STFT Short time Fourier transform Or windowed Fourier

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STFT (Short time Fourier transform) Or windowed Fourier transform

STFT (Short time Fourier transform) Or windowed Fourier transform

This is the basis for most computer generated spectrograms (display pixel intensity on a

This is the basis for most computer generated spectrograms (display pixel intensity on a log scale by limiting the dynamic range to about 60 -80 d. B).

Ejemplos de espectrogramas Here is the sum of two parallel linear chirps with its

Ejemplos de espectrogramas Here is the sum of two parallel linear chirps with its spectrogram.

Here is the sum of two hyperbolic chirps and its spectrogram.

Here is the sum of two hyperbolic chirps and its spectrogram.

Introducción a Wavelets

Introducción a Wavelets

four frequency components at different times. The interval 0 to 250 ms is a

four frequency components at different times. The interval 0 to 250 ms is a sinusoid of 300 Hz, and the other 250 ms intervals are sinusoids of 200 Hz, 100 Hz, and 50 Hz w(t)=exp(-a*(t^2)/2)

Wavelet de Morlet

Wavelet de Morlet

The mexican hat wavelet

The mexican hat wavelet

 Gráficos de varios tipos distintos de wavelets. (a) Wavelet de Haar, (b) Wavelet

Gráficos de varios tipos distintos de wavelets. (a) Wavelet de Haar, (b) Wavelet de Daubechies, (c) Wavelet de Morlet. (Cortesía de Ofer Levi, Universidad de Stanford)

Escala

Escala

(CWT) Continuous Wavelet Transform ¨escalograma¨ These signals are drawn from a database signals that

(CWT) Continuous Wavelet Transform ¨escalograma¨ These signals are drawn from a database signals that includes event related potentials of normal people, and patients with Alzheimer's disease.

En un espectrograma:

En un espectrograma:

En un escalograma:

En un escalograma:

Suma de dos señales CHIRP hiperbólicas Windowed fourier transform (Espectrograma) Continuous Wavelet Transform CWT

Suma de dos señales CHIRP hiperbólicas Windowed fourier transform (Espectrograma) Continuous Wavelet Transform CWT (Escalograma)

Representación frecuencia-tiempo para: (a) Datos muestreados (b) FT (c) WFT (d) CWT

Representación frecuencia-tiempo para: (a) Datos muestreados (b) FT (c) WFT (d) CWT

MATLAB “cwt” COEFS = cwt(S, SCALES, 'wname') computes the continuous wavelet coefficients of the

MATLAB “cwt” COEFS = cwt(S, SCALES, 'wname') computes the continuous wavelet coefficients of the vector S at real, positive SCALES, using the wavelet whose name is 'wname'

DWT (Discrete Wavelet Transform)

DWT (Discrete Wavelet Transform)

Ahora dejamos fija la Ondeleta y lo que vamos comprimiendo por etapas es la

Ahora dejamos fija la Ondeleta y lo que vamos comprimiendo por etapas es la señal

El análisis multiresolución se consigue a través de filtrado y submuestreo de la señal

El análisis multiresolución se consigue a través de filtrado y submuestreo de la señal original. n La exploración en tiempo se consigue a través de operaciones de convolución (filtrado digital). n

Sub-band coding

Sub-band coding

Sub-band coding algorithm

Sub-band coding algorithm

Transformada inversa

Transformada inversa

2 -D Discrete Wavelet Transform

2 -D Discrete Wavelet Transform

Wavelet Packet

Wavelet Packet

En resumen: CWT DWT 2 D - DWT

En resumen: CWT DWT 2 D - DWT

. . . En resumen: CWT DWT 2 D - DWT

. . . En resumen: CWT DWT 2 D - DWT

n http: //www. gisdevelopment. net/techn ology/ic/techip 0003 a. htm COMPRESION DE LA DCT A

n http: //www. gisdevelopment. net/techn ology/ic/techip 0003 a. htm COMPRESION DE LA DCT A WAVELETS http: //www. acm. org/crossroads/xrds 6 -3/sahaimgcoding. html#Fig 6