Digital Signal Processing Reference
In-Depth Information
This points to the orthogonal structure of the so-called HAAR wavelets. The HAAR func-
tions appear to be only of academic interest on account of their simplicity.
There are no rectangular patterns in reality, are there? Wrong! What wavelet would you
use to reconstruct a pale, scratched and blurred image of the brick wall of a house?
We can summarize as follows:
The wavelet transformation appears as the most universal
process for filtering patterns of the most various kinds from a
background of data.
The Continuous Wavelet Transformation CWT provides a very
detailed and informative picture but it contains a high level of
redundancy. There are many applications in which this may be
desirable and tolerable.
The Discrete Wavelet Transformation DWT is a process which
makes it possible to avoid this redundancy and this without any
loss of information.
Both processes attempt to find similarity between a pattern and a
signal or a set of data on different scales via a cross correlation -
a correlation between two different signals.
Only by means of a suitable basic pattern can a signal or set of
data be efficiently transformed. This means finding as few as
possible pronounced values diverging from zero in the wavelet
transformation. This is the prerequisite for the efficient
compression or the elimination of noise from the source signal.
The so-called wavelet compression comprises the DWT and subsequent compression by
means a suitable coding process as has already been explained in part in this chapter. The
DWT therefore does not compress but by the transformation creates a favourable basis for
compression.
Exploiting psycho-acoustic effects (MPEG)
The frequency domain so far does not seem to play a part in the encoding or compressing
of audio signals. However, hearing is entirely in the frequency domain, that is we hear
only sinusoidal signals of different frequencies. A really intelligent method of compres-
sion ought to include the frequency domain.
Audio-signals such as language and music do not contain redundant features, unlike text
where the letter "e" occurs much more freequently than "y". As a result it is difficult to
allocate a shorter code to a sound or tone.
