By Palle E. T. Jorgensen, B. Treadway
Combines research and instruments from probability, harmonic research, operator concept, and engineering (signal/image processing)
Interdisciplinary focus with hands-on method, beneficiant motivation and new pedagogical techniques
Numerous workouts strengthen primary options and hone computational skills
Separate sections clarify engineering phrases to mathematicians and operator idea to engineers
Fills a spot within the literature
Read or Download Analysis and Probability Wavelets, Signals, Fractals PDF
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Additional info for Analysis and Probability Wavelets, Signals, Fractals
From the left, we start with (signal) input. The signal is then split into two frequency bands with two filters mo and m \. The first filter, mo, passes low frequencies, and the second, wi, passes high. " We get two signal strands which are now each followed by signal down-sampling. As we move right, the two bands are then up-sampled. The processed signal bands then pass dual filters, and are finally merged again with H- into an output signal. "Perfect reconstruction" means that the output signal to the right is matched up perfectly with the input from the left.
152-153). 5 (pp. g.. 3 (p. 113). For this purpose, the algorithm is used in the two figures with two different initializations. 4, pp. 118-119), and it makes the dyadic subdivision especially transparent. 16, pp. 120-121 and 134). 5. Notice especially two aspects of the progression of functions in the sequence of graphs inside the respective figures: In moving from one graph to the next, the numerical frequency appears to increase with each subdivisionstep. , longer wavelength) appears to "capture" and group the functions themselves into packets, much like the enveloping "beats" from music composition.
We hope students will acquire a handson feeling for the various basis fimctions already discussed in the book; and more importantly, get started at building bases of his/her own. , [Hal67]. , [Dav96]. Finally, several of our exercises have been put in to expand on themes inside the text, pointing the reader to new developments in the subject, and especially stressing links to neighboring subjects and to applications; pointing to connections between modem trends and classical subjects, highlighting an especially powerfiil (and beautifiil) idea, or even suggesting unorthodox applications.