Fourier Transforms in Radar And Signal Processing_5 doc
Fourier Transforms in Radar And Signal Processing_2 pdf
... 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...
Fourier Transforms in Radar And Signal Processing_3 pot
... 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...
Fourier Transforms in Radar And Signal Processing_4 ppt
... 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....
Fourier Transforms in Radar And Signal Processing_5 doc
... 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...
Fourier Transforms in Radar And Signal Processing_6 ppt
... (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...
Fourier Transforms in Radar And Signal Processing_7 docx
... 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...
Fourier Transforms in Radar And Signal Processing_9 doc
... ]
ͮ
(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...
Fourier Transforms in Radar And Signal Processing_2 docx
... 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...
Fourier Transforms in Radar And Signal Processing_3 doc
... 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...
Fourier Transforms in Radar And Signal Processing_6 doc
... 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...
Fourier Transforms in Radar And Signal Processing_7 doc
... 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 ±...
Fourier Transforms in Radar and Signal Processing_1 doc
... 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...
Fourier Transforms in Radar and Signal Processing_2 doc
... 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...
Fourier Transforms in Radar and Signal Processing_5 pdf
... −
␣
)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...
Fourier Transforms in Radar and Signal Processing_9 doc
... 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...
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