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new technology -- rediscovered by I. Daubechies in 1987
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signal analysis - weighted sum of basis functions
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infinitely many possible sets of wavelets (= small waves)
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coefficients contain information about the signal
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basis functions
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impulse function reveals information only about the time domain behavior of the signal because of infinitesimally small support of impuls function
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Fourier representation reveals information about signal's frequency domain behavior because of infinite support of sines and cosines
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we want to have representation which contains info about both the time and frequency (frequency content of the signal at the particular instant of time)
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Heisenberg inequality - resolution in time and in frequency cannot both be made arbitrarily small
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