DSP Robotics Support

Something isn't working, so let see if I understand it correctly.

Let say that I have 1kHz sine signal, buried in noise, so that I don't see any spike of it on the FFT spectrum.

Because (let say) I don't know where the burried signal is - carrier wave/frequency (CF node on schematic) should go step by step through the whole spectra, processing the whole file per each step. (we simplify it to 2 steps, one around measured freq and one far away from it).

The step size is defined by filter width around (shouldn't be a bandpass filter there or perhaps FFT filter?) the carrier wave CF, which is 2Hz in the schematic (cutoff frequency). I'm guessing this is width of detection, so step size can be a bit smaller (to 1Hz?)

So. If the window size is 2Hz, then the file should be processed per each 2Hz step, and - the end result perhaps can be mixed with sum of previous steps, to keep it in memory and not in harddrive as separate files. To simplify, we can get a segmented spectra that way.

The technique works so (?), that if around carrier wave CF (within this 1-2Hz window detection?) - buried fixed frequency is present, then overall amplitude should rise, and if there is no fixed frequency - amplitude goes to (almost) zero.

The result. If I'm deciding to detect 1kHz signal within 2kHz frequency band, and at step size 2Hz, then I will have 1000 steps (iterations), that I can mix into single file, and within that file, on FFT analyzer - I will see the 1kHz spike or so, and no (or small) noise?

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The problem is, that I'm getting nowhere with the schematic, because I'm not sure what should I get on output and under what conditions. I'm also not sure about the order of things there. The input that goes to lock-in routine - should be a mix of sine (at low level, let say 1000.1Hz) and noise. I'm guessing that then the CF should be let say 1000Hz, and on output -of the "Dual Phase Lock-In Amp" - I should get something, that will show a visible peak in FFT analyzer. (and no visible peak if the CF is far away from 1000.1Hz).

So. Martin - what do I missed or what is wrong in the schematic?

And - should there be any additional phase offset (of carrier wave) calibration done per step, to emphasize burried signal?

I think your idea of the lock-in amplifyer is wrong.

Its purpose is to provide a way of transmitting a signal through a noisy channel, by essentially using only a narrow strip of the spectrum so only a small portion of the noise gets in the way. It relies on the transmitter and the receiver using the same (known) frequency (or better still, the same oscillator instance).

The lock-in amplifier is not an analysis tool.
It cannot magically reveal hidden vibrations.

The Wikipedia article is not bad, please give it a try.

Why do you think there are spectral lines burried in the noise background anyway?

Martin, from what I see in several articles, stepped lock-in amplifiers are used for weak signal detection, for signals deeply buried in noise. To give some examples, page 166 here or indication on page 2 here

Until yesterday I did not uderstood how exactly this work (I still don't get all parts of it), but now I see, that this is not a file filter, this is rather an analyzer, that plots frequency graph by measuring the product of some sort of detection (burried signal vs reference signal when they are close to each other, and "modulator" frequency extracted from that - is around DC).

Tester, the second article you quote is about measurement of the dielectric response at a given excitation frequency. Is your setup similar to their figure 3? Then you could use the excitation signal directly instead of a separate sine generator in the lock-in amp. (For a dual-phase configuration you would still need the "cosine", i.e. a 90 degrees phase shifted copy.). It is actually simpler than my demo above.
Edit: Something like this.

From what I see in articles on practical measurements - the reference signal is stepped by a fraction of Hz, and per each step - measurement of outcoming voltage is taken as a "data point" and assigned to stepped frequency.

If I understand now this correctly, when the referfence signal approaches signal burried in noise - the (de)modulation part starts to produce relatively constant/stable DC output, which is averaged and taken as the measurement per point.

There are some vague adnotations on phase callibration, but I'm not sure what they mean - manually to what or automatic to what.

These articles were written several years ago, 5 to 15, by people who are rather old-school researchers. Nowadays we have different hardware capabilities (like cheap and sensitive, low noise instrumentation amps), and processing powers.

My design captures the signal from in-amp setup, at very high amplification (let say, that ecg signal will overdrive the line-in), and I can capture that as 96kHz and 24bit wave files. There is no problem with 50/60Hz harmonics, because this is differential amp, which means that such stuff is relatively well removed. There are some spikes artifact, but not too many and not too high, which means they are predictable and in bot - measurements and references.

Now, as for these lock-in amps versus what I do. If I understood correctly, the spectral noise levels may be high enough to hide fixed frequencies some decibels below the FFT registered and averaged floor, which means that on FFT analyzer I will get only a higher floor level, but no spikes. Indirect indication in articles says, that using lock-in amps - I should be able to get a FFT-like plot, with better exposed stable signal.

So I thought it's worth checking.

And I'm guessing, that from such FFT artificial plot - I can create time-domain based audio file as well, to hear the result (although the file will be not the filtered input).

Checking your schematic, thanks.

Works like a charm. When I approach with the ref frequency to noisy signal, averaged measurements go higher. I'm not sure if I wired the averaging part efficiently, but performance is comparable to averaged signal on FFT analyzer I use.

Although the performance is very similar to regular averaging in FFT analyzer, current test was done on uniform white noise. I guess, that the difference in performance will show up in irregular noise patterns, and perhaps on lower part of the spectra. Also, I'm guessing time matters here.

So the destination circuit will probe the same fraction of a file again and again (using mem, to avoid green timing), at selected frequency step and time window length (synced with ref cycle length?).

Any hints on what could be improved and how?

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p.s.:
Thank you Martin!

A quick realtime homodyne/phase/lock-in frequency analyzer.

It's CPU hungry, and it uses multiple points instead of frequency sweeping, but this way it can work live - at least if I understand correctly.

It measures signals within a limited frequency range, but in comparison to FFT analyzers - it can be more accurate (like 0.1Hz or better) - at least theoretically; I'm not sure if this would not require change within filter.

Not sure if/how this can be optimized or extended (within live preview domain).

From what I see, the advantage over FFT analyzers is - pretty good preview, and at carefully selected settings - few decibels better for detecting signal burried in uniform noise. Not tested with dynamic noises yet.