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There is a recording which contains very noisy voice. (voice with a low Signal-to-Noise ratio).

It is a female voice of a stationary speaker (right in front of the microphone) and there are many other recordings of the same speaker with much better quality.

What can be done to denoise the audio?

From the other recordings, it might be possible to extract statistical values that allow some model to filter the speaker's voice.

Existing questions only address snoring, have non-random noise, want to identify a specific artifact or a moving speaker. The question is-it-possible-to-filter-out-a-persons-voice-out-of-100-of-other-voices is similar, but the answer there lacks details and is more about distinguishing, less about extraction.

Some of the tapes are direct copies, some are copies of copies, which have also been recorded using a lower speed setting (4.75 cm/s). This affected the quality prior to digitalization.

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    $\begingroup$ The distorted recording sounds more like the speaker has a large obstacle between themselves and the microphone. The noise is relatively low level. I'm wondering if it's more of a recording problem (e.g. bad tape bias?). $\endgroup$
    – Peter K. ♦
    Commented Sep 1, 2015 at 11:46
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    $\begingroup$ Well, it might mean you are looking for a non-stochastic solution. A simpler "de-biassing" filter might do (though this might exacerbate the noise). You might want to compare the spectrum of the noisy speech with the spectrum of the non-noisy speech and see if you can infer what the "de-biassing" filter's frequency response might look like. $\endgroup$
    – Peter K. ♦
    Commented Sep 1, 2015 at 15:51
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    $\begingroup$ For clarity: you still might want to do some stochastic filtering to remove the random noise. $\endgroup$
    – Peter K. ♦
    Commented Sep 1, 2015 at 15:51
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    $\begingroup$ By "bias" I mean magnetic / electromagnetic bias in the recording medium. The way that would affect the recording is to filter it. It sounds like it's a low-pass filter operation.... so you may need to invert that (make a high-pass filter?). $\endgroup$
    – Peter K. ♦
    Commented Sep 1, 2015 at 16:03
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    $\begingroup$ In general, a good method of removing noise would be useful to a lot of people. The examples in this question aren't good examples of that use case, though. The recording that most needs help isn't just noisy, it has actually had a lot of its content filtered out before being digitized. I also strongly suspect it was originally sampled at only 8 bits, so there's not much chance of rooting some remnant of the signal out of the noise floor. $\endgroup$
    – JRE
    Commented Sep 2, 2015 at 12:52

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I am afraid there's not much you can do. The voice part seems to have gone through the equivalent of a low pass filter with a cut off of around 1000 Hz. Basically, all of the speech components above 1000Hz are gone.

The filtering action may not have been an intentional filter, but may have been due to the improper biasing of the tape during recording. If it is an old tape, it may simply have deteriorated over time. Also, the playback head may have needed degaussing.

Running it through a high pass flattens the frequency response, but doing so pushes the level down so far it drowns the signal in the noise - no help there.

The best result I got was from using a very steep low pass with a cutoff of 1000Hz together with a very steep high pass with a cutoff of 160 Hz. That gets rid of the noise by only passsing what is left of the actual speech, but obviously it can't recover what was lost.

Your real problem is not the noise, it is the lost frequency range.

This is the spectrum of the bad recording: enter image description here

This is the spectrum of the good recording: enter image description here

As you can see, there's a lot of stuff missing from the bad recording. So, it isn't simply a problem of removing noise. The problem is that there's stuff that's just GONE.

Look at the range from 1000Hz to 7000Hz. There's lots of stuff there in the good recording, but in the bad one it is just a flat spectrum a good 30dB below the voice peaks aroudn 400Hz.

Some of what's missing might be buried in the noise, but recovering it would cause artifacts that are worse than the noise and muffled sound.

Looking at just the noise, it doesn't seem like there would be much to recover out of it. It looks just like the portions with speech (except for between 160Hz to 1000Hz,) so anything that is in there is going to be buried really deep. enter image description here

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    $\begingroup$ That would be a lot of manual work. I've ofthen thought that it might be possible to use voice sythesis software to analyse a large body of recordings from one person and then use that to synthesize recordings of the person speaking new texts. That'd be a lot of work too, though. Depending on how many bad recordings you've got, it might be cheaper or easier to find a voice actor (synchronsprecher) and have them re-read the texts. $\endgroup$
    – JRE
    Commented Sep 4, 2015 at 8:21
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    $\begingroup$ Just had a really silly idea. I'll see if I can find time to try it out and post back later, maybe this week end. $\endgroup$
    – JRE
    Commented Sep 4, 2015 at 8:54
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    $\begingroup$ Silly ideas are often the most fun. :-) $\endgroup$
    – Peter K. ♦
    Commented Sep 4, 2015 at 12:07
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    $\begingroup$ Maybe bandwidth extension techniques can help to recover the part above 1kHz. $\endgroup$
    – Brian
    Commented Sep 4, 2015 at 12:43
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    $\begingroup$ Silly idea didn't pan out. I used a cleaned up copy of the good recording to create an FIR filter that passes components of the woman's voice. Then pushed white noise through the filter and modulated the output with the envelop of the bad recoding (after first filtering out the noise.) The spectrum looked good, but it just sounded like a bunch of noise bursts. Oh, well. It was fun to try. $\endgroup$
    – JRE
    Commented Sep 6, 2015 at 12:51
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The noise sounds very stationary, so I guess spectral subtraction should work well. Note however that most implementations usually have quite a few parameters to tweak, and spectral subtraction can sound either very good or completely useless depending on whether the parameters are chosen well for the given problem. If you search for Matlab implementations you find several ones, among which is this one which you could try to get some idea of what spectral subtraction can do.

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  • $\begingroup$ First attempts at using spectral subtraction (via the "Remove Noise" function of audacity) did not work well, leaving artifacts. Maybe I did not tweak the parameters enough. $\endgroup$
    – serv-inc
    Commented Sep 1, 2015 at 15:48
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On file: noisy_00_41_718_to_01_04_287.wav, I tried spectral subtraction and then some high-pass filtering to taste. You can download the snippet here.

There are definite artifacts, but I fear the source audio is too degraded. Noise aside, the speaker is very muffled and it is hard (esp. not speaking Schwiizertüütsch) to make out anything clearly. High pass filtering, brought out some detail, but again, not enough to be useful.

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  • $\begingroup$ Thank you for confirming that just doing a spectral subtraction creates a great many artifacts. $\endgroup$
    – serv-inc
    Commented Sep 3, 2015 at 12:10
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Thank you very much, to all who provided solutions.

Summary

This is a summary of what has been proposed, with an example of what it does to the noisy soundfile when combined. If you like it, please do upvote the originals.

  1. (Kudos to @PeterK) The recording has a DC bias. You can see that most of the waves center below the 0:

    DC bias

    This can for example be removed via Audacity's "Normalize..." with default settings.

  2. (Kudos to @MattL) When this is normalised, spectral subtraction can be used. I got the same results as @ruohoruotsi when I tried it at first, leaving me to abandon that, but if you tweak (as suggested) for example the Sensitivity setting to 5dB, you get very little to no artifacts. The waveform looks different: enter image description here

  3. (Great Kudos to @JRE) This can be further filtered with a high pass as proposed to get some more of the noise out. Yet, as @JRE also said, there is very little information in the signal above 1000Hz. Thus, for example the section between 12 and 14 seconds remains very hard to hear.

You can listen to the result of all three approaches combined.

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