A Mexican Hat wavelet and a logarithmic sampling grid. The left plot
a displays a Mexican Hat wavelet as a function of time (in seconds). The scale (approximate wavelength) is \(s=0.3\) s and the time shift (the position of the maximum) is \(t=0.4\) s. The right plot
b displays a log-grid in the t-s-plane (t at the horizontal axis, s at the vertical axis, both measured in seconds). The scale-invariant sampling rate is \(R=10\) pps. Note that the number of sampling points in the time interval \(0 \le t < 0.2\) at \(s=0.2\) is the same, as in the interval \(0 \le t < 0.3\) at \(s=0.3\), and as in the interval \(0 \le t < 0.4\) at \(s =0.4\), etc., and as the number of lines of points in the scale interval \(0.2 \le s < 0.4\), which in turn is the same as in the interval \(0.4 \le s < 0.8\), etc.