Showing posts with label mathematical analysis. Show all posts
Showing posts with label mathematical analysis. Show all posts

Numerical Methods for Engineers Review

Numerical Methods for Engineers
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This is a very good book. The authors focus very well on the audience they are trying to commuinicate with and they have plenty of well thought out examples. The book is easy to read and has a nice selection of topics. This would make a good textbook or a nice reference. The book does lack much of the mathematical development, but that really isn't the driving force for the text. If you are interested in just the how to's and not really the why then this is a great book for you.

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This book introduces numerical methods, emphasizingthe practical aspects of their use and establishing their limitations,advantages and disadvantages. It is intended to assistfuture as well as practicing engineers in fully understanding thefundamentals of numerical methods, most notably their application,limitations and potentials.

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Fast Fourier Transform and Its Applications Review

Fast Fourier Transform and Its Applications
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Fourier transforms used to scare me. I got brain-lock, and couldn't even use them effectively in a package like Matlab or IDL. I got lost in integrals and delta functions and found myself rapidly sinking into mathematical quicksand. Evoking qliphotic demons from within a pentagram of power would have been simpler and less arcane.
Then along came Brigham. Although his book had all the gnarly math of any other Fourier transform explanation I had ever seen, he also drew diagrams--diagrams which allowed me to "get" what the language of mathematics had so clearly expressed. All of a sudden the integrals were tamed. I wasn't in quicksand, just a damp sidewalk at Adventureland, waiting for the Jungle Cruise.
And that was just the first couple of chapters! Brigham quickly moved into transform theory, applying the Fourier integral to convolution and correlation. Then into sampled waveforms and the discrete Fourier transform and its applications.
Finally, he presented the Fast Fourier Transform. Once again, he clarifies without obfuscating. I found the FFT moving from the hyper-arcane to the land of "Well, duh!" (Beware: The actual FFT code included is not particularly efficient. Find source code for implementation *elsewhere*.) He extends the FFT to convolution and correlation, as well as to two dimensions. He doesn't skimp on applications, either. He clarifies interferometry, time-difference-of-arrival, power spectrum analysis, and beamforming.
If you're not a signal processing wonk already, read this book. You may find it a powerful cure for DSP-phobia.

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The Fast Fourier Transform (FFT) is a mathematical method widely used in signal processing. This book focuses on the application of the FFT in a variety of areas: Biomedical engineering, mechanical analysis, analysis of stock market data, geophysical analysis, and the conventional radar communications field.

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