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By Walsh J.L.

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Example text

A subsequent section will present real data. 1 Noise Reduction The distinction between signal and noise depends upon how the measured signal models reality, in other words, upon the assumed relations between the signal and the phenomenon represented by the signal. Thus, depending upon the assumed nature of the noise, several methods exist to eliminate or attenuate noise. 1 Random Noise If the noise has a random nature, then removing wavelets with random coefficients can help in restoring a noiseless signal.

A) Explain how a62 - 2) = (b) Explain how cci2 (c) Explain how 2) 6 relates to the sample. = 1 relates to the sample. c62- 1) = 2 relates to the sample. (d) Explain how c;2-1) = 2 relates to the sample. 24. Assume that the Haar Wavelet Transform of a sample (so. SI, S2, S3) produces the results c(2-1) = (2,0), c(2-2) = (2), and 3(2-2) (4). aci2- 2) = 4 relates to the sample. Explain how cci2- 2 ) = 2 relates to the sample. (a) Explain how (b) (c) Explain how c62 -1) = 2 relates to the sample. (d) Explain how c;2-1) = 0 relates to the sample.

40. \'2, 053) produces the results (4,2,2,0). Apply the inverse transform to reconstruct the sample 8. 41. \'7), the In-Place Fast Haar Wavelet Transform produces the result (4, -1, -1. 2, 0, 1. -2. -2). Apply the inverse transform to reconstruct the sample s. 42. \'2, the In-Place Fast Haar Wavelet Transform produces the result (5, 1, 1, 0, - 3, - 1, 0, 1). Apply the inverse transform to reconstruct the sample 8. 43. Assume that the In-Place Fast Haar Wavelet Transform stops at the end of the £th sweep.

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