[Windowed Fourier Transform] [Continuous Wavelet Transform]

E,
red
= real part, green = imaginary part_{3}(t) =exp(32pi^{.}it)^{.} |

E,
red = real part, green = imaginary part_{-3}(t) =exp(-32pi^{.}it)^{.} |

The wave form is the same asEabove,
sampled at the points_{3}(t)
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 |

Gaussian windowing function g(t)
=exp(-t^{2}) |

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

The Mexican hat mother wavelet =
second derivative of exp(-t^{2}) |

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