The Fast Fourier Transform: An Introduction to Its Theory by E. Oran Brigham PDF

By E. Oran Brigham

ISBN-10: 013307496X

ISBN-13: 9780133074963

Here's a new booklet that identifies and translates the fundamental fundamentals of the quick Fourier rework (FFT). It hyperlinks in a unified presentation the Fourier rework, discrete Fourier remodel, FFT, and primary purposes of the FFT. The FFT is turning into a major analytical instrument in such varied fields as linear structures, optics, chance concept, quantum physics, antennas, and sign research, yet there has constantly been an issue of speaking its basics. hence the purpose of this ebook is to supply a readable and practical therapy of the FFT and its major functions. In his Preface the writer explains the association of his subject matters, "... each significant idea is built by way of a three-stage sequential procedure. First, the concept that is brought via an intuitive improvement that's frequently pictorial and nature. moment, a non-sophisticated (but completely sound) mathematical remedy is constructed to aid the intuitive arguments. The 3rd level includes sensible examples designed to check and extend the idea that being mentioned. it truly is felt that this three-step process supplies which means in addition to mathematical substance to the elemental houses of the FFT. --- from book's dustjacket

Show description

Read or Download The Fast Fourier Transform: An Introduction to Its Theory and Application PDF

Best analysis books

Download e-book for iPad: Risk-Based Reliability Analysis and Generic Principles for by Michael T. Todinov

For a very long time, traditional reliability analyses were orientated in the direction of deciding upon the extra trustworthy process and preoccupied with maximising the reliability of engineering platforms. at the foundation of counterexamples despite the fact that, we display that identifying the extra trustworthy approach doesn't inevitably suggest choosing the approach with the smaller losses from mess ups!

Download PDF by Djairo G de Figueiredo, João Marcos do Ó, Carlos Tomei: Analysis and Topology in Nonlinear Differential Equations: A

This quantity is a set of articles offered on the Workshop for Nonlinear research held in João Pessoa, Brazil, in September 2012. The effect of Bernhard Ruf, to whom this quantity is devoted at the celebration of his sixtieth birthday, is perceptible during the assortment through the alternative of issues and strategies.

Additional info for The Fast Fourier Transform: An Introduction to Its Theory and Application

Example text

EXAMPLE To =4 h(1) (2-17) 2-4 Consider the function (2-20) (2-22) 18 Chap. 2 THE FOURIER TRANSFORM Sec. 2-3 THE FOUJUER TRANSFORM 19 By means of Condition 2, the Fourier transform pair HIli hIlI· 2Afo sin 1:°11 2Af, sin (2n/ot) o 2n/ot 01 B ~f H(/) = A 1/1

From Condition 2 the Fourier transform of h(t) exists and is given by f~ 2Af, sin (2ft/ot) e- 12• /1 dt H(f) = _~ ~ f~ sin (2n/ot)[cos (2n/t) n _~ t = 1 2n/ot 0 j sin (2n/t)] dt = ~ f~ sin (2n/ot) cos (2n/t) dt n _~ t (2-23) The imaginary term integrates to zero since the integrand term is an odd function. 1. 1. S(t)e- 12 • ,t dt = Ke O = K r~ [~]eI2,'t d/ = r~ K cos ~2n/t) d/ + j f~ K sin (2nft) d/ (2-30) 2nt (2-31) Because the integrand of the second integral is an odd function, the integral is zero; the first integral is meaningless unless it is interpreted in the sense of distribution theory.

Fl·H(f) (3-20) The· time-shifted Fourier transform pair is 2A h(1 - 10 ) EXAMPLE ·To H(f)e-/hfl' (3-21) 3-6 A pictorial description of this pair is illustrated in Fig. 3-4. As shown, timeshifting results in a change in the phase angle (J(f) = tan-I[/(f)/R(f)]. Note that time-shifting does not alter the magnitude of the Fourier transform. ;Hl(f) (3-22) 4h(4t) H(~ 4 4A where H(f) has been assumed (0 be real for simplicity. These results are easily extended to the case of H(f), a complex function.

Download PDF sample

The Fast Fourier Transform: An Introduction to Its Theory and Application by E. Oran Brigham

by Richard

Rated 4.14 of 5 – based on 18 votes