4 4 fourier transform methods

Tài liệu Fast Fourier Transform part 4 pdf

Ngày tải lên : 21/01/2014, 18:20

... functions used by the Fourier transform (a), sine transform (b), and cosine transform (c), are plotted The ﬁrst ﬁve basis functions are shown in each case (For the Fourier transform, the real and ... inverse transform for the case isign=-1 Fast Sine and Cosine Transforms Among their other uses, the Fourier transforms of functions can be used to solve differential equations (see §19 .4) The ... separately below i4=1+(i3=np3-(i2=1+(i1=i+i-1))); h1r=c1*(data[i1]+data[i3]); The two separate transforms are seph1i=c1*(data[i2]-data[i4]); arated out of data h2r = -c2*(data[i2]+data[i4]); h2i=c2*(data[i1]-data[i3]);...

12
414
0

The Discrete Fourier Transform

Ngày tải lên : 13/09/2012, 09:49

... 8 4 0 -4 -4 -4 -8 -8 10 12 14 16 -8 10 12 14 16 -4 10 12 14 16 10 12 14 16 10 12 14 16 10 12 14 16 10 12 14 16 -4 0 10 12 14 16 8 4 8 -4 -8 -8 10 12 14 16 -8 10 12 14 16 8 4 0 -4 -4 -4 -8 -8 ... -8 10 12 14 16 -8 10 12 14 16 Sine Waves 8 4 0 -4 -4 -4 -8 -8 10 12 14 16 -8 10 12 14 16 8 4 0 -4 -4 -4 -8 -8 10 12 14 16 -8 10 12 14 16 8 4 0 -4 -4 -4 -8 -8 10 12 14 16 -8 10 12 14 16 FIGURE ... number 48 64 32 Sample number 48 64 d s3[ ], basis function being sought Amplitude Amplitude 16 c s3[ ], basis function being sought -1 -1 -2 -2 16 32 Sample number 48 64 16 32 48 64 32 48 64 Sample...

28
677
0

Fourier Transform Properties

Ngày tải lên : 13/09/2012, 09:49

... -900 64 128 192 256 320 Sample number 3 84 448 512 511 0.2 0.3 0 .4 0.5 0.1 0.2 0.3 0 .4 0.5 0.1 0.2 0.3 0 .4 0.5 0 .4 0.5 Frequency 900 b f 600 Phase (radians) Amplitude 0.1 300 -300 -600 -1 -900 64 ... 64 128 192 256 320 Sample number 3 84 448 512 511 Frequency 900 g c Phase (radians) Amplitude 600 300 -300 -600 -1 -900 64 128 192 256 320 Sample number 3 84 448 512 511 900 d h 600 Phase (radians) ... Frequency 0 .4 0.5 0.1 0.2 0.3 Frequency 0 .4 0.5 0 .4 0.5 0 .4 0.5 Decompose 20 b x1[ ] e Mag X1[ ] Amplitude Amplitude Amplitude h Phase X1[ ] 15 10 -1 -2 -3 -1 - 64 -32 32 Sample number 63 64 -4 0.1...

24
477
0

Fourier Transform Pairs

Ngày tải lên : 13/09/2012, 09:49

... 0 .4 0.2 0.5 0.3 0 .4 0.5 Frequency h Phase Phase (radians) Amplitude Amplitude 0.1 15 10 -2 -4 -6 -5 Sample number 0 .4 -2 g Magnitude 128 127 0.3 0.5 20 f Rectangular pulse 96 0.5 -6 64 0 .4 -4 ... -4 -2 -0.5 -1 16 32 48 Sample number 64 63 Frequency Amplitude Phase (radians) 1 0.5 0.5 0.5 Frequency e Magnitude d Impulse at x [4] Amplitude -6 -0.5 0.5 -1 f Phase -2 -4 -2 -0.5 -1 16 32 48 ... pulse from a pure sinc function y(x) = x 1.2 y(x) 2 14 0.8 y(x) = sin(x) 0.6 0 .4 0.2 0.0 0.2 0 .4 0.6 0.8 x 1.0 1.2 1 .4 1.6 Chapter 11- Fourier Transform Pairs 215 This turns the sinc function into...

16
495
1

The Fast Fourier Transform

Ngày tải lên : 13/09/2012, 09:50

... CINT(LOG(N%)/LOG(2)) 340 0 LE% = CINT(2^L%) 341 0 LE2% = LE%/2 342 0 UR = 343 0 UI = 344 0 SR = COS(PI/LE2%) 345 0 SI = -SIN(PI/LE2%) 346 0 FOR J% = TO LE2% 347 0 JM1% = J%-1 348 0 FOR I% = JM1% TO NM1% STEP LE% 349 0 IP% ... IMX[IP%]*UR 140 0 REX[IP%] = REX[I%]-TR 141 0 IMX[IP%] = IMX[I%]-TI 142 0 REX[I%] = REX[I%]+TR 143 0 IMX[I%] = IMX[I%]+TI 144 0 NEXT I% 145 0 TR = UR 146 0 UR = TR*SR - UI*SI 147 0 UI = TR*SI + UI*SR 148 0 NEXT ... 0 -4 -1 -8 16 32 Sample number 48 64 63 16 32 Freqeuncy 48 63 b Imaginary part d Imaginary part (odd symmetry) Amplitude Amplitude 0 -4 -1 -8 16 32 Sample number 48 63 64 16 32 Frequency 48 63...

18
555
1

The Complex Fourier Transform

Ngày tải lên : 13/09/2012, 10:20

... be divided by two Fourier Transform complex transform real transform %4 synthesis x(t ) ' m X (T) e x(t ) ' dT &4 analysis %4 synthesis jTt m %4 X (T) ' x(t ) e & jTt dt 2B m &4 analysis Re X (T) ... period, from to B TABLE 31-1 The Fourier Transforms Chapter 31- The Complex Fourier Transform 579 Fourier Series complex transform real transform j 2Bk t /T j X [k] e %4 synthesis x(t ) ' synthesis ... types of Fourier transforms: the Discrete Fourier Transform (discrete, periodic), the Discrete Time Fourier Transform (discrete, aperiodic), the Fourier Series (continuous, periodic), and the Fourier...

14
651
0

Các phương pháp xử lý tín hiệu dùng bộ lọc, phương pháp Fourier Transform, STFT( Short Time Fourier Transform)

Ngày tải lên : 01/04/2013, 16:14

... thúc kiện Fourier không phát 2 .4. 2 Phương pháp STFT: Để đạt biến đổi Fourier cục bộ, định nghĩa biến đổi Fourier cửa sổ Tín hiệu đầu vào nhân với hàm cửa sổ W (t - τ) sau lấy biến đổi Fourier Kết ... , n = 1,2 … −∞ 2 .4. 1.3 Chuỗi Fourier: Cho hàm tuần hoàn F(t) với chu kỳ T: F(t+T) = F(t) Nó biểu diễn tổ hợp tuyến tính số mũ phức với tần số nω 0, ω0 = 2π/T Khai triển chuỗi Fourier F(t) f (t ... TRƯỜNG ĐHBK TP.HCM-năm2007 LUẬN VĂN TỐT NGHIỆP 2 .4. 1.2 Tính chất: Dịch :Nếu miền thời gian f(t) bị dịch đoạn t0 miền tần số biến đổi Fourier nhân với hệ số pha: f (t − t ) ↔ e − jωt Ngược...

11
1.5K
5

Real-Time Digital Signal Processing - Chapter 7: Fast Fourier Transform and Its Applications

Ngày tải lên : 28/10/2013, 05:15

... obtain W4 W4 1, W4 W4 Àj, W4 W4 À1, and W4 j The IDFT can be computed with P 1T1 T x T 4R1 P 1T1 T 4R1 1 j À1 Àj 1 À1 W4 À2 W4 À2 W4 4 W4 À3 W4 À1 À1 À6 W4 Q À3 W4 U U X À6 U W4 S ... matrix formulation as P T T1 T XT T T1 R P T T1 T T T T1 R 1 1 W4 W4 W4 W4 W4 W4 1 Àj À1 À1 j À1 Q U W4 U U Ux 6U W4 U S W4 Q QP Q P 1 U UT U T j UT U T À j U U UT U T U, UT U T U UT U T ... x(0) x (4) X(0) W8 N /4- point W8 DFT X(1) −1 X(2) −1 X(3) W8 x(3) x(7) N /4- point DFT W8 N /4- point W8 DFT −1 −1 −1 W8 x(1) x(5) k 0, 1: N /4- point DFT x(2) x(6) nk xnW2 , −1 W8 −1 W8 −1 X (4) X(5)...

47
634
0

Tài liệu Table of Fourier Transform Pairs ppt

Ngày tải lên : 13/12/2013, 12:15

... t e -t a2 +w2 /( 2s ) s 2p e -s w2 / a + jw u (t )e -at u (t )te -at (a + jw ) Ø Trigonometric Fourier Series ¥ f (t ) = a + å (a n cos(w nt ) + bn sin(w nt ) ) n =1 where a0 = T T ò0 2T f (t ... )dt , a n = ò f (t ) cos(w nt )dt , and T0 2T bn = ò f (t ) sin(w nt )dt T Ø Complex Exponential Fourier Series f (t ) = ¥ å Fn e jwnt , where n = -¥ Signals & Systems - Reference Tables 1T Fn...

5
453
0

Tài liệu Fast Fourier Transform part 1 doc

Ngày tải lên : 21/01/2014, 18:20

... This result shows that multiplying the 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 the Fourier transform (We’ll use the “⇐⇒” symbol to indicate transform pairs.) If h(t) ⇐⇒ H(f) is such a pair, then other transform pairs are h(at) ⇐⇒ f H( ) |a| a “time scaling” (12.0 .4) t ... of a simple transform pair g ∗ h ⇐⇒ G(f)H(f) “Convolution Theorem” (12.0.9) In other words, the Fourier transform of the convolution is just the product of the individual Fourier transforms The...

5
305
0

Tài liệu Fast Fourier Transform part 2 ppt

Ngày tải lên : 21/01/2014, 18:20

... 1-800-872- 742 3 (North America only),or send email to trade@cup.cam.ac.uk (outside North America) hn h(t) = ∆ 502 Chapter 12 Fast Fourier Transform h(t) ∆ t T H( f ) f ( b) aliased Fourier transform ... summation in equation (12.1.6) is called the discrete Fourier transform of the N points hk Let us denote it by Hn , 5 04 Chapter 12 Fast Fourier Transform The discrete form of Parseval’s theorem ... 1 942 , provides one of the clearest derivations of the algorithm Danielson and Lanczos showed that a discrete Fourier transform of length N can be rewritten as the sum of two discrete Fourier transforms,...

5
292
0

Tài liệu Fast Fourier Transform part 3 docx

Ngày tải lên : 21/01/2014, 18:20

... problem of computing the transform of its N /4 even-numbered input data and N /4 odd-numbered data ee eo In other words, we can deﬁne Fk and Fk to be the discrete Fourier transforms of the points ... 1-800-872- 742 3 (North America only),or send email to trade@cup.cam.ac.uk (outside North America) real array of length N real real array of length N Fast Fourier Transform 12.2 Fast Fourier Transform ... Fast Transforms: Algorithms, Analyses, Applications (New York: Academic Press) Brigham, E.O 19 74, The Fast Fourier Transform (Englewood Cliffs, NJ: Prentice-Hall) [1] Bloomﬁeld, P 1976, Fourier...

7
387
0

Tài liệu Fast Fourier Transform part 5 pptx

Ngày tải lên : 21/01/2014, 18:20

... http://www.nr.com or call 1-800-872- 742 3 (North America only),or send email to trade@cup.cam.ac.uk (outside North America) row 5 24 Chapter 12 Fast Fourier Transform { } Sample page from NUMERICAL ... ifp1=ifp2; } nprev *= n; } 525 12.5 Fourier Transforms of Real Data in Two and Three Dimensions CITED REFERENCES AND FURTHER READING: Nussbaumer, H.J 1982, Fast Fourier Transform and Convolution Algorithms ... rely on someone else having done the bookkeeping for once and for all The inverse transforms of (12 .4. 1) or (12 .4. 3) are just what you would expect them to be: Change the i’s in the exponentials...

5
309
0

Tài liệu Fast Fourier Transform part 6 pdf

Ngày tải lên : 21/01/2014, 18:20

... FURTHER READING: Brigham, E.O 19 74, The Fast Fourier Transform (Englewood Cliffs, NJ: Prentice-Hall) Swartztrauber, P N 1986, Mathematics of Computation, vol 47 , pp 323– 346 Sample page from NUMERICAL ... where to ﬁnd the real and imaginary components of the transform at some particular frequency!) We will implement the multidimensional real Fourier transform for the three dimensional case L = 3, with ... http://www.nr.com or call 1-800-872- 742 3 (North America only),or send email to trade@cup.cam.ac.uk (outside North America) float data[1 nn1][1 nn2][1 nn3] 528 Chapter 12 Fast Fourier Transform #include ...

8
260
0

Tài liệu Fast Fourier Transform part 7 docx

Ngày tải lên : 21/01/2014, 18:20

... 5 34 Chapter 12 Fast Fourier Transform } j=1; The second phase of the transform starts here Now, the remaining permutations are sufﬁciently local to be done in place for (;;) { theta=isign*3. 141 592653589793/(n/mm); ... renumbers the four ﬁles { int i; FILE *ftemp; for (i=1;i< =4; i++) rewind(file[i]); SWAP(file[2],file [4] ); SWAP(file[1],file[3]); *na=3; *nb =4; *nc=1; *nd=2; } For one-dimensional data, Singleton’s ... wr,wi,wpr,wpi,wtemp,theta; static int mate[5] = {0,2,1 ,4, 3}; Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5) Copyright (C) 1988-1992 by Cambridge University...

5
402
0

Báo cáo khoa học: Determination of thioxylo-oligosaccharide binding to family 11 xylanases using electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry and X-ray crystallography pot

Ngày tải lên : 07/03/2014, 17:20

... 19508. 048 19656.067 198 04. 087 208 24. 850 21136. 942 21285.9 64 2 143 3.983 21582.002 21680.189 21993.279 22 141 .298 22289.317 2 243 7.336 ) 1.0 + + + ) 1.6 0.7 0.2 1.3 + + + ) 0.8 0 .4 1 .4 3.5 + 5.1 + 4. 3 ... lm TRX II with 50 lm methyl 4, 4II,4III,4IV-tetrathio-a-xylopentoside (S-Xyl5-Me), 50 lm methyl 4, 4II,4III-trithio-a-xylotetroside (S-Xyl4-Me), and 50 lm methyl 4, 4II-dithioa-xylotrioside (S-Xyl3-Me) ... 2-O B3 3-O Glu178 OE2 HOH 440 HOH438 HOH 441 Tyr78 OH Tyr172 OH Tyr172 OH HOH1 HOH450 HOH357 HOH450 Glu178 OE1 HOH192 HOH436 Tyr78 OH Tyr172 OH Tyr172 OH HOH6 HOH 145 HOH372 3.08 2.60 2.55 2.52...

17
382
0

Báo cáo khoa học: Light-induced reactions of Escherichia coli DNA photolyase monitored by Fourier transform infrared spectroscopy pot

Ngày tải lên : 16/03/2014, 18:20

... the enzyme [41 44 ] Therefore, an additional difference band at 1 244 ⁄ 12 24 cm)1 can be detected in Fig 7B Interestingly, the kinetics of the formation of the positive band at 12 24 cm)1, which ... (L)1), g Tris, 0.35 g K2HPO4, g glucose, 0.138 g MgSO4, g 15NH4Cl, 5.55 mg CaCl2, mL vitamin concentrate, mL trace metal mix, 40 mg tryptophan, 40 mg threonine, 40 mg lysine, 40 mg methionine, 15 mg ... Biochemistry 28, 1 148 –1152 48 Ramaiah D, Koch T, Orum H & Schuster GB (1998) Detection of thymine [2+2] photodimer repair in DNA: selective reaction of KMnO4 Nucleic Acids Research 26, 3 940 –3 943 49 Zamenhof...

12
393
0

Comparison between the Matrix Pencil Method and the Fourier Transform Technique for High-Resolution Spectral Estimation

Ngày tải lên : 26/03/2014, 00:29

... b f The same input data as in Fig 7, but SNR Å 20 dB 117 04- 18-96 17:38:26 88.2 113 .4 178.2 23 .4 88.2 113 .4 178.2 23 .4 THE FOURIER TRANSFORM ESTIMATOR For the best estimate, and f2 f1 Å 0.070 ... p (4. 3.2.2) and a minimum if ( vm )(N 1) Dt / 2( um un ) Å l p (4. 3.2.3) In both Eqs (4. 3.2.2) and (4. 3.2.3), m, n, and l have to satisfy for all m x n; m, n Å 1, , K; l integer (4. 3.2 .4) ... Rz Å 2s IN1N (4. 2.17) [F]mn Å E ͫ Ì ln fzÉa(zÉa) Ì ln fzÉa(zÉa) r Ìam Ìan m, n Å 1, , 3K (4. 2.13) ͬ ; (4. 2.18) The last equation, using (4. 2.12), can be rewritten [1] as (4. 2. 14) Also, a is...

18
415
0

mathematics of the discrete fourier transform

Ngày tải lên : 31/03/2014, 15:21

... 136 137 138 140 140 141 142 145 145 146 146 148 148 148 151 1 54 155 155 156 158 160 163 165 165 166 167 169 171 173 DRAFT of “Mathematics of the Discrete Fourier Transform (DFT),” ... 39 40 40 41 41 43 43 44 45 46 52 53 53 53 58 58 59 61 61 63 64 65 66 69 69 70 71 72 73 74 76 DRAFT of “Mathematics of the Discrete Fourier Transform (DFT),” by J.O Smith, ... of irrational numbers include π = 3. 141 59265358979323 846 2 643 3832795028 841 971693993751058209 749 e = 2.71828182 845 9 045 23536028 747 135266 249 7757 247 0936999595 749 669 Let xn denote the n-digit decimal...

247
352
0

The discrete fourier transform

Ngày tải lên : 08/06/2014, 20:19

... x[n] -4 20 40 90 130 70 90 -40 20 40 90 130 90 130 50 130 n 70 90 -40 20 40 90 130 y[n +4] y[n] y[n -4] 70 90 -40 s[n] (sum of above) 4 x((n)) x(n) 5 4 −2 −6 10 s(n) = x(n) (5) h(n) h(n) 4 −2 ... 30 40 -30 s(1) = 40 + 120 - 30 = 130 -1 10 h((2-m)) n=2 20 30 30 40 60 -40 s(2) = 60 + 30 - 40 = 50 30 20 h((3-m)) 10 40 60 n=3 80 -10 s(3) = 80 + 60 - 10 = 130 c J Fessler, May 27, 20 04, 13: 14 ... h(n) h(n) 4 −2 10 4 −2 10 4 −2 10 4 −2 n 10 20 0.8 0.6 0 .4 0.2 −6 1 −6 4 −2 15 10 −6 10 20 x((n)) y(n) 15 10 −6 −2 −6 10 20 s(n) = x(n) (8) h(n) h(n) 4 0.8 0.6 0 .4 0.2 −6 4 −2 n 10 15 10 −6...

31
320
0