There is only an approximate answer for the relationship between
scale and frequency.

In wavelet analysis, the way to relate scale to frequency is to determine the
center frequency of the wavelet, *F*_{c}, and
use the following relationship:

where

*a* is a scale.

*F*_{c} is the center frequency
of the wavelet in Hz.

*F*_{a} is the pseudo-frequency
corresponding to the scale *a*, in Hz.

The idea is to associate with a given wavelet a purely periodic signal of
frequency *F*_{c}. The frequency maximizing the
Fourier transform of the wavelet modulus is
*F*_{c}. The `centfrq`

function computes the
center frequency for a specified wavelet. From the above relationship, it can be
seen that scale is inversely proportional to pseudo-frequency. For example, if the
scale increases, the wavelet becomes more spread out, resulting in a lower
pseudo-frequency.

Some examples of the correspondence between the center frequency and the wavelet
are shown in the following figure.

As you can see, the center frequency-based approximation (red) captures the
main wavelet oscillations (blue). The center frequency is a convenient and simple
characterization of the dominant frequency of the wavelet.