[sdiy] [synth-diy] lock-in amplifiers

[rburnett at richieburnett.co.uk]

On 2014-01-26 16:33, Tom Wiltshire wrote:
> I think what you're describing might actually be fourier analysis
> looked at a different way....

That's exactly what it is Tom.  It's also often called "Complex 
Demodulation" in DSP textbooks.  To be specific the lock-in amplifier 
detection technique evaluates a single frequency bin of the Fourier 
analysis.  For this reason it is very computationally efficient if 
you're only interested in finding the magnitude and phase of a 
particular frequency component in a signal, and couldn't give a rats 
backside about the rest of the signal's spectrum.  (It's very similar to 
the Goertzel algorithm for evaluating single FFT bins.)

As Damian said it's good for pulling out weak radio transmissions that 
are burried well below the noise level.  It's commonly used for this 
type of task and for low-level measurement applications where it eschews 
DC offset and drift problems.

I'm not sure how applicable it would be to music synthesis though.  In 
order to use it as a resonator you need to implement a couple of 
double-balanced mixers which are hard to do in analogue electronics 
without bleed-through of the inputs.  Whilst you can implement perfect 
mixers digitally, you can also implement resonators very easily 
directly, so I don't see any immediate benefit.

The lock-in amplifier technique really just shifts the audio band down 
to DC.  It just implements a frequency translation, so in order to get a 
narrow and sharp-sided bandpass filter response you still need a high 
order filter.  It just makes it so that this filter needs to be two 
high-order lowpass filters near DC rather than a single high-order 
bandpass filter at whatever AC frequency you want it to appear at.

The only time where I have found this method beneficial is using it 
combined with multi-rate DSP techniques.  Damian, I recommend you take a 
look at a PDF called "Multirate Filter Design - An Introduction - 
Momentum Data Systems" if you want to see how this can be used in DSP 
land.

-Richie,