# FFT Signal Processing to Clean Up Distortion/Noise

• singedang2
In summary, the problem with trying to remove noise from a signal is that it may also remove the original signal.
singedang2
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)

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?

I haven't studied this in any good detail, so my answer is not going to be the best. But I think your solution is correct, and that the problem with this is a fundamental problem with removing noise. I have been searching my files because I remember reading all about this, but I can't find what I read anywhere.

I think the answer is in choosing the right method of suppressing low frequencies, for example, multiplying the Fourier transform by some function which is inversely proportional to frequency.

I wish I had this book though! By the way, is * a convolution in your notation or multiplication?

singedang2 said:
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)

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?

I have the same question as MikeyW. You say in your post that g(t) is added, but are using * as the combination symbol. If the g(t) is just added, and is lower frequency, they it seems that running h(t) through a DSP highpass filter would do what you want?

sorry for the confusion. it's a multiplication. by 'add' i meant the two signals got mixed altogether.

singedang2 said:
sorry for the confusion. it's a multiplication. by 'add' i meant the two signals got mixed altogether.

Why are they multiplied? Where is the non-linearity? Or is this just a coursework exercise? What is the context please?

i don't know about the non-linearity. this is for a course, and we've only learned fft and some Fourier analysis.

the questions is we're suppose to receive am radio singal, but due to atmospheric/weather condition, loudness of the signal changes.

so the original signal we wanted to receive was v(t), but instead we get v(t)*g(t),
and g(t) has relatively low frequency compared to v(t).

Can you double check that it's not a convolution?

If you multiply two functions v(t)g(t) would be my notation, to me v(t)*g(t) suggests convolution, especially in signal processing... is the question in original form specific about what the symbol "*" means?

i've checked and it's multiplication, NOT CONVOLUTION. so v(t)g(t), instead of v(t)*g(t).
sorry for the confusion.

i was able to solve this problem.

the key was to take log of the function.

then it becomes logv(t) + log(g(t))
then we do the usual fft then do the filtering, then do inverse fft to get back the original signal.

singedang2 said:
i was able to solve this problem.

the key was to take log of the function.

then it becomes logv(t) + log(g(t))
then we do the usual fft then do the filtering, then do inverse fft to get back the original signal.
Well you would not have the original signal, you would have log( original signal ).

BTW, as pointed out above the expression v(t) times g(t) is not an addition of noise, it is a modulation, a non-linear operation for any non-trivial g(t). No linear filter operation will recover the v(t). You'd need another non-linear operation to recover v(t), such as a demodulation.

## 1. What is FFT signal processing?

FFT (Fast Fourier Transform) signal processing is a mathematical technique used to analyze signals in the time domain and convert them into their frequency domain representation. It decomposes a signal into its individual frequency components, allowing for the identification and removal of any unwanted distortions or noise.

## 2. How does FFT signal processing clean up distortion and noise?

FFT signal processing works by taking a time-domain signal and converting it into a frequency-domain representation. This allows for the identification of any unwanted frequency components, such as noise and distortion. Once identified, these components can be eliminated or filtered out, leaving behind a cleaner signal.

## 3. What types of signals can FFT signal processing clean up?

FFT signal processing can clean up a wide range of signals, including audio, video, and digital signals. It is commonly used in audio processing applications, such as noise reduction and equalization, and also in image processing, where it can remove noise from digital images.

## 4. Is FFT signal processing a real-time process?

FFT signal processing can be performed in real-time, depending on the complexity of the signal and the processing power of the device. For simple signals, such as low-frequency audio, real-time processing is achievable. However, for more complex signals, such as high-resolution images or high-frequency audio, real-time processing may not be feasible.

## 5. Are there any limitations to FFT signal processing?

While FFT signal processing is a powerful tool for cleaning up distortion and noise, it does have some limitations. It is most effective for signals with a clear frequency-domain representation, so highly complex or noisy signals may not be fully cleaned up. Additionally, FFT signal processing may introduce artifacts or distortion in the signal if not used carefully.

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