How Audacity Noise Reduction Works

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Gale 19Dec14: I think because of the slightly unfortunate rename of the effect, this page needs to state it is nothing to do with http://en.wikipedia.org/wiki/Dolby_noise-reduction_system, or should be moved to How Audacity Noise Reduction Works.
  • Peter 08Mar15: I'm not convinced that Dolby own the term "noise reduction" any more than National Semiconductor do. I suspect that thy respectively own "Dolby noise reduction" and "Dynamic Noise Reduction" an extension of Dolby techniques for telephony. "Noise reduction" is used in pretty common parlance - indeed if you look at the Wikipedia page on Noise Reduction it even states "Most general purpose voice editing software will have one or more noise reduction functions (Audacity, WavePad, etc.)".

    Having said all that however, I think the page title does read better as How Audacity Noise Reduction Works so I will change it to that.

About the Noise Reduction algorithm

The noise reduction algorithm uses Fourier analysis : it finds the spectrum of pure tones that make up the background noise in the quiet sound segment that you selected - that's called the "frequency spectrum" of the sound. That forms a fingerprint of the static background noise in your sound file. When you reduce noise from the sound as a whole, the algorithm finds the frequency spectrum of each short segment of sound. Any pure tones that aren't sufficiently louder than their average levels in the fingerprint are reduced in volume. That way, (say) a guitar note or an overtone of the singer's voice are preserved, but hiss, hum, and other steady noises can be minimized. The general technique is called spectral noise gating .

The first pass of noise reduction is done over just noise. For each windowed sample of the sound, we take a Fast Fourier Transform (FFT) using a Hann window and then statistics, including the mean power, are tabulated for each frequency band.

During the noise reduction phase, those statistics and the Sensitivity setting determine a threshold for each frequency band. We start by setting a gain control for each frequency band such that if the sound has exceeded the threshold, the gain is set to 0 dB, otherwise the gain is set lower to the Noise Reduction slider setting (e.g. -18 dB), to suppress the noise.

Then time-smoothing is applied (so that the gain for each frequency band moves slowly), followed by frequency-smoothing (so that a single frequency is never suppressed or boosted in isolation). Prior to 2.1.0 release, the user could specify a single value that determined both "attack" and "decay" time-smoothing. The 2.1.0 code has provision for separate "attack" and "release" sliders but these are currently hidden, with hardcoded time-smoothing applied instead. Lookahead is employed in time-smoothing, so that if this effect was redesigned for real-time there would be some delay.

The gain controls are then applied to the complex FFT of the signal and the inverse FFT applied, followed by another Hann window. The output signal is then pieced together using overlap/add of one-fourth the window size.

  • Paul 24Jan15: Time smoothing alludes to the attack and release. It was lately decided to hide those controls at least for 2.1.0, but there is still some nonzero time smoothing hardcoded, so this is still worth mention. The prior description said frequency smoothing was applied before time smoothing, which was incorrect both for 2.0.6 and for the rewritten effect.
    • Gale 25Jan15: I included the mention in the text above. Please correct it if it is wrong.
    • Paul 27Jan15: It's good. I never agreed with hiding attack and release (release may be the more useful) but I got overruled. Longer release might give better results when the sound has reverb or percussive notes with decaying tails.
    • Gale 27Jan15: People do try to use Noise Reduction as a poor-man's deverb. Is the current hardcoded attack and release still 20 ms and 100 ms respectively, and do you agree with the hardcoded release time?
    • Paul 27Jan15: Yes, those values, which Bill recommended as defaults in case we exposed the controls.
    • Paul 28Jan15: One might want increased Release precisely because the deverbing effect is not wanted.

Frequency Bands

In Audacity we use an FFT size of 2048, which results in 1025 frequency bands.

Artifacts

You may get tinkly artifacts when individual pure tones are near the threshold to be preserved - they are small pieces of the background soundscape that survived the thresholding, perhaps because the background noise is slightly different from the fingerprint or because the main sound has overtones that are imperceptible but that boost them slightly over the threshold. They may also be seen as spots in spectrogram views, including some at frequencies too high to be audible.

Any Fourier-based noise reduction algorithm will have some artifacts like the "tinkle-bells". They are a symptom of the problem of discrimination - deciding whether a particular analog signal is above or below a decision threshold - that is central to the fields of digital data processing and information theory. In general the tinkle-bell artifacts are quieter than the original noise. The real question is whether they are more noticeable than the original noise. (For example, noise-gating the Beatles' Sun King track off the Abbey Road album is a bad idea, because the soft brushed cymbal sounds merge smoothly into the tape hiss on the original master recording, so tinkle bells and a related problem -- fluttering -- are prominent in noise-gated versions of that track.)

The Sensitivity slider biases the thresholds of all frequency bands. Each unit increase of Sensitivity increases the average time between artifacts approximately tenfold when the profile and the treated sound have a typical white or red noise spectrum. Higher settings will thus reduce the number of artifacts, but at the risk of introducing the opposite discrimination error, in which parts of the desired signal are misclassified as noise and so reduced. The purpose of the Residue radio button is to pass the difference between the original sound and what would result from choosing Reduce. When the Sensitivity is excessive, "tinkle-bells" will be heard in Residue rather than in Reduce, and where the original had louder sounds, rather than in the pauses between sounds. By previewing the results of Residue before applying the effect, the best Sensitivity balance can be found.

  • Paul 24Jan15: I almost want this paragraph in the Manual rather than here. Just remove the talk of "discrimination."
    • Gale 25Jan15: I assume you mean the paragraph above this ednote, Paul? The final paragraph below this note would need a lot more explanation if it was in the Manual. If you mean above, I'll see if I can work it in to the Manual if no-one else does - that page looks somewhat unfinished (still two P1's).

      Can "Residue" still be roughly described as per the Development Manual's current description "the sound that is removed"? "Residue" probably means less to most users than the old (not working properly) "Isolate" did, so I guess few will use it. Should it have been called "Invert" or "Difference"?

    • Paul 27Jan15: I mean the previous paragraph. "Residue" was Steve's preferred term. One might want the difference of wet and dry signals (Residue), or to pass the noisy part of the signal full strength, ignoring the reduction, attack/release, and frequency smoothing (Isolate). Old Noise Removal's buggy Isolate didn't really do either. The alpha version of Noise Reduction made both available. I think "sound that is removed" [be careful not to say "noise"] describes not Isolate but Residue, well enough. Finally the suggestion for mixing below isn't from me. I never tried that. What I have written is still an incremental update of an original that I think was Dominic's.
    • Gale 27Jan15: Thanks, Paul. What was your preferred term for "Residue"?
  • Peter 27Jan15: Rather than copy this rather technical detail to the Manual, I placed links on the Manual page to the two main sections of this page, this also helps avoid duplication which is something we always strive to do in the documentation

The Frequency Smoothing slider does not affect the number of artifacts, but it can make each less evident by spreading the effects of discrimination errors among nearby frequency bands.

You can reduce the effect of tinkly-bells by noise gating sounds that are well separated (either in volume or frequency spectrum) from the background noise, or by mixing a small amount of the original noisy track back into the noise gated sound. Then the muted background noise tends to mask the tinkle bells. That technique works well for (e.g.) noisy microcassette recordings, where the noise floor might only be 20 dB below the loudest sounds on the tape. You can get about 10dB of noise reduction that way, without excessive tinkly artifacts.

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