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## Main Question or Discussion Point

Hello--

I've been working with a time-domain function to calculate the Ricker (Mexican Hat) wavelet for [tex] -0.2 \leq t \leq 0.2 [/tex]. This function is given as [tex]s(t)[/tex]:

[tex]

s(t) = \left( 1 - \frac{1}{2} \omega_0^2 t^2 \right) \mbox{exp} \left ( -\frac{1}{4} \omega_0^2 t^2 \right )

[/tex]

In the equation above, [tex]t[/tex] is time (s), and [tex]\omega_0[/tex] is the angular frequency (1/s).

What I would like to do is find an analytical expression to determine the width of this wavelet, which is the time between the two side-lobes of the wavelet. The wavelet consists of a maximum value at [tex]t = 0[/tex], and the side-lobes are situated on either side. I think that it is a very pretty wavelet.

I am wondering if it would be possible to do this type of calculation in the frequency domain.

A paper that I am reading informs me that the width [tex]w[/tex] of the Ricker wavelet is

[tex]

w = \sqrt(6) / \pi / f0

[/tex]

where [tex]f0[/tex] is the peak frequency (Hz) of the wavelet. However, I am uncertain as to how this expression is derived.

I've been working with a time-domain function to calculate the Ricker (Mexican Hat) wavelet for [tex] -0.2 \leq t \leq 0.2 [/tex]. This function is given as [tex]s(t)[/tex]:

[tex]

s(t) = \left( 1 - \frac{1}{2} \omega_0^2 t^2 \right) \mbox{exp} \left ( -\frac{1}{4} \omega_0^2 t^2 \right )

[/tex]

In the equation above, [tex]t[/tex] is time (s), and [tex]\omega_0[/tex] is the angular frequency (1/s).

What I would like to do is find an analytical expression to determine the width of this wavelet, which is the time between the two side-lobes of the wavelet. The wavelet consists of a maximum value at [tex]t = 0[/tex], and the side-lobes are situated on either side. I think that it is a very pretty wavelet.

I am wondering if it would be possible to do this type of calculation in the frequency domain.

A paper that I am reading informs me that the width [tex]w[/tex] of the Ricker wavelet is

[tex]

w = \sqrt(6) / \pi / f0

[/tex]

where [tex]f0[/tex] is the peak frequency (Hz) of the wavelet. However, I am uncertain as to how this expression is derived.