#### Discrete Wavelet Transform

The*discrete wavelet transform*is a discrete-time, discrete-frequency counterpart of the continuous wavelet transform of the previous section:

where and range over the integers, and is the mother wavelet, interpreted here as a (continuous) filter impulse response.

The inverse transform is, as always, the signal expansion in terms of the orthonormal basis set:

(12.120) |

We can show that discrete wavelet transforms are constant-Q by defining the center frequency of the th basis signal as the geometric mean of its bandlimits and ,

*i.e.*,

(12.121) |

Then

(12.122) |

which does not depend on .

**Next Section:**

Discrete Wavelet Filterbank

**Previous Section:**

Continuous Wavelet Transform