A signal from a measurement is filtered with an analog 2nd order low pass filter.
The original signal which consists of the sum of two exponentials (one positive amplitude the other one negative amplitude) slightly changes its shape.
Since the information of important parameters can only be extracted from the unfiltered signal, I would like to undo the filtering digitally. I am aware that it is not possible to obtain the full original bandwidth, but could I theoretically increase the bandwidth?
The filter's transfer function numerator is 1 while the denominator is a 2nd order polynomial.
Added:
My goal is to determine the values of an RC low pass (life science application).
A voltage pulse is applied to the low pass filter.
The arising current (which is a mono-exponential and contains the information of the R,C values in its time constant) is converted to a voltage (with an I-V-converter).
The signal is then low-pass-filtered with a 2nd order Bessel filter.
The sampling rate of the system is 20 kHz while the cutoff frequency of the filter is 3 kHz.
Fitting algorithms are used to cancel noise in the output.
My goal is to obtain the mono-exponential for any output signal.
Added:
This is the actual circuit I wish to analyze.
I would like to obtain the current input at the ampere-meter for any output voltage. Of course in this simulation there is no noise. Before I apply the method to the real system I would like to make it work for the simulation.
I've been using the MATLAB system identification toolbox in order to estimate the transfer function. By applying the inverse transfer function to the output I should be able to recover the original current input.
Best Answer
In the noiseless case, any signal attenuation can be reversed, by implementing the inverse filter.
In the noisy (that is real world) case, you will be limited by signal to noise ratio. If your small signal has been heavily attenuated, then your recovered signal will be noisier than if it had had neither filtering operation.