Calibrated radio frequency analog spectrum analyzer

An analog radio frequency spectrum analyzer (10) includes a calibration section (30) for compensating distortions. The spectrum analyzer includes a first reflective array compressor or "RAC" (12), a frequency sweep section (20), and a second RAC (14). Frequency domain compensations introduced at the signal input by the calibration section compensate distortions in the time domain at the output of the spectrum analyzer. This system corrects, for example, nonlinearities in the second RAC. The calibration function is determined by a network analysis of the spectrum analyzer and is specific to the RAC included. The function is stored in a ROM or other memory as a sequence of complex digital words. An address generator (36) directs the words to a complex multiplier (32) so that each input symbol period is multiplied by the sequence. Each complex digital word corresponds to an amplitude and phase modulation of the incoming signal over a fraction of a symbol period. The resulting output of the spectrum analyzer is that which would be expected without calibration given an ideal second RAC.

BACKGROUND OF THE INVENTION 
The present invention relates to spectrum analyzers and, more particularly, 
to a calibrated radio frequency analog spectrum analyzer. 
Analysis of signals in the frequency domain is widely used to obtain 
physical and electrical system performance information. For example, 
manufacturers of mechanical structures, such as aircraft and bridges, can 
use a motion-to-electrical signal transducer. A spectrum analysis of the 
resulting signal can permit monitoring of vibration components associated 
with imbalance and worn bearings and gears. In addition, a system's 
natural modes of vibration can be identified. 
Spectrum analyzers are also used in electronic testing to assess non-linear 
effects of amplification, mixing and filtering, to determine the purity of 
signals, to measure radio frequency power, frequency and modulation 
characteristics, and to provide amplitude analysis of electrical networks. 
In telecommunications, transceivers and multiplex systems are assessed 
with respect to their spectrum, modulation, wave and audio 
characteristics. 
Of central concern herein, is the use of spectrum analyzers for determining 
the spectral components of a radio frequency (rf) signal. A communications 
system, for example, can incorporate such a spectrum analyzer to transform 
a frequency division multiplexed (FDM) signal to a time division 
multiplexed (TDM) signal. 
Spectrum analysis can be performed digitally by employing a Fourier 
transformation. For some applications, the computational power 
requirements for a desired input bandwidth are impractical. This is 
particularly true in satellite communications where system power and 
weight are severely constrained. In addition, the digital processing 
introduces undesirable delays. Furthermore, it is difficult to build 
sufficiently high speed analog-to-digital converters. 
Analog spectrum analyzers offer the prospect of near real time 
transformations without great demands on processing power. Traditional 
analog spectrum analyzers either employ filter banks or swept filters. 
Filter banks are very bulky while swept filters are unsuitable for some 
applications such as demodulators where it is necessary to sample each 
frequency continuously. 
Analog spectrum analyzers are known which include a pair of frequency x 
delay dispersion sections with an intervening frequency sweep section. The 
first dispersion section introduces delays as a function of frequency to 
an incoming signal, such as a FDM signal. The frequency sweep signal 
converts the frequency components of the dispersed FDM signal into a 
series of sweeps. The second dispersion section collapses each sweep into 
a pulse so that the series of sweeps becomes description of the spectrum 
of the input signal. 
The dispersion sections in such devices include devices generically 
classified as dispersive filters. These filters are also known as surface 
acoustic wave (SAW) dispersive or linear frequency modulated chirp 
filters. The first such devices were based on interdigital electrode 
transducers (IDTs). The IDT consists of a set of interleaved metal 
electrodes deposited on the surface of a set of piezoelectric substrate, 
normally quartz. However, IDT based spectrum analyzers have not provided 
the time-bandwidth product sufficient for some satellite communications 
applications. 
More recently, devices with greater time-bandwidth products have been 
provided using reflective array compressors (RACs). The RAC can be 
manufactured by etching into a crystalline substrate, e.g. lithium 
niobate, a multitude of slits, e.g. 8,000, each tuned to reflect a given 
frequency. By reflecting different frequencies at different slits, and 
thus different locations, differential delays are introduced in a 
throughgoing signal as a function of frequency. 
RACs are difficult to manufacture with the precision required for satellite 
applications. Furthermore, the cost of manufacturing a single RAC renders 
impractical the discarding of RACs not meeting design specifications. What 
is needed is an analog spectrum analyzer with the time-bandwidth product 
of RAC based devices, but without vulnerability to RAC imperfections. 
SUMMARY OF THE INVENTION 
In accordance with the present invention, a spectrum analyzer provides for 
compensation of distortions introduced by dispersion filters. The spectrum 
analyzer includes two dispersion sections and an intermediate frequency 
sweep section. A calibration section processes a throughgoing signal 
according to a function corresponding to the distortions introduced by one 
or more of the dispersion sections. 
In one realization of the invention, the spectrum analyzer is designed to 
convert FDM signals to TDM signals. The calibration section preprocesses 
the incoming signal prior to the introduction of delays by the first 
dispersion section. The calibration section processes the signal by 
multiplying it by a calibration function. The calibration function can be 
in the form of a series of complex digital words permitting amplitude and 
phase variations upon the incoming signal. The complex digital words can 
include a sign bit so that inversions as well as scaling can be 
introduced, and so that the power level of the output can be adjusted to 
that of the input. 
The determination of a suitable calibration function is greatly simplified 
by the recognition that the impact of the distortions introduced by the 
first dispersion section is negligible in comparison to those introduced 
by the second dispersion section. Accordingly, the calibration function 
can be determined by a network analysis of the circuit from the frequency 
sweep section through the second dispersion section. The results of the 
network analysis are subtracted from expected ideal values to determine 
the compensation required according to an algorithm disclosed herein. 
Thus, the present invention provides for the compensation of distortions 
introduced by the RACs or other devices in a spectrum analyzer. 
Accordingly, the advantages of high time-bandwidth product analog spectrum 
analyzers are maintained while the problems in manufacturing precision 
RACs are circumvented.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
A spectrum analyzer 10 includes first and second RACs 12 and 14, and an 
intermediate frequency sweep section 20 including a timing generator 22, a 
pulse source 24, a frequency sweep 26, and a bilinear mixer 28. The 
spectrum analyzer 10 serves to convert FDM signals to TDM signals. In 
accordance with the present invention, the spectrum analyzer 10 includes a 
calibration section 30 to compensate for distortions introduced by the 
components of the analyzer, particularly the second RAC 14. 
The calibration section 30 includes a complex multiplier 32 for multiplying 
the incoming signal by a calibration function in the form of a series of 
complex digital words. The calibration function is stored in a memory 34, 
such as a ROM (read only memory). The individual digital words are 
introduced in response to signals from an address generator 36. 
As a signal converter, the spectrum analyzer 10 is itself a component of an 
incorporating communications system which synchronizes the action of the 
address generator 36 of the calibration section 30 and the timing 
generator 22 of the frequency sweep section 20 with the onset of symbol 
periods of the incoming signal. 
In the illustrated embodiment, the incoming FDM signals are more 
specifically characterized as multiplexed frequency shift keyed (MFSK) 
signals within a predetermined frequency range, e.g. the 50 MHz range from 
250 MHz to 300 MHz. Within this range are included a multitude, e.g. 1000, 
narrow band channels, each assignable to a frequency shift keyed (FSK) 
signal. 
Each FSK channel presents a stream of binary data at a predetermined common 
baud rate. All channels switch from one bit or symbol to the next 
simultaneously. By way of example, the baud rate is 10 kHz, with a 
corresponding symbol duration of 100 microseconds. The output of the 
spectrum analyzer 10 is a series of 100 microsecond segments, each 
comprising 1000 "pulse windows" spaced 100 nanoseconds apart. In other 
embodiments, the pulse spacings would be decreased to provide slack 
between TDM segments, and to permit the inclusion of timing information 
within the pulse train. 
In response to cues from the incorporating communications system, the 
timing generator 22 fires the pulse source once per symbol period, e.g. 
every 100 microseconds. Each pulse includes frequency components over the 
desired sweep range, which is twice the frequency range of the incoming 
signal. In the illustrated embodiment, the frequency range of the sweep is 
100 MHz, i.e. 100 MHz to 200 MHz. 
The frequency sweep 26 converts each pulse into a linear sweep with a 
maximum differential delay of twice the symbol period, e.g. 200 
microseconds. In this specific example, the 100 MHz component of a given 
sweep exits the sweep 200 microseconds after the 200 MHz components. Thus 
the output of the frequency sweep 26 is a series of overlapping linear 
sweeps, as represented in FIG. 2. 
The sequential processing of an incoming signal is described in greater 
detail with reference to FIGS. 3a-d. The role of the calibration section 
30 is discussed after the functions of the other sections are detailed. 
The incoming signal is represented in FIG. 3a and comprises 1000 
synchronized FSK signals, each with an assigned channel frequency within 
the allotted 50 MHz range. One set of symbol segments, each 100 
microseconds long, is illustrated. 
The purpose of the first RAC 12 is to introduce differential delays as a 
function of frequency into the incoming signal. The same purpose could be 
served by a sequence of RACs or other dispersion filters, such as IDTs. 
The delay introduced at the low end of the incoming signal frequency range 
is one symbol period longer than the delay introduced into the high end of 
the frequency range. The first RAC 12 is nominally linear so that the 
delays nominally introduced at intermediate frequencies are readily 
determined by interpolation. The originally concurrent segments of the 
incoming signal are staggered as they exit the first RAC 12, as indicated 
in FIG. 3b. 
The staggered segments are mixed with the frequency sweep output at the 
bilinear mixer 28. The frequency sweep section 20 is synchronized with the 
incoming signal so that each frequency sweep sweeps an entire set of 
staggered segments. A post mixer filter 42 eliminates the sum term from 
the mixing, so that only the difference term of the product progresses 
through the system. 
A local oscillator 44 generates a translation signal for centering the 
frequency range of the series of sweeps on the center frequency of the 
passband of the second RAC 14, which, in this embodiment is the same as 
that of the first RAC 12. The translation signal, which can have a 
frequency of 150 MHz, is mixed with the series of sweeps at a second mixer 
46. 
The series of sweeps has components outside the approximately 50 MHz 
passband of the second RAC. Hence, many components of the series of sweeps 
are filtered out by the second RAC 14. The components of the sweeps 
entering the second RAC 14 which are not going to be eliminated are 
represented in FIG. 3c. Each series includes 1000 sweeps and has an 
overall duration of 200 microseconds. Each sweep within the series has a 
duration of 100 microseconds. 
The second RAC 14 is nominally identical to the first RAC 12. In other 
words, it introduces differentials as a monotonic function of frequency 
into the throughgoing signal. The maximum differential is 100 microseconds 
between the highest and lowest frequencies of the passband. The effect of 
the second RAC 14 is to "stand up" or collapse each sweep into a pulse. 
The output of the second RAC 14 is a series of pulses, as illustrated in 
FIG. 3d, each pulse corresponding to a sweep and hence to one of the 
original FSK channels. 
The basic operation of the spectrum analyzer 10 having been reviewed, the 
effects of imperfections in the RACs 12 and 14 are now considered. 
Imperfections in a RAC can result in amplitude and phase deviations from 
the nominal monotonic, e.g. linear delay x frequency, function of the RAC. 
Phase distortions introduced by the first RAC 12 result in relative timing 
shifts of the individual channels. In other words, a particular segment of 
a given channel could be advanced or retarded relative to its nominally 
expected position. Where the segment is advanced, the corresponding sweep 
includes more low frequency and less high frequency content than expected. 
Likewise, where a segment is retarded, the corresponding sweep includes 
more high frequency and less low frequency content than expected. 
However, within the anticipated range of distortions, all the components 
within the passband of the second RAC 14 are present at its input and 
arrive at the proper time. Thus, errors introduced by the first RAC 12 
are, for the most part, eliminated by the filtering action of the second 
RAC 14 and have negligible impact on the output of the spectrum analyzer 
10. 
Amplitude distortions introduced by the first RAC 12 result in constant 
relative attenuation differentials between channels. However, there is 
essentially no impact on amplitude differentials between successive 
symbols within a channel. In practice these errors are not problematic, 
and in any event can be dealt with in the design of the readout (not 
shown) of the spectrum analyzer 10. 
Distortions introduced by the second RAC 14 can contribute significantly to 
intersymbol interference, and thus impair the performance of the spectrum 
analyzer 10. Phase distortions introduced by the second RAC 14 result in 
the misalignment of the frequency components of the pulse outputs. In 
other words, the durational centers of the frequency components of a given 
component will occur at slightly different times. This results in symbol 
spreading which in turn contributes to intersymbol interference. 
Furthermore, pulse height is reduced impairing the signal-to-noise ratio 
of the system. 
Amplitude distortions affect the frequency distribution of the pulses. 
Since certain frequency distribution permit better differentiation of 
successive pulses, amplitude distortion also contributes to intersymbol 
interference. 
The character of a spectrum analyzer is such that the frequency-varying 
time deviations at its outputs can be precompensated by introducing 
complementary time-varying frequency deviations at its input. Furthermore, 
time-varying amplitude control over the input permits control over output 
pulse shape so that intersymbol interference can be minimized. 
The premodulation can be applied by multiplying the incoming signal by a 
complex time-varying function. Since the function is complex, both phase 
and amplitude can be modified. In the illustrated embodiment, the complex 
multiplier 32 is designed to multiply the incoming analog signal by a 
series of complex digital words, including a sign bit. Thus the 
calibration function is represented in a memory by a series of complex 
digital words, numbering, for example, 128. These are applied seriatum in 
response to signals from the address generator 36. 
The series of digital words, or the calibration function in whatever form 
it takes, is tailored to the specific second RAC 14. In order to determine 
the calibration function to be applied by the complex multiplier 32 to the 
incoming signal, the calibration set up of FIG. 4 is used. A frequency 
synthesizer 52 is used to introduce a sine wave at the signal input while 
a network analyzer 54 introduces a sine wave input into the frequency 
sweep 26. The network analyzer 54 provides a phase and amplitude function 
of frequency. 
In order that the frequency of the network analyzer input and output are 
matched, two mixers 56 and 58 are provided. One of these mixers 56 
parallels the function of the translation mixer 46, stepping the input up 
by the translation frequency. The lower sideband of the mixer 56 is 
rejected by the following filter 60, which thus parallels the filtration 
function of the second RAC 14. 
The spectrum analyzer output is mixed with the translated reference output 
of the filter 60 and the other added filter 62 rejects the upper sideband 
of the mixer 58. The retained lower sideband is at the frequency of the 
network analyzer output. The network analyzer 54 determines the amplitude 
and phase changes in its signal and the results are stored in the 
computer. This process is iterated through small frequency steps through 
the range of the frequency sweep. The result is a phase shift and 
amplitude function of frequency stored in a computer 64. 
Preferably, the network analyzer 54 is used to determine the transfer 
characteristics of the second added filter 62. The resulting phase and 
amplitude function is then subtracted by the computer from the system 
transfer characteristic. In this way, any distortions introduced by the 
filter 62, which is not part of the spectrum analyzer, are ignored in 
determining the calibration function. 
The purpose of the calibration function is to predistort the incoming 
signal so as to minimize intersymbol interference in the TDM output. 
Intersymbol interference can be minimized where the individual pulses have 
a frequency distribution corresponding to a Kaiser-Bessel weighting 
function W(f). In the illustrated embodiment a Kaiser-Bessel window with 
a=1.7156 is used. 
The transfer function determined by the network analysis is characterized 
in terms of complex Legendre Polynomials and the linear phase term is 
subtracted. Then this modified transfer characteristic of the converter is 
expanded in a set of polynomials R.sub.i (f), where is the set of 
nonnegative integers. The R polynomials satisfy the following conditions: 
##EQU1## 
Experience has shown that where the linear phase term is removed, as 
above, fewer than ten term are required to represent the transfer 
characteristic. A correction exponent is then formed: 
EQU C.sub.o R.sub.o (f,t).times.[C.sub.o R.sub.o (f,t)+C.sub.1 R.sub.1 (f,t)+ . 
. . +C.sub.9 R.sub.9 (f,t)].sup.-1 
The coefficients are derived from the integral over the system pass band of 
the weighted signal function and the R polynomials, i.e. 
##EQU2## 
Note that if S(f) is complex, C.sub.k is a complex constant. 
The calibration function is the natural logarithm, e, raised to the 
correction exponent. In the illustrated embodiment, the correction factor 
is evaluated at 128 times during a symbol period and applied to the 
incoming signal the same number of times. The calibration function is 
stored in the memory 34 in the form of complex digital words, and fed to 
the complex multiplier 32 in response to timing and address cues from the 
address generator 36. The address generator 36 itself responds to system 
timing information from the communications system incorporating the 
spectrum analyzer. The calibration function can be checked by resetting 
the frequency synthesizer 52 at different points in the passband of the 
first RAC 12. 
In accordance with the foregoing, a high time-bandwidth product radio 
frequency analog spectrum analyzer incorporates a calibration section to 
compensate for distortions introduced by analog dispersion sections. The 
invention provides for many alternatives including, analog instead of 
digital representation of the calibration function and different location 
of the calibration section, are available. Also, the functions performed 
by single RACs can be distributed among plural RACs or performed by 
different dispersion means. Accordingly, the scope of the invention is 
limited only by the following claims.