Fourier Transforms in Radar and Signal Processing 8 pptx

... y)* dy (2.24) 28 Fourier Transforms in Radar and Signal Processing 4. ͐ ∞ −∞ sinc (x − m) sinc (x − n) dx = ␦ mn Using the result in item 3 above, if m = n the integral is ͵ ∞ −∞ sinc 2 (x − n) ... from the rules. Writing out Rule 7 using the definitions of Fourier transform and convolution [(2.1) and (2.15)] gives 26 Fourier Transforms in Radar and Signal...

Ngày tải lên: 18/06/2014, 10:05

... Rising edge of width ␶ . 52 Fourier Transforms in Radar and Signal Processing Figure 3.13 Power spectra for rect and exponential impulse responses. 32 Fourier Transforms in Radar and Signal Processing This ... for integral. 46 Fourier Transforms in Radar and Signal Processing Figure 3 .8 Asymmetric trapezoidal pulse spectra: (a) edges 0.2T and 0....

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... containing energy at all frequencies from zero up to some maximum W beyond which there is no 58 Fourier Transforms in Radar and Signal Processing As a check, we note that if we used a single ... examples demonstrate various ways of applying the method to yield solutions neatly and concisely without any explicit integration. 68 Fourier Transforms in Radar and Sig...

Ngày tải lên: 18/06/2014, 10:05

... sampling with a finite window width on a high IF may require 82 Fourier Transforms in Radar and Signal Processing above, in particular from the point of view of finding the minimum sampling rate needed ... interpolating function. The minimum required sampling rate, relative to the minimum rate, equal to the bandwidth W,isr = W ′/W = 1 + ␣ /k 80 Fourier Transforms in R...

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... by 98 Fourier Transforms in Radar and Signal Processing Figure 5 .8 FIR interpolation weights with oversampling. Figure 5.9 Trapezoidal spectral gate. 102 Fourier Transforms in Radar and Signal Processing Figure ... (5.24) = sinc x ͫ sinc y + 1 2 sinc ( y − 1) + 1 2 sinc ( y + 1) ͬ Putting sinc ( y ± 1) = sin ␲ ( y ± 1) ␲ ( y ± 1) = −sin ␲ y ␲ ( y ± 1) we have 1...

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... 120 Fourier Transforms in Radar and Signal Processing Let the number of taps in the interpolation filter be m and the number in the Gaussian FIR filter is, from (5.50), 0. 684 f s / ␴ (+1, ... to 122 Fourier Transforms in Radar and Signal Processing 5.6 Summary In this chapter we have shown how the rules -and- pairs method can be used to obtain simply resul...

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... 20% oversampling; and (b) four taps, 50% oversampling. 156 Fourier Transforms in Radar and Signal Processing Figure 6.15 Difference beam gain response against frequency offset: (a) linear response; ... though of course wider signal bandwidths require proportionally higher sampling rates (further raised by oversampling.) 1 48 Fourier Transforms in Radar and Signal...

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... raised cosine weighting (solid line). 180 Fourier Transforms in Radar and Signal Processing and the weight function, given by the Fourier transform of (7. 28) , is a(x) = (u 0 /U ) comb 1/U [sinc (u 0 x) ... ] ͮ (7.9) 1 68 Fourier Transforms in Radar and Signal Processing Figure 7.3 Beam patterns for uniform linear array with raised cosine shading: (a) u -spa...

Ngày tải lên: 18/06/2014, 10:05

... with oversampling and, Wiener-Khinchine relation, 26–27, 111 Woodward, P. M., 2–3, 65103 1 98 Fourier Transforms in Radar and Signal Processing Rules and pairs method (continued) Sinc functions, ... 190 Fourier Transforms in Radar and Signal Processing time processing, and more comprehensive simulations. Cost could also be a significant factor, particular fo...

Ngày tải lên: 18/06/2014, 10:05

... trapezoidal pulse: (a) linear form; and (b) logarithmic form. 48 Fourier Transforms in Radar and Signal Processing Figure 3.9 Raised cosine pulse: (a) normalized waveform; and (b) normalized spectrum. frequency ... 2B.1 Contour for integral. 32 Fourier Transforms in Radar and Signal Processing This is in the form of a Fourier series, with period 1/X = Y,...

Ngày tải lên: 18/06/2014, 15:20