WAVELETS AND NOISE CANCELLATION IN MOBILE COMMUNICATION

                   Niclas Svensson

         Matematisk Statistik, Lunds Universitet

Mobile communication is often disturbed by various kinds
of noise. This noise arises in many different environments,
for example humming from the road or the car engine. This
noise may be very annoying for the receiver and even make
communication impossible. Furthermore, speech coders are
dependent on a ``pure'' speech signal and performance may
be very poor if the speech is contaminated with noise. The
need for efficient noise reduction algorithms is therefore
apparent.  

In this thesis the discrete wavelet transform and its
relatives, the wavelet packet and the cosine packet
transforms, are applied to the noise reduction problem.
Mobile communication as a real time application imposes
constraints on available computing power and limitation in
data length. The limitations in data lengths introduces
edge effects and this problem have been solved by using
overlapping triangular windows. The wavelet packet
transform requires O(nlog(n) computations which make it
computationally feasible. 

The transforms have been applied, together with standard
denoising algorithms, on speech signals affected by
Gaussian white noise and proved useful. When the
disturbance was coloured noise two approaches were tried 
  1. linear modeling of the coloured noise with stable
     ARMA-models, 
  2. adopting thresholds according to an estimated
     wavelet-packet spectrum.
The first approach produced discouraging results, ruling
it out as a feasible solution, whereas the second indicated
performance comparable to common methods, i.e. spectral
subtraction.