the discrete fourier transform part 3

... on the shape of the waveform being decomposed. Chapter 8- The Discrete Fourier Transform 145 Type of Transform Example Signal Fourier Transform Fourier Series Discrete Time Fourier Transform Discrete ... another chunk of data. Let's see how this applies to the topic at hand: the Discrete Fourier transform. Notation and Format of the Real DFT As shown in Fig. 8 -3, the discrete Fourier transform ... X[N/2] Synthesis, Calculating the Inverse DFT Pulling together everything said so far, we can write the synthesis equation: Chapter 8- The Discrete Fourier Transform 1 63 Frequency 0 0.1 0.2 0 .3 0.4...

Ngày tải lên: 13/09/2012, 09:49

... discrete Fourier transforms, e.g., for N =2 ,3, 4,5,7,8,11, 13, 16. The algorithms also use a new and clever way of combining the subfactors. The method involves a reordering of the data both before the ... In other words, data[1] is the real part of f 0 , data[2] is the imaginary part of f 0 , and so on up to data[2*nn-1],which is the real part of f N−1 ,anddata[2*nn], which is the imaginary part ... W k F o k (12.2 .3) In the last line, W is the same complex constant as in (12.2.1), F e k denotes the kth component ofthe Fourier transform oflengthN/2 formed fromthe even components of the original...

Ngày tải lên: 21/01/2014, 18:20

... CONTENTS 3. 1.9 Derivatives of f(x)=a x 32 3. 1.10 Back to e 33 3. 1.11 Sidebar on Mathematica . . . . . . . . . 34 3. 1.12 Back to e jθ 34 3. 2 Informal Derivation of Taylor Series . . . . . . 36 3. 3 ... irrational numbers include π =3. 1415926 535 897 932 384626 433 832 7950288419716 939 937 51058209749 e =2.718281828459045 235 36028747 135 26624977572470 936 999595749669 Let ˆx n denote the n-digit decimal expansion ... http://www-ccrma.stanford.edu/~jos/mdft/. CHAPTER 3. PROOF OF EULER’S IDENTITY Page 31 and, using overbar to denote the repeating part of a decimal expansion, x =0. 1 23 ⇒ 1000x = 1 23. 1 23 = 1 23 + x ⇒ 999x = 1 23 ⇒ x = 1 23 999 Other examples...

Ngày tải lên: 31/03/2014, 15:21

... ω 0 = 2π N k 0 , then the sinc is sampled only at the peak and the nulls, which gives the Dirac impulse form above. Otherwise the sinc is sampled at many nonzero values, which gives the messy form ... circle. For the above example, s[0] = x[0] h[0] + x[1] h [3] + x[2] h[2] + x [3] h[1] = 2 · 10 + 0 · 40 + 3 30 + (−1) ·20 = 90. • Shift the folded sequence by rotating CCW around the circle, then multiply ... X co I [k] Note: (5.2 .31 ) looks different than (4 .3. 37) only because the order of terms differs. 5.16 c  J. Fessler, May 27, 2004, 13: 14 (student version) Symmetries The next set of properties of the DFT...

Ngày tải lên: 08/06/2014, 20:19

... eigenvectors of the DFT matrix inspired by the ideas behind bilinear transform. The bilinear transform maps the analog space to the discrete sample space. As jω in the analog s-domain is mapped to the unit ... The discrete fractional Fourier transform, ” IEEE Transactions on Signal Processing, vol. 48, no. 5, pp. 132 9– 133 7, 2000. [7] S C. Pei, W L. Hsue, and J J. Ding, Discrete fractional Fourier transform ... Processing, vol. 30 , no. 1, pp. 25– 31 , 1982. [ 13] F. A. Gr ¨ unbaum, The eigenvectors of the discrete Fourier transform: a version of the Hermite functions,” Journal of Mathematical Analysis...

Ngày tải lên: 21/06/2014, 16:20

... 124 Total 35 0 34 2 31 2 646 594 36 6 The gate count is measured as equivalent gates as used in cell- based ASIC design. The latency is the number of clock cycles the FFT core needs until the first ... 1990. [31 ] C. Rader, Discrete Fourier transform when the number of data samples is prime,” Proceedings of the IEEE, vol. 56, no. 6, pp. 1107–1108, 1968. [32 ] J. McClellan and C. Rader, Number Theory ... 4 RAG-CZT Size 9970 13 728 22 578 39 234 73 171 Latency 4444 4 Xilinx Radix-2 Si ze — — 29 535 30 455 32 255 Min. Resource [5] Latency — — 45 112 265 Xilinx Radix-4 Si ze — — — — 137 952 Stream I/O...

Ngày tải lên: 22/06/2014, 23:20

... = IMX(N%/4) 33 20 REX(ND2%) = IMX(0) 33 30 IMX(N% *3/ 4) = 0 33 40 IMX(ND2%) = 0 33 50 IMX(N%/4) = 0 33 60 IMX(0) = 0 33 70 ' 33 80 PI = 3. 14159265 'Complete the last FFT stage 33 90 L% = CINT(LOG(N%)/LOG(2)) ... an Chapter 12- The Fast Fourier Transform 235 TABLE 12-4 The Fast Fourier Transform in BASIC. 1000 &apos ;THE FAST FOURIER TRANSFORM 1010 'Upon entry, N% contains the number of points in the DFT, ... 2 3 4 5 6 7 8 9 10 11 12 13 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 7 150 How the...

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 ... Laplace and z-transforms. These complex transforms are the foundation of theoretical DSP. The Real DFT All four members of the Fourier transform family (DFT, DTFT, Fourier Transform & Fourier Series) ... Fourier Transforms A time domain signal can be either continuous or discrete, and it can be either periodic or aperiodic. This defines four types of Fourier transforms: the Discrete Fourier Transform...

Ngày tải lên: 13/09/2012, 10:20

... volitans The volitan lionfish is the one most often found in the aquarium trade. It gets accustomed to dead foodstuffs. The membrane linking the spokes of the pectoral fins runs to the rear end of their body, ... the live prey that make up their diet. They are usually found in fairly shallow water. They can raise themselves slightly by supporting themselves on their ventral fins. Their cylindrical body is ... because they can blow up their bodies. Easy to keep, they feed on crustaceans and mollusks. They are aggressive towards members of their own species, but are placid in the company of other fish. Canthigaster...

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Ngày tải lên: 24/12/2013, 01:18

... about the furthest parts of the universe. Q6 practice 2 W: After World War II, the city of Berlin was divided into four parts. One part was controlled by each of the countries that won the war; ... Berlin. All during the 1950s, people living in the communist part of Berlin could see that life was better for people living in the capitalist part of the city, so they moved to the west side. As ... called the Hubble telescope, orbits the Earth in space and is used to study the furthest sections of the universe. Sample response: In this lecture, the professor talks about telescopes. The first...

Ngày tải lên: 24/12/2013, 02:16