Reverse Bessel Low Pass Filtering

I did a current measurement on a system with an integrated Bessel low pass filter with cutoff frequency 3 kHz. I would like to undo the bessel filtering digitally using matlab. What is the best way to do so?

Answer 1

[Star Strider]

The filter is most likely an anti-aliasing filter, since Bessel filters implemented in hardware have a maximally flat phase characteristic (so they do not introduce any phase distortion in your sampled signal). Its purpose is to filter out all frequencies above the Nyquist frequency (apparently 3 kHz) in your ADC that was likely sampling at 6 kHz.

If that is the situation, you not only do not want to reverse its effect, you cannot reverse its effect because there are no frequencies above 3 kHz in your sampled signal.

[twig27]

Shouldn't it be possible to recover at least some of the previous bandwidth since the filter is not ideal? My approach was to calculate the transfer function coefficients (a,b), transform the the transfer function to the time domain and then divide the signal in the fourier domain by the transfer function. By inverse FFT I obtain the signal before filtering. I'd be glad for some comments on this approach.

[Star Strider]

The filter may not be ideal, but the frequency components it significantly attenuated (probably on the order of 200 dB or so if it was designed correctly) will only be present in your sampled signal as aliased signals. (A correctly-designed hardware Bessel anti-aliasing filter will reduce the amplitude of the rejected signals to the order of noise introduced by the sampling process.)

Due to the Nyquist-Shannon sampling theorem, it is not possible to recover unique frequencies greater than the Nyquist frequency (half the sampling frequency) in a sampled signal.

It would be a complete waste of your time and effort to even try to recover them. They’re not there!