much of the HF noise and I can see what I'm doing again.

I'm also using the spectrum display, set to 20 kHz range, 8192 bins, 2.44 Hz bin size. The spectrum panel says "40 kSamples/s" and "Time Gate 204.8 ms". That's consistent with taking 8192 samples at 25 us intervals, 40 kSamples/s. So is the FFT software just sampling the raw input at that rate?

There is much more information than that available: all the 25*5=125 other samples the scope collects every 25 us. Does the FFT software average all of those to measure every sample it takes? Would that work to reduce aliassing of high frequency signals? Would the FFT still make sense?

And, the FFT software could be even more aggressive. It could take samples from the output of the Y-axis digital filter. Does it? Would it work? Would that reduce aliased signals from high frequencies?

I ask because I run into trouble with HF noise from my input - Radio 5 Live, among others - aliassing down into audio frequencies for the spectrum display. I'm going to build an external analog lowpass filter, but I'd like to understand the limits of the FFT too.

PLUS: The "averaging" display mode of the spectrum analyser. Just what does the FFT average? It seems to get awfully stuck in its ways. If I leave it looking at one signal for a long time, then that signal changes somehow, it takes forever to begin to change to the new average, if I don't stop and restart the scope to begin a new average. How many traces are being averaged? The last 64, say? Or all the traces since the last restart?

Thanks for any insight!

Gerry
PICO STAFF
PICO STAFF
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Joined: Mon Aug 11, 2014 11:14 am

Re: How the spectrum analyser works

Post by Gerry »

Hi picoperson,

Sorry for the long delay in answering, I've been on annual leave.

First of all, our Spectrum Mode is optimised for plotting spectrums of Signals as opposed to Noise (unfortunately, you can't get accurate measurements of both using an FFT plot). You can plot signals accurately using a Linear Spectrum (Vrms/Hz), in PicoScope 6, because we apply Coherent Gain to the window function, in order to ensure the amplitude level is conserved before and after the FFT. What this means in terms of noise is that, with the frequently used Window Functions, e.g. Blackman, the noise level will decrease in level by -3dB, if you double the number of bins used for the spectrum plot, due to the applied Coherent Gain.
So, for accurate noise measurements you really need to use a Power Spectrum (Vrms/√Hz), which, unfortunately, you would have to implement yourself, using our Software Development Kit (see here: https://www.picotech.com/library/oscill ... nt-kit-sdk) which you can download from here: https://www.picotech.com/downloads/_lig ... kit-32-bit or here: https://www.picotech.com/downloads/_lig ... -kit-64bit, our code examples, detailing how to implement the basic Data Acquisition functions of our devices, which you can download from here: https://github.com/picotech, and an FFT Library that plots Vrms/√Hz.

To respond to your first query, the Bandwidth Limiter is a means of limiting higher frequencies, but only applications that have a significantly higher bandwidth than the cut-off frequency (e.g. Ultra Sound) will benefit from significantly reductions in higher frequency components. The Bandwidth Limiter is a 1st order Low pass filter, with a roll-off of, at 200kHz, of 3dB/octave, so it will reduce waveforms at 500kHz by just 7dB (you can see this in an example Gif file, that you can download from here: https://drive.google.com/file/d/1LOKH5q ... sp=sharing).

I'll respond below your other questions: pasted below in italics:

So is the FFT software just sampling the raw input at that rate?
Yes, that's correct.

There is much more information than that available: all the 25*5=125 other samples the scope collects every 25 us.
If by this you mean the additional samples collected when using a Secondary Spectrum View to display the Spectrum plot, for example, below a Scope Mode plot, then yes there is more data that is not plotted, but if it was plotted then you would have to wait longer to display the spectrum (for a detailed explanation, see here: topic40873.html?&p=145458&hilit=seconda ... ow#p145458).

Does the FFT software average all of those to measure every sample it takes?
The Software will average across successive captures of waveforms in order to reduce the variance in the display, when you select 'Average' or 'Peak hold' for the Display Mode in the 'Spectrum Options'.

Would that work to reduce aliassing of high frequency signals?
No, the only ways that you can reduce aliasing of high frequency signals would be to either (1) reduce the bandwidth of the waveforms that you are capturing first passing them through an anti-aliasing filter, or (2) raise the sample rate to move the Nyquist or Folding frequency further away from the highest harmonics of your waveforms being captured.

And, the FFT software could be even more aggressive. It could take samples from the output of the Y-axis digital filter. Does it? Would it work? Would that reduce aliased signals from high frequencies?
This is what we call 'Resolution Enhancement', and it's, in essence, a moving average filter that can both reduce variance and reduce the vertical distance between samples. However, the filter behaves like a low pass filter (removing high frequency content from the data), so, if the FFT plotted the Res Enhanced data, then, yes, it would reduce any aliasing, because the signal frequencies that contribute to the aliasing would be reduced. Unfortunately, Resolution Enhancement is a 'Scope Mode' only function, so it can't be used in a Spectrum plot.

I ask because I run into trouble with HF noise from my input - Radio 5 Live, among others - aliassing down into audio frequencies for the spectrum display.
Perhaps you could show us exactly what the problem is in a data file, and explain why you believe the noise is being aliased down into audio frequencies.

How many traces are being averaged?
The number of traces being averaged is the last x traces, where x is the number of captures over which measurement statistics are calculated (which can be adjusted by going to Tools->Preferences->General->Measurement Statistics). So, averaging continues until you stop the captures, but at any time only x waveforms contribute to the averaged value being calculated. As you have found, if you start a series of captures with different data, then you should clear the preceding data by restarting the Spectrum plot.

Regards,

Gerry
Gerry
Technical Specialist

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