Fourier Transforms in Radar and Signal Processing 4 pdf

... 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 − ... 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 P...

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... 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 is in the form of a Fourier series, ... 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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... 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 3. 14, the difference of the expo- nential terms ... bandwidth. Thus, any sampling rate greater than 2W is also adequate. Figure 4. 1 Gated repeated waveform. 74 Fourier Transforms in Radar and Signal Process...

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... will in fact sample correctly, but at the cost, compared with Hilbert sampling, of requiring an increased 76 Fourier Transforms in Radar and Signal Processing sampling rate, the rate depending ... [− ␲ in( k − 1 ⁄ 2 )] or −i n for k odd and i n for k even. However, sampling with a finite window width on a high IF may require 82 Fourier Transforms in Radar and Sig...

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... (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 14 Fourier Transforms in Radar and Signal Processing 5.3.3 ... by 98 Fourier Transforms in Radar and Signal Processing Figure 5.8 FIR interpolation weights with oversampling. Figure 5.9 Trapezoidal spectral gate. 10...

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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), 0.684f s / ␴ (+1, ... it is 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 Signal...

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... Transforms in Radar and Signal Processing Figure 6. 14 Difference beam response: (a) difference beam with narrowband weights; (b) difference beam with equalization. 142 Fourier Transforms in Radar and Signal ... bandwidths, we simply see that the initial 144 Fourier Transforms in Radar and Signal Processing Figure 6.9 Sum beam response with frequency o...

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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. 176 Fourier Transforms in Radar ... raised cosine weighting (solid line). 180 Fourier Transforms in Radar and Signal Processing and the weight function, given by the Fourier transfor...

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... 47 49 Narrowband rectangular, 49 defined, 137 regular RF train, 58–59 steering, 147 rounded, 49 –53 Narrowband waveforms, 24 symmetrical trapezoidal, 40 41 Hilbert transformer and, 74 symmetrical triangular, 41 44 spectra, ... 121gain response against frequency offset, 156 Gaussian, 120 for interpolation, 91, 109with narrowband weights, 1 54 196 Fourier Transforms in Rada...

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... 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 Signal Processing Figure 3.9 Raised cosine ... 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) edge...

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