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