# Sample-rate, filtering, digital-filtering and aliasing

I am strugling with a question that I hope someone can help me with.

I am recording single molecule events which I detect is picoampere square deflections.

I wish to use as gentle low-pass bessel filtering as possible.

The lowest filter settings my amplifier allow are 10 kHz and 100 kHz, and my digitizer have a maximal sampling rate of 500 kHz. I am afraid of corrupting my signal to much, but do not have the intuitive understanding of sampling and filtering to know if I am doing something wrong. Here is what I do:

I filter the signal with a 100 kHz bessel filter and digitize it with a 500 kHz sampling rate. I then wish to filter my digitized data with a 35 kHz digital filter.

Would this mess up my data? I hear people say that I am on safe ground if i sample at appropximatly 10x my filter settings, but I get to this 'safe zone' only when I do the post-sampling digital filtering. So I guess what I realy do not understand is if the order of filtering, sampling, filtering does something nasty to the data.

I hope I was able to communicate my question clear enough.

Thank you very much, Best regards, Michael

• Do you know what the bandwidth of your signal is, and what the order of the 100 kHz Bessel filter is? – Ill-Conditioned Matrix Jan 24 at 16:41
• It is a 4-pole low-pass bessel filter. The signal I am recording are square-signal up and down deflections lasting for up to several milliseconds and down to fast deflections below what I would be able to record (<microsecond scale). My goal is to detect as fast signals as possible. – Biologichael Jan 25 at 11:32

An ideal square pulse - which I assume is a model for your up-and-down deflections - would have an infinite bandwidth, but the bulk of the energy is within a bandwidth of $$1/T$$, where $$T$$ is the pulse duration. Roughly speaking, therefore, the 100 kHz Bessel filter will thus allow you to detect pulses of duration $$10 \mu s$$ and above. It will also limit the sharpness of the up-and-down transition.