# Banding in the derivative of a lock-in amplifier signal

I'm analysing several measurements taken with a SR830 lockin amplifier.

These measurements look similar to this one. Since I'm interrested in the derivative of the signal I took the numerical difference. What I found was this. One can clearly see two bands in the signal. I'm no expert, but I'm guessing it might be related to digitalisation in the lock-in amplifier.

So this leads me to two questions:

• What could be the origin of these two bands and how to avoid them in the first place?
• How should I correct the data already taken?
• I don't know much about lock-in amps, but your plot looks like the differential non-linearity plot that you might see for an analog-to-digital converter. Since it is hardware-related, maybe try moving this over to electronics.stackexchange.com. – Jason R Apr 7 '13 at 1:09
• That does look like the effects of quantization error + noise, so we'll just call is quantization noise. Can you create a difference of two sliding window averages? The idea is, to some degree, to average out the quantization noise. You'll have to get the scaling right. The derivative will be slightly delayed, but if you can tolerate the delay, you should get a smoother representation of the derivative – user2718 Apr 7 '13 at 1:10
• One approach to correct the data might be to create a lookup table that describes the nonlinear input-output characteristic. Just make the table large enough to capture the region where there is nonlinear slope, then linearly interpolate between table elements as needed. – Jason R Apr 7 '13 at 1:11

## 1 Answer

It might not be so straight forward to simply take the derivative of the output from a lock-in amplifier. If you think about how a lock-in works, the final stage of a lock-in amplifier is the low-pass filter. So if you then simply take the sample-to-sample derivative, you will simply be undoing the work of the low-pass filter and getting noise. Instead, you need to decimate your time domain signal, and then take the derivative.