Fourier Transforms in Radar And Signal Processing 6 doc
Fourier Transforms in Radar And Signal Processing_2 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
͵
∞...
Fourier Transforms in Radar And Signal Processing_3 pot
... −
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...
Fourier Transforms in Radar And Signal Processing_4 ppt
... ′>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...
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 Processi...
Fourier Transforms in Radar And Signal Processing_6 ppt
... 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...
Fourier Transforms in Radar And Signal Processing_7 docx
... 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...
Fourier Transforms in Radar And Signal Processing_8 pdf
... 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...
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.
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...
Fourier Transforms in Radar And Signal Processing_10 pot
... 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...
Fourier Transforms in Radar And Signal Processing_1 ppt
... 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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