Wavelet



  Introduction to Wavelet.ppt (Size: 315 KB / Downloads: 0)

OVERVIEW


Wavelet
A small wave
Wavelet Transforms
Convert a signal into a series of wavelets
Provide a way for analyzing waveforms, bounded in both frequency and duration
Allow signals to be stored more efficiently than by Fourier transform
Be able to better approximate real-world signals
Well-suited for approximating data with sharp discontinuities
“The Forest & the Trees”
Notice gross features with a large "window“
Notice small features with a small



Mathematical Transformation


Why
To obtain a further information from the signal that is not readily available in the raw signal.
Raw Signal
Normally the time-domain signal
Processed Signal
A signal that has been "transformed" by any of the available mathematical transformations
Fourier Transformation
The most popular transformation


FREQUENCY ANALYSIS


Frequency Spectrum
Be basically the frequency components (spectral components) of that signal
Show what frequencies exists in the signal
Fourier Transform (FT)
One way to find the frequency content
Tells how much of each frequency exists in a signal


STATIONARITY OF SIGNAL


Stationary Signal
Signals with frequency content unchanged in time
All frequency components exist at all times

Non-stationary Signal
Frequency changes in time
One example: the “Chirp Signal”


MULTIRESOLUTION ANALYSIS (MRA)


Wavelet Transform
An alternative approach to the short time Fourier transform to overcome the resolution problem
Similar to STFT: signal is multiplied with a function
Multiresolution Analysis
Analyze the signal at different frequencies with different resolutions
Good time resolution and poor frequency resolution at high frequencies
Good frequency resolution and poor time resolution at low frequencies
More suitable for short duration of higher frequency; and longer duration of lower frequency components