# Smearing an audio recording using Fourier transform

• dwarp
In summary, the goal is to smear an audio recording where the frequency content audibly changes, into an audio recording where it does not. The process involves computing an STFT and then combining the resulting windows into an average.
dwarp
Hi!

I'd like to smear an audio recording, where the frequency content audibly changes, into an audio recording where it does not. Here's a recording of a sampled piano playing a melody, which will serve as an example:

https://dl.dropboxusercontent.com/u/9355745/oldmcdonald.wav

The frequency content changes, both during each note played and because different notes are being played. I'd like to use the Fourier transform to somehow produce something like this:

https://dl.dropboxusercontent.com/u/9355745/oldmcdonaldsmear.wav

This was created by repeatedly playing the original recording into a reverb with a very high decay. There's still some "shimmering" in the recording, so the result isn't completely smeared out.

One way I can think of doing this is by computing an STFT and then combining the resulting windows into an average, which is then used as input to the reverse Fourier transform to produce a new audio recording (and I'm guessing this is what the reverb is actually doing). Is there a simpler, perhaps more elegant way of doing this?

The reason I'm asking is that for the longest time, I thought the result of the DFT *was* the average frequency content of the input. It seems this is only true if the frequency content in the input signal does not change over time - if I had been able to smear the signal completely, the DFT of that smeared signal *would* have been the average frequency content of the smeared signal. Imagine, for instance, if I'd run 4 seconds of a square wave at 80 Hz - the DFT would give me the same thing an EQ analyzer would.

But then, since the un-smeared signal can be accurately represented by a sum of sine and cosine waves (that is, the result of the DFT), its frequency content does not, in fact, change over time. Obviously, though, if you listen to the unsmeared signal, its frequency content DOES change over time, or there wouldn't be a melody! I find all this incredibly confusing.

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What is the purpose for such a process? Could you for instance, under perfect conditions, go backwards and end up with the same notes in the right sequence?

The purpose is getting an idea of the frequency content in an audio recording - whether there's a lot of bass, a lot of treble, etc. I also like the idea of getting the "average sound" of a longer recording just to hear what it sounds like. I don't expect to be able, and am not interested in being able, to reproduce the original signal from the result, as I would be able to with a straight up DFT, no.

Also, since I believed the DFT contained the average frequency content, I did try ifft(abs(fft(signal), and I actually got kind of close to what I was trying to achieve - the result is kind of smeared - but it's also still "pulsating" (the volume is modulating) at the same frequency that the notes were played in the original recording (4 Hz):

https://dl.dropboxusercontent.com/u/9355745/newmcdonald.wav

Last edited by a moderator:

## 1. How does Fourier transform work in smearing an audio recording?

Fourier transform is a mathematical tool that breaks down a complex signal, such as an audio recording, into simple sine waves of different frequencies. In the context of smearing an audio recording, Fourier transform is used to analyze the frequency components of the signal and manipulate them to create a smearing effect.

## 2. What is the purpose of smearing an audio recording using Fourier transform?

The purpose of smearing an audio recording using Fourier transform is to create a distorted or blurred effect that can enhance the sound quality or create a specific artistic effect. It can also be used to remove unwanted noise or to modify the time duration of the audio signal.

## 3. Can Fourier transform be used to reverse the smearing effect on an audio recording?

Yes, Fourier transform can be used to reverse the smearing effect on an audio recording by applying an inverse Fourier transform. This will reconstruct the original signal by removing the smearing effect and restoring the original frequencies and amplitudes.

## 4. Is smearing an audio recording using Fourier transform a reversible process?

No, smearing an audio recording using Fourier transform is not a reversible process. The original signal is permanently altered, and it is not possible to completely reverse the smearing effect using the inverse Fourier transform. However, the effect can be partially reversed by applying a deconvolution process.

## 5. Are there any limitations or drawbacks of smearing an audio recording using Fourier transform?

Yes, there are some limitations and drawbacks of smearing an audio recording using Fourier transform. The smearing effect can introduce unwanted artifacts and distortions in the audio signal. It also requires a certain level of expertise and understanding of signal processing techniques to achieve the desired effect without compromising the overall quality of the audio recording.

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