Fourier Transforms in Radar and Signal Processing 2 doc

... 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 Si...

Ngày tải lên: 18/06/2014, 10:05

... of the signum function used in obtaining P2a, and the comb and rep transforms. Figure 2B.1 Contour for integral. 46 Fourier Transforms in Radar and Signal Processing Figure 3.8 Asymmetric trapezoidal ... h ͩ t − T 2 ͪ (3.9) Figure 3.6 Rising edge of width ␶ . 52 Fourier Transforms in Radar and Signal Processing Figure 3.13 Power spectra for rect and e...

Ngày tải lên: 18/06/2014, 10:05

... the information in the waveform is retained by sampling it at a rate 2rW, where r is given in (4.13) above. 56 Fourier Transforms in Radar and Signal Processing Using T 0 and ⌬T as given in Figure ... for t > 0 (t ∈ޒ) (3 .21 ) 72 Fourier Transforms in Radar and Signal Processing Figure 4.7 Maximum sampling rate. 2f u /k = 2( k + ␣ )W /k ≤ 2W ′ 2( k −...

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 ... discussed 88 Fourier Transforms in Radar and Signal Processing v(t) = cos 2 ␲ f 0 t + i sin 2 ␲ f 0 t = exp 2 ␲ if 0 t and so V ( f ) = ␦ ( f − f 0 )...

Ngày tải lên: 18/06/2014, 10:05

... by 98 Fourier Transforms in Radar and Signal Processing Figure 5.8 FIR interpolation weights with oversampling. Figure 5.9 Trapezoidal spectral gate. 1 02 Fourier Transforms in Radar and Signal Processing Figure ... exp ͫ − ␲ ΀ 2 ␴ √ ␲ t ΁ 2 ͬ = exp (−4 ␲ 2 ␴ 2 t 2 ) (5.48) 110 Fourier Transforms in Radar and Signal Processing p = ͵ ∞ −∞ |...

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... = ∑ ∞ n = 0 (−1) n ( ␲ y) 2n (2n + 1)! (6 .23 ) snc 1 ( y) = ∑ ∞ n = 0 (−1) n 2n( ␲ y) 2n − 1 (2n + 1)! = ∑ ∞ n = 1 (−1) n 2n( ␲ y) 2n − 1 (2n + 1)! (6 .24 ) snc 2 ( y) = ∑ ∞ n = 0 (−1) n 2n(2n − 1)( ␲ y) 2n − 2 (2n + ... 1)! = ∑ ∞ n = 1 (−1) n 2n(2n − 1)( ␲ y) 2n − 2 (2n + 1)! (6 .25 ) In general, we can put snc r ( y) = ∑ ∞ n = [(r + 1) /2] (−1) n 2n!( ␲ y) 2n − r (2n − r)!(2n + 1)...

Ngày tải lên: 18/06/2014, 10:05

... ramp 2 ( f /F ) with rect[2f /(1 + a)] is [(1 + a) /2] 2 ramp 2 [2f /(1 + a)], and, again using (6.18), the transform is given by ␳ c (t) =− ͩ 1 + a 2 ͪ 2 snc 2 ͫ (1 + a)Ft 2 ͬ sinc ͫ (1 − a)Ft 2 ͬ (6.47) Using ... taps, 20 % oversampling; and (b) four taps, 50% oversampling. 156 Fourier Transforms in Radar and Signal Processing Figure 6.15 Difference beam ga...

Ngày tải lên: 18/06/2014, 10:05

... 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) 168 Fourier Transforms in Radar and Signal Processing Figure 7.3 Beam patterns for uniform linear array with raised cosine shading: (a) u -space;...

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... 127 coefficients, 119, 121 gain response against frequency offset, 156 Gaussian, 120 for interpolation, 91, 109with narrowband weights, 154 196 Fourier Transforms in Radar and Signal Processing Least ... 125 resampling and, 120 21 rep, 17–18 spectrum independent, 90–107 repeated, overlapping, 169 summary, 122 23 sinc, 3, 13–15, 125 worst case for, 93 sketches, 4 Inverse...

Ngày tải lên: 18/06/2014, 10:05

... exp ( 2 ␲ ixy) dx = ͵ 1 /2 − 1 /2 exp ( 2 ␲ ixy) dx = exp ( 2 ␲ ixy) 2 ␲ iy | 1 /2 − 1 /2 = exp (− ␲ iy) − exp ( ␲ iy) 2 ␲ iy = −2i sin ( ␲ y) 2 ␲ iy = sinc ( y) P3b: From P3a and R4, using rect ... transforms. Figure 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