Fourier Transforms in Radar And Signal Processing_5 doc

... 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) dx = ͵ ∞ −∞ sinc 2 xdx= ... 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 Signa...

Ngày tải lên: 18/06/2014, 10:05

... 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 and 0.3T ; and (b) edges...

Ngày tải lên: 18/06/2014, 10:05

... near +f 0 . 66 Fourier Transforms in Radar and Signal Processing by specifying that U should have no power outside a certain frequency interval, and that there should be no overlapping when U 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 3....

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 ... 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 sa...

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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 114 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. 102 Fouri...

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... 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 results in the field of interpolation ... series, providing insight into the underlying principles. The first main application was to find the FIR filter weights that would provide interpolation for any band-limited s...

Ngày tải lên: 18/06/2014, 10:05

... ] ͮ (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 transform of...

Ngày tải lên: 18/06/2014, 10:05

... signal power here (from the definition of W ), 54 Fourier Transforms in Radar and Signal Processing Figure 3.14 Rising edge as the difference of two Ramp functions. 68 Fourier Transforms in Radar ... required pulse train (Figure 3.19). Again we take T for the pulse repetition interval, ␶ for 56 Fourier Transforms in Radar and Signal Processing Using T 0 and...

Ngày tải lên: 18/06/2014, 15:20

... required. Figure 4.13 Lines of relative sampling rates. 82 Fourier Transforms in Radar and Signal Processing above, in particular from the point of view of finding the minimum sampling rate needed to ... is given by Hilbert sampling and quadrature sampling, discussed 84 Fourier Transforms in Radar and Signal Processing care, as discussed in the next section, and...

Ngày tải lên: 18/06/2014, 15:20

... effect of bandwidth: (a) 10% bandwidth; and (b) 200% bandwidth. 156 Fourier Transforms in Radar and Signal Processing Figure 6.15 Difference beam gain response against frequency offset: (a) linear ... wider signal bandwidths require proportionally higher sampling rates (further raised by oversampling.) 162 Fourier Transforms in Radar and Signal Processing also usef...

Ngày tải lên: 18/06/2014, 15:20

... weights. 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. 174 Fourier Transforms in Radar ... ± ␪ 0 /2 and the corresponding u 0 value is given by 172 Fourier Transforms in Radar and Signal Processing take the amplitudes of the sinc functions at ±...

Ngày tải lên: 18/06/2014, 15:20

... convolution is shown in Figure 3.4, with A = 1 and T = 1 in this case.) 28 Fourier Transforms in Radar and Signal Processing 4. ͐ ∞ −∞ sinc (x − m) sinc (x − n) dx = ␦ mn Using the result in item 3 above, ... (2.24) 14 Fourier Transforms in Radar and Signal Processing Figure 2.2 sinc functions: (a) sinc (x); (b) A sinc [( f − f 0 )/F ]. function than sin x/x, w...

Ngày tải lên: 19/06/2014, 22:20

... 52 Fourier Transforms in Radar and Signal Processing Figure 3.13 Power spectra for rect and exponential impulse responses. 36 Fourier Transforms in Radar and Signal Processing P2b: From P2a and ... = ∑ ∞ n =−∞ u(nX ) exp (−2 ␲ inXy) 32 Fourier Transforms in Radar and Signal Processing This is in the form of a Fourier series, with period 1/X = Y, an...

Ngày tải lên: 19/06/2014, 22:20

... − ␣ )Y ] 102 Fourier Transforms in Radar and Signal Processing Figure 5.11 Trapezoidal rounding. w r ( ␶ ) = ␾ [(r − ␳ )T ′] = sinc x sinc (1 − ␣ )y sinc ␣ y (5.21) = sin X sin Y 1 sin Y 2 XY 1 Y 2 where ... by 106 Fourier Transforms in Radar and Signal Processing Figure 5.14 Filter weights with oversampling and raised cosine rounded gate. 111 Interpolation for Delay...

Ngày tải lên: 19/06/2014, 22:20

... modified, 80–81 198 Fourier Transforms in Radar and Signal Processing Rules and pairs method (continued) Sinc functions, 3, 13–15, 125 amplitudes, 172regular linear arrays and, 187 uses, 2 convolution, ... adaptive interference cancellation, particularly for radar; adaptive arrays; superresolution parameter estimation; and, recently, blind signal separation. 191 186 Fourie...

Ngày tải lên: 19/06/2014, 22:20