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Wavelet - vikramdandyan - 10-04-2017 Wavelet [attachment=444] 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 |