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of this spike gives fine frequency resolution-it is a
frequency vernier. The frequency resolution in the v
direction is
where
-r/r,
AV = _ A6oo =
-X/_p
2rt Vc
Vc
A_oo =
2_p
For N signal scan lines, the total temporal duration of
the signal within the input window is T = Nb/V.
According to Thomas, there are at least N resolution
elements along a frequency locus within Ivl _< kf[2c.
Thus Av = _f[Nc which gives a frequency resolution of
The output format consists of a family of frequency
loci as shown in Figure 11-2. For a given signal
component at wo the output display is a set of bright
spots spaced _f/c apart along the line u = (?,f/2rrlOtOo.
The row of spots moves downward with increasing Wo.
As one spot moves below v = -(?_¢/2c), another crosses
downward through v = (hf/2c) on the next higher frequency
locus. There is always one spot within iv[ < _ff'/2c
and its location determines _Oo.
The input scan line cross section was assumed to be
rectangular in the above discussion; this introduced a
sinc 2 weighting of the spectral display in the v direction. In
practice, the scan lines will not have a rectangular cross
section and the spectral weighting will not be sinc 2. In
general, if the cross-section distribution is _(.v/a), then
the spectral weighting will be I_l(av/Xf) 2 where _b(r/) is
the Fourier transform of _b(_).
Vc
p=--Av=
kfo
V
Nb
REFERENCES
or
1
p = --
T
We see that the frequency resolution achieved is as good
as can theoretically be expected, the reciprocal of the
integration time.
1. Goodman, J.W.: Introduction to Fourier Optics.
Chap. 8, McGraw-Hill 1968.
2. Thomas, Carlton E.: Optical Spectrum Analysis of
Large Space Bandwidth Signals. Applied Optics, 5,
1966, p. 1782.
3. Markevitch, Bob. V.: Optical Processing ofWideband
Signals. Third Annual Wideband Recording Symposium,
Rome Air Development Center, April 1969.
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