Restoration of clipped audio
Restoration of clipped (audio) signals is a challenging
and very often ill-posed problem. Clipping refers to the truncation
of the aplitude of a signal above and/or below a certain treshold
(clipping level). Clipping can appear in the analog-to-digital
conversion of a signal, during the recording of music with a
suboptimal microphone or more generally, during data transmission.
See the figure below for an example of a clipped audio
The problem of restoring the missing samples in a clipped signal is
usually more challenging than the irregular sampling problem.
The difficulty arises from following facts:
- Missing samples are consecutive, resulting in possibly large missing
- Missing samples and sampling energy of the signal in clipped areas
are obviously intrinsically connected.
- Typical regularization approaches that minimize the norm/seminorm
of the signal fail (due to the reason above)
- Fast algorithms are required if on-line processing is necessary
The algorithm I have developed for this purpose uses local and
global informatiom and combines a statistical with a deterministic
Here is an example for the restoration of a clipped audio signal:
You can download an example (I agree, it's not really a
great song) in WAV-format here:
Unclipped signal (8 seconds, thanks to Earl
Vickers for recording it)
The original signal of the example above, the clipped version, and
the restoration are displayed in the figure below. The restoration
is not yet perfect (but better than existing patented algorithms).
Click on the image to see a larger version.
The next figure shows the semgment of the signal above, which
suffered most from clipping first together with the clipped signal (above)
and then together with its restoration (below). Click on the image to see
it in a better resolution.