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Scale to frequency

`F = scal2frq(A,'`

* wname*',DELTA)

scal2frq(A,'wname')

scal2frq(A,'

`wname`

`F = scal2frq(A,'`

returns
the pseudo-frequencies corresponding to the scales given by * wname*',DELTA)

`A`

and
the wavelet function `'wname'`

(see `wavefun`

for more information) and the
sampling period `DELTA`

.`scal2frq(A,'wname')`

is equivalent to `scal2frq(A,'`

.* wname*',1)

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:

$${F}_{a}=\frac{{F}_{c}}{a}$$

where

*a*is a scale.*F*is the center frequency of the wavelet in Hz._{c}*F*is the pseudo-frequency corresponding to the scale_{a}*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

`centfrq`

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.

**Center Frequencies for Real and Complex Wavelets**

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

Abry, P. (1997), *Ondelettes et turbulence. Multirésolutions,
algorithmes de décomposition, invariance d'échelles*,
Diderot Editeur, Paris.