Fourier Transforms in Radar And Signal Processing_4 ppt

... 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...

Ngày tải lên: 18/06/2014, 10:05

... (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...

Ngày tải lên: 18/06/2014, 10:05

... 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

... 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; ... Transforms in Radar and Signal Processing Figure 6.14 Difference beam response: (a) difference beam with narrowband weights; (b) difference beam with equalization. 142...

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

... 190 Fourier Transforms in Radar and Signal Processing time processing, and more comprehensive simulations. Cost could also be a significant factor, particular for real-time signal processing—it ... oversampling (only by a relatively small factor in some cases) in reducing the amount of computation needed in the signal processing under consideration. As computing speed...

Ngày tải lên: 18/06/2014, 10:05

... 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 ... 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, and the coeff...

Ngày tải lên: 18/06/2014, 15:20

... 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

... sampled with a finite window. 92 Fourier Transforms in Radar and Signal Processing u(t) = F sinc (Ft) ⊗ 1 F comb 1/F u(t) = sinc (t /T ) ⊗ comb T u(t) (5.2) where T is the sampling period and T = 1/F. ... required. Figure 4.13 Lines of relative sampling rates. 90 Fourier Transforms in Radar and Signal Processing mean square error (or error in power) between the int...

Ngày tải lên: 19/06/2014, 22:20

... Transforms in Radar and Signal Processing Figure 6.8 Sum beam frequency response; effect of bandwidth: (a) 10% bandwidth; and (b) 200% bandwidth. 144 Fourier Transforms in Radar and Signal Processing Figure ... the initial 146 Fourier Transforms in Radar and Signal Processing spectrum. The filter length has been kept at 9 in Figure 6.10(b), and the rela...

Ngày tải lên: 19/06/2014, 22:20

... 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. 182 Fourier Transforms in Radar and Signal ... Fourier Transforms in Radar and Signal Processing where ␲ snc 1 is the derivative of the sinc function, as defined in Section 6.3 above [see (6.17)]. U...

Ngày tải lên: 19/06/2014, 22:20