the discrete fourier transform part 1

... 4 6 8 10 12 14 16 -8 -4 0 4 8 0 2 4 6 8 10 12 14 16 -8 -4 0 4 8 0 2 4 6 8 10 12 14 16 -8 -4 0 4 8 0 2 4 6 8 10 12 14 16 -8 -4 0 4 8 0 2 4 6 8 10 12 14 16 -8 -4 0 4 8 0 2 4 6 8 10 12 14 16 -8 -4 0 4 8 0 ... 4 6 8 10 12 14 16 -8 -4 0 4 8 0 2 4 6 8 10 12 14 16 -8 -4 0 4 8 0 2 4 6 8 10 12 14 16 -8 -4 0 4 8 0 2 4 6 8 10 12 14 16 -8 -4 0 4 8 0 2 4 6 8 10 12 14 16 -8 -4 0 4 8 0 2 4 6 8 10 12 14 16 -8 -4 0 4 8 0 ... 16 -8 -4 0 4 8 0 2 4 6 8 10 12 14 16 -8 -4 0 4 8 0 2 4 6 8 10 12 14 16 -8 -4 0 4 8 0 2 4 6 8 10 12 14 16 -8 -4 0 4 8 0 2 4 6 8 10 12 14 16 -8 -4 0 4 8 Cosine Waves Sine Waves FIGURE 8-1b Example of Fourier decomposition....

Ngày tải lên: 13/09/2012, 09:49

... case (12 .0 .11 ) becomes the transform pair Corr(g, g) ⇐⇒ | G ( f ) | 2 “Wiener-Khinchin Theorem” (12 .0 .12 ) The total power in a signal is the same whether we compute it in the time domain or in the ... that multiplyingthe Fourier transform of one function by the complex conjugate of the Fourier transform of the other gives the Fourier transform of their correlation. The correlation of a function ... 12 .1. From equation (12 .0 .1) it is evident at once that Fourier transformation is a linear operation. The transform of the sum of two functions is equal to the sum of the transforms. The transform of...

Ngày tải lên: 21/01/2014, 18:20

... in C/C++ by starting the number with “0x”, e.g., 0x1ED = 1 · 16 2 +15 · 16 1 +14 · 16 0 = 493 decimal = 1, 111 0 ,11 01 binary). Note, however, that the representation within the computer is still ... numbers. For example, in the case of 3-bit binary numbers, we have the assignments shown in Table 4.3. Binary Decimal 000 0 0 01 1 010 2 011 3 10 0 -3 10 1 -2 11 0 -1 111 -0 Table 4.3: Three-bit ... 1. 10944723 819 596i 1. 300 519 17307206 - 1. 10944723 819 596i -0.755047925 017 55 + 1. 275 010 619 23774i -0.755047925 017 55 - 1. 275 010 619 23774i -1. 09094249 610 903 Matlab has the following primitives for complex...

Ngày tải lên: 31/03/2014, 15:21

... equivalent to writing the sequence CCW around a circle, and then reading the values CW. Example . If x[n] = {10 , 11 , 12 , 13 , 14 } and N = 6, then x[−n mod N] = {10 , 0, 14 , 13 , 12 , 11 }. Picture of circle We ... 8. 15 10 −5 0 5 10 15 0 1 2 3 4 5 n x(n) L=6 Time−limited signal x(n) 15 10 −5 0 5 10 15 0 1 2 3 4 5 n x((n)) N Periodic extension x((n)) N with N=6 N 2N−N−2N 15 10 −5 0 5 10 15 0 1 2 3 4 5 n x(n) L=6 Time−limited ... writing the sequence CCW around a circle, and then reading the values CCW starting from point −l. Example. If x[n] = {10 , 11 , 12 , 13 , 14 } and N = 6 and l = 2, then x[n −l mod N] = {14 , 0, 10 , 11 , 12 ,...

Ngày tải lên: 08/06/2014, 20:19

... crossings log 10 (norm of error) B 1 S 2 S 6 S 16 (a) 10 −8 10 −7 10 −6 10 −5 10 −4 10 −3 10 −2 10 1 10 0 010 2030405060 Number of zero crossings log 10 (norm of error) B 1 S 2 S 6 S 16 (b) Figure ... Signal Processing Volume 2 010 , Article ID 19 1085, 7 pages doi :10 .11 55/2 010 /19 1085 Research Article Eigenvectors of the Discrete Fourier Transform Based on the Bilinear Transform Ahmet Serbes and ... for B 1 . We define the total norm of error as sum of norms of error for each eigenvector. Figure 2(a) shows the total norm of error 10 −6 10 −5 10 −4 10 −3 10 −2 10 1 10 0 0 5 10 15 20 25 30 Number...

Ngày tải lên: 21/06/2014, 16:20

... coefficients. DFT length 7 17 31 61 127 257 C N 6 16 30 60 12 6 256 R N 6 16 30 60 12 4 253 CSD 21 59 10 0 2 01 428 810 MAG 18 51 85 17 5 360 688 RAG-n 11 23 35 61 124 237 (3) N multiplications with W k 2 /2 N . This ... 43 CSD 6 10 19 38 70 14 8 MAG 6 917 346 212 9 RAG-n 5 711 1924 44 identical. For instance, the length-8 CZT has an FIR filter of length 15 , C(n) = e j2π((n 2 /2mod8)/8) , n = 1, 2, , 15 , but there are ... Heidelberg, Germany, 19 90. [ 31] C. Rader, Discrete Fourier transform when the number of data samples is prime,” Proceedings of the IEEE, vol. 56, no. 6, pp. 11 07 11 08, 19 68. [32] J. McClellan...

Ngày tải lên: 22/06/2014, 23:20

... 0000 1 00 01 8 10 00 2 0 010 4 010 0 3 0 011 12 11 00 4 010 0 2 0 010 5 010 1 10 10 10 6 011 0 6 010 0 7 011 1 14 11 10 8 10 00 1 00 01 9 10 01 9 10 01 10 10 10 5 010 1 11 10 11 13 11 01 12 11 00 3 0 011 13 11 01 11 1 011 14 ... 14 15 0 2 4 6 8 10 12 14 1 3 5 7 9 11 13 15 0 4 8 12 2 6 10 14 1 5 9 13 3 7 11 15 8 4 12 2 10 6 14 1 9 5 13 3 11 7 15 0 8 4 12 2 10 6 14 1 9 5 13 3 11 7 15 0 How the FFT works The FFT is a complicated ... J% THEN GOTO 11 90 11 30 TR = REX[J%] 11 40 TI = IMX[J%] 11 50 REX[J%] = REX[I%] 11 60 IMX[J%] = IMX[I%] 11 70 REX[I%] = TR 11 80 IMX[I%] = TI 11 90 K% = ND2% 12 00 IF K% > J% THEN GOTO 12 40 12 10 J%...

Ngày tải lên: 13/09/2012, 09:50

... we restrict the mathematics to be real numbers, problems arise. In other words, these problems are not solved by the complex Fourier transform, they are introduced by the real Fourier transform. In the ... the Discrete Fourier Transform (discrete, periodic), the Discrete Time Fourier Transform (discrete, aperiodic), the Fourier Series (continuous, periodic), and the Fourier Transform (continuous, ... version, so do the other members of the Fourier transform family. This produces the zoo of equations shown in Table 31- 1. Rather than studying these equations individually, try to understand them as...

Ngày tải lên: 13/09/2012, 10:20

... dollars,” the driver said. The man drew out his wallet and took out a 10 0-dollar bill, then gave it to the driver. “Keep the change”. Book 1- Part 1- The Beginning of an End October 1, 2 012 . 81 ... towards the door while the rest followed him. 14 . They entered the dinning-room that was at the end of a long corridor. They saw a long round table and a huge mirror on the wall. The table ... leave the castle for nights, you won’t be bothered.” As soon as the gate disappeared in the top part of the wall, the car rushed inside. Behind the front wall, was a courtyard very well-kept. There...

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... you the questions from the audioscript. The audioscript is in the back of this book. There are four parts to the Listening Comprehension section. NUMBER OF QUESTIONS TIME Parti: Photos 10 ... foreign speakers. I. Title. PE 112 8.L647 2007 428.0076—dc22 2006039603 Printed in the United States of America 3 4 5 6 7 8 9 10 -BAII -11 10 09 08 07 LONGMAN ON THE WEB Longman.com offers online ... photocopying, recording, or otherwise, without the prior permission of the publisher. Pearson Education, 10 Bank Street, White Plains, NY 10 606 Staff credits: The people who made up the Longman Preparation...

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