COMPOUND WAVELETS: WAVELETS FOR SPEECH RECOGNITION

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INTRODUCTION
The wavelet transform has become a popular tool for
image and speech processing[lO, 111. It has been used
successfully in speech processing for analysis [l], pitch
detection [7] and speech recognition in previous work


The wavelet transform (WT) has the best features of narrow
band and wide band analysis within one transform.
The WT of a speech signal produces fine time resolution
at high frequencies and fine frequency resolution at low
frequencies.

WAVELET THEORY
Wavelet theory is based on generating a set of filters by dilation
and translation of a generating wavelet. All of the waveletsare
scaledversions of the “motherwavelet”. This requires
that only one filter is designed and the others will follow the
scaling rules in both the time and frequency domain.


WAVELET PARAMETERISATION
This work uses a generating wavelet based on the Hanning
window[l]. The Hanning window is modulated to 4000Hz
and thus becomes the highest frequency wavelet. This
wavelet is used as the mother wavelet.

COMPOUNDING WAVELETS
The motivation for compounding wavelets is to increase
the bandwidth of a wavelet without significantly affecting
the time resolution. The operation is described by the following
formula showing the compounding of two wavelets: