Convenient way to filter sinusoidal noise from decay data?

Hi,

I have decay data (approximated by exp decay) from my spectrometer which is corrupted by sinusoidal noise, presumably from the moving components in scans.

I'd like to filter out the frequency of the noise, leaving behind the decay only (image, all data before time zero is zero)

I've tried multiple ways with no success, FFT->frequency spectrum-> remove noise frequencies ->iFFT, or fitting data to exponential*sine->deconv(data,sine)/ perhaps something went wrong with those methods? for example my deconv command only returned one point from 2 even arrays.

Could someone suggest a method to remove sinusoidal noise from my decay curve?

Thanks

[Bruno Luong]

Just redo your experiment again. It is not clear how you can be sure the fitting could possibly give meaningful result back with such corrupted data.

[Gregory Manoukian]

The experiment is consistent, my signal is quite small, and the lower the signal the more clear this sinusoidal trend is. It is the same problem with all of the data for this sample set.

Is it possible to remove the noise? If the filtered data is unusable, I will show that, I just need to try.

Answer 1

[Image Analyst]

Why not just leave the data as they are and fit an exponential decay to the whole thing? See attached demo.

[Gregory Manoukian]

This is an option we are considering, but we wanted to see if we could remove the noise. Technically, the signal from the spectrometer is more complicated than a simple multi-exponential, but if we can remove the noise, that would simplify our analysis.

Is it possible?

[Image Analyst]

I don't know how you are collecting your signal with periodic noise on it, but maybe you should consider a lock-in amplifier. https://en.wikipedia.org/wiki/Lock-in_amplifier

If you take the FFT, you might see a spike right at the frequency of the noise that is being injected into your time domain signal. Then set those frequencies to zero and inverse transform. A 2-D image version is in the attached demo.

[Gregory Manoukian]

This data is taken through a SR580 lock-in amplifier. the noise presumably comes from the moving components (a screw motor pushing a mirror), and so for the lock-in, looks like more or less signal coming through at each full rotation of the motor.

When I follow this approach, my issue comes in reconstituing the complex array which to ifft. I had identified the peaks and set them to zero in both, but was unable to ifft the data.

Answer 2

[Star Strider]

If you want to use a frequency-selective filter, first do a fft of the data to determine the frequency components, then use the lowpass filter (with the 'ImpulseResponse','iir' name-value pair for best results) to eliminate the high-frequency (sinusoidal) noise. (The lowpass filter function requires the Signal Processing Toolbox.)