Fourier Transforms in Radar and Signal Processing 6 pdf

... 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 Processing Taking the particular ... 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 ͵ ∞...

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... − 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 exponential impulse responses. 32 Fourier Transforms in Radar and Signal ... for integral. 46 Fourier Transforms in Radar and Signal Processing Figure 3.8 Asymmetric trapezoidal pulse spectra: (a) edges 0.2T...

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... ′>W, corresponding to sampling at the rate W ′, we still have a nonoverlap- Figure 4.9 rep W V ( f ) near +f 0 . 66 Fourier Transforms in Radar and Signal Processing by specifying that U should ... 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 Fi...

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... 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 ... will in fact sample correctly, but at the cost, compared with Hilbert sampling, of requiring an increased 76 Fourier Transforms in Radar and Signal Processi...

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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 114...

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... Transforms in Radar and Signal Processing snc r ( y) = 1 ␲ r d r dy r sinc ( y) (6. 17) then, from (6. 12), (6. 16) becomes ramp r (x) ⇔ i r snc r ( y) (6. 18) We note from (6. 11) and (6. 16) that we ... usual, using the narrowband condition, to introduce the phase shift ␾ ( ␪ ) = 2 ␲ f 0 ␶ ( ␪ ) = 2 ␲ (d / ␭ 0 ) sin ␪ (6. 29) 140 Fourier Transforms in Radar and Sig...

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... difference to the integrals in (6. 6) and (6. 7). Thus, we can replace S by S( f ) rect ͩ f F ͪ = ͫ rect ͩ f F ͪ + ␾ 2 ramp ͩ f F ͪͬ exp (2 ␲ if ␶ ) (6. 37) Putting this into (6. 6) and (6. 7) (in place of ... However, 141 Equalization Figure 6. 7 Array response with equalization: (a) five taps, 20% oversampling; and (b) four taps, 50% oversampling. 1 56 Fourier Transforms in...

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... ] ͮ (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; (b) angle space. 1 76 Fourier Transforms in Radar ... and the corresponding u 0 value is given by 170 Fourier Transforms in Radar and Signal Processing where ␲ snc 1 is the derivative of the sinc fun...

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... with oversampling and, Wiener-Khinchine relation, 26 27, 111 Woodward, P. M., 2–3, 65 103 198 Fourier Transforms in Radar and Signal Processing Rules and pairs method (continued) Sinc functions, ... of, 16 continuous, 167 , 187 properties, 15 discrete, 187 scaled, 16 17 phase shift, 162 in time-domain, 16 sampled, 164 Array beamforming, 161 –88 Aliasing basic principles...

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... exp (−2 ␲ inXy) 46 Fourier Transforms in Radar and Signal Processing Figure 3.8 Asymmetric trapezoidal pulse spectra: (a) edges 0.2T and 0.3T ; and (b) edges 0.6T and 0.8T. 37 Rules and Pairs where ... Signal Processing Figure 3.3 Spectrum of low side-lobe trapezoidal pulse: (a) linear form; and (b) logarithmic form. 48 Fourier Transforms in Radar and...

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