Model Waveforms

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

Continuous period 1 waveforms

 E3(t) =exp(, red = real part, green = imaginary part

 E-3(t) =exp(,  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