How can I inverse a digital low pass filter?

Hello,

in Matlab it's easy to implement low pass filter. But how can I create another filter, which reverses the first filter, i.e. overall gain of 1 for all frequencies.

My idea is just to use the feedback function, i.e. put the low pass transfer function in the negative feedback. This means:

if true
num = 1;
den = [1/3000 1];
tf1 = tf(num,den);
bode(tf1)
tf_neg_feed = feedback(1,tf1);
bode(tf_neg_feed)
end

I would expect a frequency response of gain 1 up to a certain frequency, and a linear increase for higher frequencies. What I get however looks like this:

What is wrong with my approach? Thanks!

Answer 1

[Jayaram Theegala]

You can create the inverse of the original filter by exchanging the numerator and denominator of the filter transfer function, in other words:

 if true
    num = 1;
    den = [1/3000 1];
    tf1 = tf(num,den);
    bode(tf1);
    figure;
    tf_inverse = tf(den,num);
    bode(tf_inverse);
 end

However, the inverse filter designed by the above approach may become unstable at higher frequencies. To design a inverse filter that is stable at higher frequencies you can refer to the following stackoverflow post:

http://dsp.stackexchange.com/questions/24557/how-to-design-an-inverse-for-a-butterworth-low-pass-filter

Answer 2

[Thierry Zerozerosept]

Like already answered, many techniques are unstable.

What I do is making a pulse signal of the length of the filtered signal [1,0,0,0,0,0 ... ]

I pass it through the filter to have the impulse response of the filter.

I do a deconvolution of the signal with the impulse response of the filter like that: real(ifft(fft( signal )./fft( impulseresponse )))

This strongly amplifies the high frequency noise but it is not unstable.