## Model Waveforms

[Continuous Periodic Exponential Waves] [Discrete Sampled Exponential Waves]
[Windowed Fourier Transform] [Continuous Wavelet Transform]

#### Continuous period 1 waveforms

 E3(t) =exp(3.2pi.it), red = real part, green = imaginary part E-3(t) =exp(-3.2pi.it),  red = real part, green = imaginary part

Sampled waveforms and stemplots

 The wave form is the same asE3(t) above, sampled at the points r/32, r=0,...,31 Stemplot of the real part of the sampled waveform, emphasizing discrete nature. Stemplot of the imaginary part of the sampled waveform

#### Windowing function and windowed waveforms

 Gaussian windowing function g(t) =exp(-t2) Real (red) and imaginary (green) parts of windowed waveform exp(-iqt)g(t-p), p=1, q=15

#### Mother wavelet, translated wavelets, and scaled wavelets

 The Mexican hat mother wavelet = second derivative of exp(-t2) Translates of a scaled version of the mother wavelet Translates of different scaled versions of the mother wavelet.  Each has the same energy accounting for the different heights

Transform Methods Webpage