Wavelet filterbank

To represent the wavelet transform as Eq. (), we will redesign the gammatone filter by the Hilbert transform. As a results, basic wavelet becomes

$$\psi(t)=At^{N-1}e^{j2\pi f_0 t-2\pi b_f t},$$ (15)

wavelet filterbank is designed with a center frequency f₀ of 600 Hz, a bandpassed region from 60 Hz to 6000 Hz, and a number of filters K of 128. For convenience, we have used the integral (continuous) wavelet transform; however, when the wavelet filterbank is implemented on a computer, we will use a discrete wavelet transform with the following conditions[18]: sampling frequency f_s=20 kHz, the scale parameter $a=\alpha^p, -\frac{K}{2} \leq p \leq \frac{K}{2},\alpha=10^{2/K}$, and the shift parameter b=q/f_s, where $p,q\in {\bf {Z}}$. Frequency characteristics of the wavelet filterbank are shown in Fig. . Amplitude characteristics of this filterbank overlap completely with the bandpassed region as shown in Fig. while ERB (Equivalent Rectangular Bandwidth) of the filters are do not [18].