Cleaning Up Signal Distortion Using FFT: Devising an Effective Method

[singedang2]

Homework Statement

hello!

i'm given a signal h(t) = v(t)*g(t)
where g(t) is a distortion/noise that got added
and has a very low frequency compared to v(t)

i need to devise a method to clean up g(t)

The Attempt at a Solution

i'm thinking of to do the fft on the signal h(t),
and remove the lower frequencies and do the inverse fft,
but this might not just remove g(t), but it may as well remove v(t)

any hints?

 

[bhupala]

This is called inverse problem and its an ill-posed problem. There are many methods especially Wiener filtering method to extract v(t).

 

[Redbelly98]

The Attempt at a Solution

i'm thinking of to do the fft on the signal h(t),
and remove the lower frequencies and do the inverse fft,
but this might not just remove g(t), but it may as well remove v(t)

any hints?

You would have to have some idea of the lowest frequencies present in v(t). Only then can you choose a suitable high-pass filter.

Have you taken a look at the FFT of h(t) yet?

 

[singedang2]

You would have to have some idea of the lowest frequencies present in v(t). Only then can you choose a suitable high-pass filter.

Have you taken a look at the FFT of h(t) yet?

i'm not actually given a function h(t).
which I mean we're not doing an actual experiment, where I get h(t) and to try to recover v(t).

i'm learning fft and Fourier analysis in school, and this is just one of the questions that is application of fft.

problem is, my idea of doing fft to h(t) and remove lower frequencies and do ifft might just remove both v(t) and d(t)

I need to somehow process h(t), so that, when I fft it, it separates well, and able to remove lower frequencies that are v(t) only.

btw * is a multiplication from the h(t) I've written. it looks kinda similar to convolution operator and makes it confusing

 

[Redbelly98]

In practice, you would look at the spectrum and make a judgement about where the low frequency limit of v(t) is. Then you could choose a suitable cutoff frequency for the filter.