Abstract:
Communication apparatus and method that includes generating a series of successive spread-spectrum chirp signals, which are progressively swept within a defined bandwidth. The chirps are divided into two frequency-swept portions, one beginning at an intermediate frequency within the bandwidth being swept to one end of the frequency range of the chirp, and a second beginning at the other end of the frequency range and being swept to the intermediate frequency. This has the effect of moving the frequency transition from the boundaries of the chirp to its center, with the result that the discontinuities introduced at the boundaries by phase reversals due to successive modulated chirps generate less out-of-band energy. In preferred embodiments, the full frequency range of the chirp is at least about two octaves (two doublings of frequency), and the intermediate frequency is at least about one octave (one doubling of frequency) from the either end of the range, whereby the one-half and double frequency components that result from phase reversals remain within the band. The method and apparatus may be used for communication over power lines.

Description:
Cross Reference To Related Applications 
     This application is related to co-pending application entitled TIMING FOR SPREAD-SPECTRUM NETWORK COMMUNICATION, Ser. No. 07/863,213, filed Apr. 3, 1992, and herein incorporated by reference. 
     BACKGROUND OF THE INVENTION 
     This application relates to chirp spread-spectrum communication systems and in particular to chirp spread-spectrum communication systems for use on noisy network media such as power lines where signal energy must be tightly contained within a frequency band. 
     Spread-spectrum communication is a method whereby information is communicated using a bandwidth that greatly exceeds that required by information theory. These methods provide signals over a wide bandwidth, and with proper signal processing the communication is immune to large amounts of noise within that bandwidth. In chirp spread-spectrum methods, a signal burst known as a chirp is transmitted. Each chirp has energy spread across a frequency range. The frequency spread may be achieved by frequency sweeping or by other known techniques (such as direct sequence). Chirps may be sent asynchronously, or at synchronous intervals, including as concatenated chirps. Data modulation of the chirp stream can be accomplished by means such as phase reversal modulation of the chirps or reversal of the frequency sequence of the chirp. A transversal filter in the receiver is matched to the chirp(s) expected, enabling individual chirps to be detected even on noisy network media such as power lines. 
     In some applications of this communications method, it is necessary or desirable that the energy of the signal beyond the nominal signalling bandwidth be kept to a very low level. For example, conducted signal energy on the power line must be below 1000 uV in the frequency range of 535 Khz to 1710 Khz to meet FCC part 15 requirements for carrier current systems. If a wideband chirp signal of substantial energy is desired, say from 100 Khz to 400 Khz, the out-of-band energy must diminish very rapidly to meet these requirements. The alternative is to limit the transmitted signal strength, which inhibits performance. Conventional spread spectrum signalling techniques cannot normally accomplish this without the addition of costly filtering. 
     Another example where tightly contained signal energy is important is when adjacent wideband signalling bands are to be used. For example, it may be desirable to have a wideband chirp signal having a frequency span of 20 Khz to 80 Khz used on the same power line as a 100 Khz to 400 Khz wideband chirp signal. The simultaneous use of adjacent bands is feasible if the out-of-band energy of each is highly constrained so as not to limit the dynamic range of the other. The same chirp signal format can be used for both bands by simply slowing the 100 Khz to 400 Khz chirp signal generation source by a factor of five. In this instance, each of the signals has the same information theory processing gain, but the lower band (20 Khz to 80 Khz) has a signal power density five times that of the higher band (100 Khz to 400 Khz) and a data rate that is one fifth the higher band. 
     In both examples given, it is more important that the high frequency portion of the band be the most tightly constrained. In the first case, the FCC part 15 limits are effective at the higher end of the 100 Khz to 400 Khz band, and in the second case, the signal energy is five times greater in the lower band than in the adjacent upper band, allowing the higher band to have more of its lower end signal energy leak into the high end of the lower band and more tightly constraining the higher end of the lower band limits of its signal energy leaking into the lower end of the higher band to have commensurate performance. 
     In my previous patent entitled SPREAD-SPECTRUM COMMUNICATIONS SYSTEM FOR NETWORKS, U.S. Pat. No. 5,090,024, herein incorporated by reference, a system is proposed for communicating over power lines and the like that employs chirp spread-spectrum communication techniques. 
     SUMMARY OF THE INVENTION 
     In a first aspect, the invention features dividing the chirp into two frequency-swept portions, one beginning at an intermediate frequency within the bandwidth being swept to one end of the frequency range of the chirp, and a second beginning at the other end of the frequency range and being swept to the intermediate frequency. This has the effect of moving the frequency transition from the boundaries of the chirp to its center, with the result that the discontinuities introduced at the boundaries by phase reversals due to successive modulated chirps generate less out-of-band energy. In preferred embodiments, the full frequency range of the chirp is at least about two octaves (i.e., two doublings of frequency), and the intermediate frequency is at least about one octave (i.e., a doublings of frequency), from either end of the range, whereby the one-half and double frequency components that result from phase reversals remain within the band. 
     In a second aspect, the invention features reducing out-of-band energy components in swept-frequency chirp communication systems, by smoothing the abrupt changes in frequency that occur at the frequency transitions between frequency swept portions. 
     In a third aspect, the invention features reducing out-of-band energy components by altering the shape of a progressively swept frequency chirp waveform by using as the waveform the product of truncating the frequency spectrums resulting from a series of non-phase-reversed chirp signals and a series of repeatedly phase-reversed chirp signals, transforming the truncated spectrums into the time domain, averaging the resulting frequency-truncated chirp signals, and repeating the truncating, transforming, and averaging steps. The waveform produced by these steps is typically further filtered before being placed on the communication channel. 
     In preferred embodiments, the chirp signals have specific waveforms defined by the values of tables in the specification. The chirps are amplified, further filtered, and coupled to AC power lines, and the frequency ranges of the chirps is 100 KHz to 400 KHz or 20 KHz to 80 KHz. Chirps of both frequency range can be transmitted simultaneously. The values of Table 2 are representative of the actual resultant waveform values obtained with the preferred embodiment as sampled on the AC power line. 
     The invention achieves the advantages of chirp spread-spectrum communication with a chirp waveform that produces reduced levels of out-of-band frequency components. The several aspects of the invention may be used individually, or together for added effectiveness. By reducing the level of out-of-band frequency components, the required FCC part 15 out-of-band limits may be achieved without costly filtering, and concurrent use of closely-spaced adjacent signalling bands is possible. 
     Other advantages and features of the invention will be apparent from the following description of a preferred embodiment and from the claims. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic diagram of a chirp signal generator for use in chirp spread-spectrum communications according to the invention. 
     FIG. 2 is a normalized plot of a pair of sequentially generated in-phase linearly swept chirp signals. 
     FIG. 3 is a plot of the spectral content of an infinitely repeating series of the pair of signals of FIG. 2 with power levels plotted on a logarithmic scale against a linear frequency scale. 
     FIG. 4 is a normalized plot of a pair of sequentially generated out-of-phase linearly swept chirp signals. 
     FIG. 5 is a plot of the spectral content of an infinitely repeating series of the pair of signals of FIG. 4 with power levels plotted on a logarithmic scale against a linear frequency scale. 
     FIG. 6 is a plot of the signal of FIG. 2 below and in registration with the signal of FIG. 4. 
     FIG. 7 is a superimposed plot of the first part of the second chirp signals of FIG. 6 shown in registration on a larger scale, after the frequency spectrum of each of them has been truncated. 
     FIG. 8 is a superimposed plot of the first part of the two signals of FIG. 7, shown in registration on an even larger scale. 
     FIG. 9 is a plot of two pairs of chirp signals which are the average of the signals of FIG. 7 shown in-phase (top) and out of phase (bottom). 
     FIG. 10 is a superimposed plot of the first part of the second chirp signals of FIG. 9 shown in registration on a larger scale, after the frequency spectrum of each of them has been truncated in a second truncation operation. 
     FIG. 11 is a plot of the signals of FIG. 6 after a total of six truncation and averaging operations. 
     FIG. 12 is a superimposed plot of the first part of the second chirp signals of FIG. 11 shown on a larger scale. 
     FIG. 13 is a plot of the spectral content of an infinitely repeating series of successive in-phase chirp signals, which are each the average of the pair of signals of FIG. 12, with power levels plotted on a logarithmic scale against a linear frequency scale. 
     FIG. 14 is a plot of the spectral content of an infinitely repeating series of successive alternately phase reversing chirp signals, which are each the average of the pair of signals of FIG. 12, with power levels plotted on a logarithmic scale against a linear frequency scale. 
     FIG. 15 is a plot of a single-period waveform that provides a linear transition beginning at a rate of change of amplitude relative to phase angle consistent with a low frequency waveform (100 KHz) and ending at a rate of change consistent with a higher frequency (400 KHz). 
     FIG. 16 is a plot of a pair of modified chirp signals being swept linearly, but with their first half-periods each being replaced with the first half-period of the waveform of FIG. 15, and their last half-periods each being replaced with the last half-period of the waveform of FIG. 15. 
     FIG. 17 is a plot of the spectral content of an infinitely repeating series of successive in-phase modified chirp signals of FIG. 16, with power levels plotted on a logarithmic scale against a linear frequency scale. 
     FIG. 18 is a plot of the spectral content of an infinitely repeating series of successive alternately phase reversing modified chirp signals of FIG. 16, with power levels plotted on a logarithmic scale against a linear frequency scale. 
     FIG. 19 is a plot of in-phase and phase-reversed pairs of the chirp signals of FIG. 16 after a total of six truncation and averaging operations. 
     FIG. 20 is a superimposed plot of the first part of the two signals of FIG. 19 shown on a larger scale. 
     FIG. 21 is a plot of the spectral content of an infinitely repeating series of successive in-phase modified chirp signals, which are each the average of the pair of signals of FIG. 19, with power levels plotted on a logarithmic scale against a linear frequency scale. 
     FIG. 22 is a plot of the spectral content of an infinitely repeating series of successive alternately phase reversing modified chirp signals, which are each the average of the pair of signals of FIG. 19, with power levels plotted on a logarithmic scale against a linear frequency scale. 
     FIG. 23 is a plot of a split-wave chirp that includes a first part beginning at an intermediate frequency followed by a second ending at the same intermediate frequency, with the two parts being separated by the transition waveform of FIG. 15. 
     FIG. 24 is a plot of the spectral content of an infinitely repeating series of successive in-phase split-wave chirp signals of FIG. 23, with power levels plotted on a logarithmic scale against a linear frequency scale. 
     FIG. 25 is a plot of the spectral content of an infinitely repeating series of successive alternately phase reversing split-wave chirp signals of FIG. 23, with power levels plotted on a logarithmic scale against a linear frequency scale. 
     FIG. 26 is a plot of phase-reversed and in-phase pairs of the signals of FIG. 23, shown in registration after a total of six truncation and averaging operations. 
     FIG. 27 is a superimposed plot of the first part of the second chirp signals of FIG. 26 shown on a larger scale. 
     FIG. 28 is a plot of the average of the sixth-order truncated-spectrum split-wave chirp signals of FIG. 26. 
     FIG. 29 is a plot of the spectral content of an infinitely repeating series of successive in-phase split-wave chirp signals of FIG. 28, with power levels plotted on a logarithmic scale against a linear frequency scale. 
     FIG. 30 is a plot of the spectral content of an infinitely repeating series of successive alternatively phase reversing split-wave chirp signals that are each the average of the chirp signals of FIG. 26, with power levels plotted on a logarithmic scale against a linear frequency scale. 
     FIG. 31 is a plot of an actual waveform of the chirp of FIG. 29 after it has been amplified, further filtered and coupled to a power line. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Referring to FIG. 1, a chirp signal generating circuit 10 for use in chirp communications includes a chirp waveform data memory element 12, such as a read-only memory (ROM), that has an address input port 14 and a data output port 16. The address port lines are responsive to the parallel output of an address counter 18, which has a clock input for receiving pulses from a clock circuit 20. The data output port 16 provides waveform data to a programmable inverter that has a pass/invert line for accepting data to be transmitted. The programmable inverter, in turn, feeds a data latch 26, and the data latch provides its output to the digital data input of a digital-to-analog converter 28. The converter supplies an analog output to an amplifier 30, which feeds a coupling circuit that may be connected to a power line 34. The above circuitry is preferably integrated into a single integrated circuit chip. 
     In operation the counter 18 counts pulses generated by the clock 20 and its parallel output therefore provides an increasing (or decreasing) sequence of addresses to the address port 14 of the memory element 12. This sequence of addresses causes the memory to access a series of digital chirp waveform values stored in sequential locations within the memory and to present them at the data output port 16. Each time the counter has stepped through an entire set of chirp waveform data locations, it may be reset to an arbitrary starting value and restarted, so as to step through the chirp waveform data locations repeatedly, with or without a delay between repetitions. Each repetition therefore presents digital data for a single chirp waveform at the data output port 16. 
     These data presented at the data output port 16 may or may not then be inverted by the programmable inverter, depending on the state of the pass/invert line. The state of the pass/invert line is generally only changed upon restarting the counter so as to provide a series of chirp waveform data sets that are each either in-phase or phase-reversed. This allows for phase-shift modulation of the series of chirp waveform data sets. 
     The digital-to-analog converter 28 then converts the modulated digital waveform data to a signal comprised of a phase-shift modulated series of analog chirps, which the amplifier 30 amplifies. The amplifier also filters (low-pass) the analog signal to remove quantization artifacts (anti-aliasing). The coupling circuit then couples the resulting signal onto the power line, for communication to one or more receivers connected elsewhere on the power line. 
     The receivers typically employ matched transversal filters to detect the chirp signals. These are described in the above-referenced U.S. Pat. No. 5,090,024, entitled SPREAD-SPECTRUM COMMUNICATIONS SYSTEM FOR NETWORKS, herein incorporated by reference. Network protocols for power lines are presented in the above-referenced application entitled TIMING FOR SPREAD-SPECTRUM NETWORK COMMUNICATION. 
     In one embodiment, the transmitter may transmit such that there are no pauses between successive chirps, whether successive chirps are phase-reversed (PRF) or not (NPRF), and the chirp signal is a product of a linear sweep from 100 KHz to 400 KHz over a duration of 100 microseconds. The signal waveform data used for this chirp is stored in 358 sequential memory locations and the counter is clocked at a 3.58 MHz clock rate. Other clock rates may be used with corresponding changes in the stored data points needed to represent this waveform. A plot of a sequentially generated pair 40 of these linearly swept signals 42, 44 is shown in FIG. 2. 
     An infinite series of these in-phase (NPRF) linearly swept chirps has the spectrum presented in FIG. 3. This spectrum contains a certain amount of energy outside of the 100-400 KHz sweep band as the result of the abrupt transition at portion 46 of the signal, where one chirp ends and the next begins. The transition generates out-of band components that are of no use in the communication of information, but create interference with the potential use of adjacent bands and thus, unless filtered, use up portions of the spectrum that could be used for other purposes. 
     FIG. 4 shows a pair 50 of linearly swept chirp signals 52, 54 that are identical to those shown in FIG. 2, except that the second chirp signal 54 is out-of-phase with respect to the first 52. An infinite series of these pairs of phase-reversed (PRF) linearly swept chirps would have the spectrum presented in FIG. 5. This spectrum contains even greater amounts of undesirable energy outside of the 100-400 KHz sweep band, attributable to the even more abrupt transition caused by the phase reversal. 
     Any arbitrary sequence of in-phase chirps 42 and out of phase chirps 54 will yield a spectrum that is a weighted sum of the spectra of FIGS. 2 and 4. Therefore, it is only necessary to consider these two cases to determine magnitude of the out-of-band spectral components for an arbitrarily modulated signal. 
     To design a chirp wave shape with reduced out-of-band energy, the spectrum of each of the waveforms 40, 50 was truncated, limiting its spectral contents to a range between 100 KHz and 400 KHz. This was done by performing a Fast Fourier Transform (FFT) on the waveform data and truncating the resulting transform. An inverse FFT was then performed on each set of truncated transformed data, to yield the superimposed chirp waveforms 60, 62 shown in FIGS. 7 and 8. Transforms and truncation were performed with the assistance of a general purpose computer. 
     The new truncated-spectrum waveforms 60, 62, which are not identical, were then averaged to yield a single truncated-spectrum chirp waveform, which is shown in phase-transition reversed 64 and non-phase-reversed 66 versions in FIG. 9. The process of truncation was then repeated on the spectra resulting from these waveforms 64, 66 to yield second-order truncated-spectrum waveforms 70, 72, which are shown in FIG. 10. The process of truncation and averaging was repeated four more times to yield sixth order truncated-spectrum waveforms 74, 76, which are shown in FIGS. 11 and 12. Further repetitions did not cause the waveforms to converge significantly closer together. The average of these sixth-order waveforms was then taken. 
     The spectra resulting from non-phase reversed and phase reversed concatenations of the average of the sixth-order truncated-spectrum waveforms 74, 76 are shown in FIGS. 13 and 14, respectively. It can be seen that there is less out-of-band energy (i.e., the bandwidth is more sharply defined) in both of the spectra. The level of worst-case out-of-band energy is more than 20 dB below the power level within the sweep band, at a frequency interval of 25 KHz from the desired band (i.e., at 75 KHz and 425 KHz). This is a clear improvement over the spectra of the simple linearly swept chirp signals 40, 50 shown in FIGS. 3 and 5, where the level of out-of-band energy at the same points in frequency was closer to 10 dB below the power level within the sweep band. At 10% below the the lower end of the band (i.e., at about 90 KHz in the 100-400 KHz example), the power level of components is preferably more than 20 dB below the average power level within the bandwidth (in the preferred embodiment, it is more than 25 dB below). At 10% above the upper end of the band (i.e., at about 440 KHz in the 100-400 KHz example), the power level of components is preferably more than 30 db below the average power level within the bandwidth (in the preferred embodiment, it is more than 40 db below). 
     The averaged sixth-order truncated-spectrum waveform can therefore be advantageously used as data in the memory 12 of the chirp signal generator of FIG. 1, in order to communicate over power lines. This generator would then use less of the useful bandwidth available on the line than would a generator that used a simply linearly swept chirp. The same truncation and averaging process can be applied to other waveforms, such as waveforms that are not linearly swept, but that are nonetheless progressively swept. 
     A further reduction in out of band energy can be achieved by shaping the time-domain signal at the transitions from high to low frequency (e.g., region 46 in FIG. 2). FIG. 15 shows a single-period transitional waveform 78 that can be used to effect a smoother frequency transition at these points. The waveform begins with a rate of change of amplitude relative to phase angle consistent with a low frequency waveform (100 KHz) and ends at a rate of change consistent with a higher frequency (400 KHz). In the present illustrative embodiment, the transitional waveform 78 is linearly swept, and is a total of 4.05 microseconds in duration. The first half-period of this waveform 78 may be substituted for the first half-period of the simple linearly swept chirp 42, and the second half-period substituted for the last half-period of the same simple linearly swept chirp. A pair of the resulting modified chirps 80, 82 is shown in FIG. 16, and the corresponding phase-reversed and non-phase-reversed spectra are shown in FIGS. 17 and 18. 
     These spectra indicate that there is somewhat of a reduction in out-of-band energy with respect to the spectra of the simple linearly swept chirp signals 40, 50 (FIGS. 2 and 4) owing to the substitution of smooth transitional waveform portions for the first and last half-periods of the chirp. The transitional waveform may extend over more than a single period, but at the expense of some loss in frequency content of the chirp within the sweep bandwidth. Also, the transitional waveform need not be swept in a linear fashion in order to reap the benefits of the invention. 
     If these modified chirps 80, 82 are further subjected to repeated truncation and averaging operations as earlier described, the reduction in out-of-band energy is improved. FIGS. 19 and 20 show sixth order truncated-spectrum modified chirps 86, 88 that result from a total of six truncation and five averaging operations, and FIGS. 21 and 22 show the spectra resulting from the average of these chirps 86, 88. These spectra confirm that there is an even more marked reduction in out-of band energy, when compared to the spectra of the simple linearly swept chirp signals 40, 50 (FIGS. 2 and 4), being approximately 30 db lower at 25 Khz from the band edges. 
     A still further reduction in out-of-band energy can be achieved by changing the manner in which the chirp is swept. FIG. 23 shows a chirp signal 90 in which the signal begins at an intermediate frequency, such as 203 KHz, and decreases over a first part 92 to a frequency at the higher end of the desired bandwidth (400 KHz). A second part 94 begins at a frequency at the lower end of the sweep bandwidth (100 KHz) and increases to the same intermediate frequency (203 KHz) at the end of the chirp. The first and second parts are separated by a transitional waveform portion 96, such as the one shown in FIG. 15, and the first and second parts are swept in a linear manner. This split-wave chirp signal may be transmitted by the generator circuit 10, and be detected by an appropriate matched filter. An equivalent mirror image of the waveform may also be produced in which frequency increases in the first part and frequency decreases in the second. 
     The in-phase and out-of-phase power spectra resulting from the split-wave chirp signal 90 are shown in FIGS. 24 and 25. These spectra indicate that there is again somewhat of a reduction in out-of-band energy with respect to the spectra of the simple linearly swept chirp signal 42 (FIGS. 2 and 4). 
     One reason for this improvement is that the frequency components resulting from the phase reversal between chirps of opposing phase have been moved within the desired band. A significant proportion of these components tend to be found at either half or twice the frequency of the signal at the phase reversal. As the phase reversal now occurs at 203 KHz, instead of at the transition from 100 to 400 KHz, the added components are at 101.5 KHz and 406 KHz, which are generally within the desired band. This advantageous placement of phase-reversal artifact energy within the desired band is possible if the signal spans more than two octaves. Embodiments that use bands that span less than two octaves will not find all of this artifact energy generated within the desired band, but may still benefit from the application of the split-wave technique. Some energy is lost at the intermediate frequency (203 KHz) with this technique, as evidenced by the gap in the spectrum of FIG. 25. 
     If this split-wave chirp 90 is subjected to the repeated truncation and averaging operations described earlier, its out-of-band energy level is further improved. FIGS. 26 and 27 show sixth-order split-wave chirps 100, 102 after a total of six truncation and five averaging operations. These have converged to be quite close, and the average of the two (FIG. 28) is quite similar to each of them. This close convergence is believed to be due to the fact that the truncation operations did not affect the phase-reversal components, 101.5 KHz and 406 KHz energy, which are now within the desired band. 
     The chirp signal waveform 104 obtained by taking the average of the sixth-order truncated-spectrum split-wave chirp signals 100, 102 is presented in FIG. 28. This waveform begins at 203 KHz and reaches a frequency of 400KHz in 66 microseconds (19 full cycles). A 4 microsecond transition portion then brings the frequency down to 100 KHz over a single cycle. The transition portion is followed by an increase from 100 KHz to 203 KHz in 33 microseconds. The entire waveform is 100 microseconds long, spanning a total of 25 cycles. 
     FIGS. 29 and 30 show the spectra of the average of the sixth-order truncated-spectrum split-wave chirps 100, 102. These indicate that there is an even more marked reduction in out-of band energy, when compared to the spectra of the simple linearly swept chirp signal 42 (FIGS. 2 and 4). Indeed, the power level of frequency components 25 KHz outside of the defined bandwidth on the high side and low side are approximately 40 dB and 25 db respectively below the average power level within the defined bandwidth for both the in-phase and phase-reversed split-wave spectra. This waveform may therefore be modulated in an arbitrary fashion using the signal generator of FIG. 1, while only generating a minimum amount of energy outside of the desired bandwidth. It is noted that the spectrum within the desired band is only slightly different from that produced by a linearly swept chirp, and a matched filter for this waveform will perform with similar noise immunity to that designed for a linearly swept chirp. 
     Table 1 presents 358 points defining this proposed waveform exactly. The transmitted chirp waveform present on the power line itself will often differ from the chirp wavefrom in this table. These differences are due to the fact that the Table 1 output of the ROM 12 is converted to an analog signal in the D/A 28, passed through the amplifier/filter 30, and then the frequency and impedance matching characteristic of the coupling circuit 32 before reaching the power line. This analog processing of the waveform further filters the waveform as well as introducing other non-linearities to the waveform. An example of a digitally sampled version of the chirp waveform as seen on power line after generation by the preferred embodiment is shown in FIG. 31 and a table of 360 points defining this waveform is given in Table 2. 
     In the preferred embodiment for use on the power line, this waveform is specified to be transmitted at an amplitude between 3 and 7 volts peak-to-peak. Such an embodiment with appropriate inexpensive filtering should enable generally reliable power line communications that satisfy the FCC part 15 requirements for carrier current conducted emissions. 
     Other embodiments are within the following claims. While the detailed description has been presented with respect to 100 microsecond pulses and a 100 Khz to 400 KHz bandwidth, the invention may readily be applied to other pulse durations and bandwidths. For example, a simple time scaling by a factor of one-fifth produces a chirp with identical spectra shaping, but over a frequency range of 20 Khz to 80 Khz. The time duration of this chirp is 500 microseconds. This lower frequency chirp can be advantageously used simultaneously on the same power line with the 100 Khz to 400 Khz chirp. Linear sweeps and the like may be replaced with less exacting progressive sweeps in connection with the principles of the invention without giving up the benefits thereof. Furthermore, various substitutions may be made in the signal generator, such as using analog modulation circuitry to replace the digital programmable inverter. 
     
                                           TABLE 1__________________________________________________________________________  0.0625  45    -0.6363          90            0.5625                 135                    -0.3125                         180                            0.8125                                 225                                    -0.1250                                         270                                            -0.1250                                                 315                                                    -0.7188 1  0.1563  46    -0.4375          91            0.7188                 136                    0.0938                         181                            0.7188                                 226                                    0.2500                                         271                                            0.0938                                                 316                                                    -0.5938 2  0.2500  47    -0.1875          92            0.7188                 137                    0.4375                         182                            0.3750                                 227                                    0.5938                                         272                                            0.2813                                                 317                                                    -0.4063 3  0.3750  48    0.1250          93            0.5313                 138                    0.6563                         183                            -0.0938                                 228                                    0.7500                                         273                                            0.4688                                                 318                                                    -0.1875 4  0.4688  49    0.4063          94            0.2188                 139                    0.6875                         184                            -0.5313                                 229                                    0.6875                                         274                                            0.6250                                                 319                                                    0.0000 5  0.4688  50    0.6250          95            -0.1563                 140                    0.5000                         185                            -0.7188                                 230                                    0.3750                                         275                                            0.6875                                                 320                                                    0.1875 6  0.4063  51    0.7188          96            -0.4688                 141                    0.1875                         186                            -0.5938                                 231                                    -0.0938                                         276                                            0.7188                                                 321                                                    0.3750 7  0.2500  52    0.6875          97            -0.6563                 142                    -0.1875                         187                            -0.2500                                 232                                    -0.5313                                         277                                            0.7188                                                 322                                                    0.5000 8  0.0313  53    0.5313          98            -0.6875                 143                    -0.5313                         188                            0.2188                                 233                                    - 0.8750                                         278                                            0.6875                                                 323                                                    0.5938 9  -0.2500  54    0.2500          99            -0.5625                 144                    -0.6563                         189                            0.5938                                 234                                    -1.0000                                         279                                            0.6563                                                 324                                                    0.656310  -0.5000  55    -0.0625         100            -0.2813                 145                    -0.5938                         190                            0.7188                                 235                                    -0.9063                                         280                                            0.5938                                                 325                                                    0.656311  -0.7188  56    -0.4063         101            0.0625                 146                    -0.3438                         191                            0.5625                                 236                                    -0.6875                                         281                                            0.5313                                                 326                                                    0.625012  -0.8125  57    -0.6563         102            0.4063                 147                    0.0625                         192                            0.1875                                 237                                    -0.4375                                         282                                            0.4063                                                 327                                                    0.500013  -0.7813  58    -0.7500         103            0.6250                 148                    0.4375                         193                            -0.2813                                 238                                    -0.2188                                         283                                            0.2500                                                 328                                                    0.312514  -0.6563  59    -0.7188         104            0.7188                 149                    0.6875                         194                            -0.6250                                 239                                    -0.0938                                         284                                            0.0313                                                 329                                                    0.062515  -0.4063  60    -0.5313         105            0.6250                 150                    0.7188                         195                            -0.7188                                 240                                    -0.0313                                         285                                            -0.1875                                                 330                                                    -0.187516  -0.1250  61    -0.2188         106            0.3750                 151                    0.5313                         196                            -0.5313                                 241                                    -0.0313                                         286                                            -0.4063                                                 331                                                    -0.437517  0.1875  62    0.1250         107            0.0313                 152                    0.1563                         197                            -0.1250                                 242                                    0.0000                                         287                                            -0.5938                                                 332                                                    -0.656318  0.4375  63    0.4375         108            -0.3438                 153                    -0.2813                         198                            0.2813                                 243                                    0.0938                                         288                                            -0.7188                                                 333                                                    -0.750019  0.6563  64    0.6563         109            -0.6250                 154                    -0.6250                         199                            0.5313                                 244                                    0.2500                                         289                                            -0.7813                                                 334                                                    -0.781320  0.7500  65    0.7500         110            -0.7188                 155                    -0.7813                         200                            0.5625                                 245                                    0.4063                                         290                                            -0.7813                                                 335                                                    -0.750021  0.7500  66    0.6875         111            -0.6583                 156                    -0.6250                         201                            0.3125                                 246                                    0.5625                                         291                                            -0.7500                                                 336                                                    -0.625022  0.6563  67    0.5000         112            -0.3750                 157                    -0.2813                         202                            -0.0625                                 247                                    0.6563                                         292                                            -0.7188                                                 337                                                    -0.468823  0.4688  68    0.1875         113            0.0000                 158                    0.1875                         203                            -0.4375                                 248                                    0.6563                                         293                                            -0.6563                                                 338                                                    -0.281324  0.2188  69    -0.1250         114            0.4063                 159                    0.5625                         204                            -0.6563                                 249                                    0.5938                                         294                                            -0.5313                                                 339                                                    -0.062525  -0.0313  70    -0.4063         115            0.6875                 160                    0.7500                         205                            -0.5938                                 250                                    0.5000                                         295                                            -0.4063                                                 340                                                    0.156326  -0.3125  71    -0.6250         116            0.7813                 161                    0.6563                         206                            -0.3125                                 251                                    0.3750                                         296                                            -0.2188                                                 341                                                    0.375027  -0.5313  72    -0.7188         117            0.6563                 162                    0.3125                         207                            0.0625                                 252                                    0.3125                                         297                                            -0.0313                                                 342                                                    0.562528  -0.6875  73    -0.6250         118            0.3125                 163                    -0.1563                         208                            0.4063                                 253                                    0.2813                                         298                                            0.2188                                                 343                                                    0.718829  -0.7188  74    -0.4375         119            -0.0938                 164                    -0.5938                         209                            0.5625                                 254                                    0.2188                                         299                                            0.4375                                                 344                                                    0.812530  -0.6250  75    -0.1250         120            -0.5000                 165                    -0.8438                         210                            0.4688                                 255                                    0.1875                                         300                                            0.6250                                                 345                                                    0.812531  -0.4375  76    0.1875         121            -0.7500                 166                    -0.7500                         211                            0.1875                                 256                                    0.0625                                         301                                            0.7500                                                 346                                                    0.718832  -0.1563  77    0.5000         122            -0.7813                 167                    -0.4375                         212                            -0.1563                                 257                                    -0.0625                                         302                                            0.7813                                                 347                                                    0.500033  0.1563  78    0.6875         123            -0.5938                 168                    0.0625                         213                            -0.4375                                 258                                    -0.2500                                         303                                            0.7813                                                 348                                                    0.250034  0.4375  79    0.7500         124            -0.2500                 169                    0.5313                         214                            -0.5000                                 259                                    -0.4375                                         304                                            0.6875                                                 349                                                    -0.031335  0.6563  80    0.6250         125            0.1875                 170                    0.7813                         215                            -0.3125                                 260                                    -0.5625                                         305                                            0.5938                                                 350                                                    -0.281336  0.7500  81    0.3438         126            0.5313                 171                    0.7500                         216                            0.0000                                 261                                    -0.6563                                         306                                            0.4688                                                 351                                                    -0.468837  0.7188  82    -0.0313         127            0.7188                 172                    0.4063                         217                            0.3750                                 262                                    -0.6563                                         307                                            0.3125                                                 352                                                    -0.531338  0.5625  83    -0.3750         128            0.6875                 173                    -0.0938                         218                            0.5938                                 263                                    -0.6250                                         308                                            0.1563                                                 353                                                    -0.500039  0.2813  84    -0.6563         129            0.4375                 174                    -0.5313                         219                            0.6250                                 264                                    -0.5938                                         309                                            -0.0313                                                 354                                                    -0.406340  0.0000  85    -0.7813         130            0.0625                 175                    -0.7813                         220                            0.4063                                 265                                    -0.5313                                         310                                            -0.2188                                                 355                                                    -0.281341  -0.3125  86    -0.7188         131            -0.3438                 176                    -0.6875                         221                            0.0625                                 266                                    -0.5000                                         311                                            -0.4375                                                 356                                                    -0.156342  -0.5625  87    -0.5000         132            -0.6250                 177                    -0.3438                         222                            -0.2500                                 267                                    -0.4375                                         312                                            -0.5938                                                 357                                                    -0.062543  -0.7188  88    -0.1250         133            -0.7188                 178                    0.1250                         223                            -0.4375                                 268                                    -0.3750                                         313                                            -0.718844  -0.7188  89    0.2500         134            -0.5938                 179                    0.5938                         224                            -0.4063                                 269                                    -0.2813                                         314                                            -0.7500__________________________________________________________________________ 
    
     
                                           TABLE 2__________________________________________________________________________  0.0000  45    -0.4295          90            -0.0536                 135                    -0.3597                         180                            -0.1073                                 225                                    -0.1019                                         270                                            -0.0644                                                 315                                                    -0.3758 1  0.0816  46    -0.3944          91            0.1479                 136                    -0.3426                         181                            0.0898                                 226                                    -0.1727                                         271                                            -0.0214                                                 316                                                    -0.3865 2  0.1328  47    -0.2861          92            0.3134                 137                    -0.2216                         182                            0.2509                                 227                                    -0.1645                                         272                                            0.0450                                                 317                                                    -0.3758 3  0.1827  48    -0.1417          93            0.4032                 138                    -0.0450                         183                            0.3223                                 228                                    -0.0615                                         273                                            0.1182                                                 318                                                    -0.3192 4  0.2149  49    0.0277          94            0.3829                 139                    0.1366                         184                            0.2717                                 229                                    0.0706                                         274                                            0.1903                                                 319                                                    -0.2377 5  0.2149  50    0.1922          95            0.2805                 140                    0.2936                         185                            0.1194                                 230                                    0.1922                                         275                                            0.2680                                                 320                                                    -0.1300 6  0.2041  51    0.3230          96            0.0953                 141                    0.3545                         186                            -0.0765                                 231                                    0.2578                                         276                                            0.3330                                                 321                                                    -0.0099 7  0.1585  52    0.4001          97            -0.0992                 142                    0.3048                         187                            -0.2281                                 232                                    0.2122                                         277                                            0.3760                                                 322                                                    0.1101 8  0.0784  53    0.4082          98            -0.2729                 143                    0.1651                         188                            -0.2899                                 233                                    0.0815                                         278                                            0.3836                                                 323                                                    0.2087 9  -0.0246  54    0.3351          99            -0.3790                 144                    -0.0235                         189                            -0.2405                                 234                                    -0.1116                                         279                                            0.3652                                                 324                                                    0.285710  -0.1479  55    0.1916         100            -0.3865                 145                    -0.1992                         190                            -0.0906                                 235                                    -0.3090                                         280                                            0.3330                                                 325                                                    0.333011  -0.2628  56    0.0225         101            -0.3174                 146                    -0.3111                         191                            0.0855                                 236                                    -0.4610                                         281                                            0.2849                                                 326                                                    0.354212  -0.3550  57    -0.1517         102            -0.1589                 147                    -0.3328                         192                            0.2163                                 237                                    -0.5000                                         282                                            0.2142                                                 327                                                    0.343713  -0.3973  58    -0.3040         103            0.0283                 148                    -0.2436                         193                            0.2578                                 238                                    -0.4600                                         283                                            0.1541                                                 328                                                    0.309914  -0.3973  59    -0.4053         104            0.2039                 149                    -0.0753                         194                            0.1963                                 239                                    -0.3383                                         284                                            0.0834                                                 329                                                    0.249815  -0.3257  60    -0.4295         105            0.3419                 150                    0.1111                         195                            0.0377                                 240                                    -0.1861                                         285                                            0.0126                                                 330                                                    0.146916  -0.2056  61    -0.3560         106            0.3867                 151                    0.2669                         196                            -0.1379                                 241                                    -0.0338                                         286                                            -0.0842                                                 331                                                    0.044717  -0.0533  62    -0.2197         107            0.3435                 152                    0.3385                         197                            -0.2578                                 242                                    0.0862                                         287                                            -0.1826                                                 332                                                    -0.080618  0.1161  63    -0.0397         108            0.1955                 153                    0.2986                         198                            -0.2899                                 243                                    0.1612                                         288                                            -0.2641                                                 333                                                    -0.206119  0.2619  64    0.1511         109            0.0135                 154                    0.1497                         199                            -0.2106                                 244                                    0.1827                                         289                                            -0.3436                                                 334                                                    -0.326120  0.3736  65    0.3067         110            -0.1777                 155                    -0.0441                         200                            -0.0608                                 245                                    0.2041                                         290                                            -0.3949                                                 335                                                    -0.384721  0.4404  66    0.4053         111            -0.3300                 156                    -0.2319                         201                            0.0939                                 246                                    0.2134                                         291                                            -0.4295                                                 336                                                    -0.429522  0.4301  67    0.4140         112            -0.3968                 157                    -0.3436                         202                            0.1929                                 247                                    0.2363                                         292                                            -0.4295                                                 337                                                    -0.419723  0.3652  68    0.3428         113            -0.3592                 158                    -0.3534                         203                            0.2041                                 248                                    0.2471                                         293                                            -0.4022                                                 338                                                    -0.364624  0.2442  69    0.2091         114            -0.2226                 159                    -0.2372                         204                            0.1154                                 249                                    0.2714                                         294                                            -0.3514                                                 339                                                    -0.279125  0.0997  70    0.0251         115            -0.0333                 160                    -0.0465                         205                            -0.0262                                 250                                    0.2793                                         295                                            -0.2821                                                 340                                                    -0.158626  -0.0529  71    -0.1636         116            0.1679                 161                    0.1443                         206                            -0.1610                                 251                                    0.2599                                         296                                            -0.2006                                                 341                                                    -0.036227  -0.2115  72    -0.3028         117            0.3104                 162                    0.2879                         207                            -0.2362                                 252                                    0.2213                                         297                                            -0.1202                                                 342                                                    0.083928  -0.3218  73    -0.3971         118            0.3760                 163                    0.3224                         208                            -0.2202                                 253                                    0.1613                                         298                                            -0.0269                                                 343                                                    0.203929  -0.3973  74    -0.4018         119            0.3520                 164                    0.2392                         209                            -0.1164                                 254                                    0.1013                                         299                                            0.0753                                                 344                                                    0.296230  -0.4008  75    -0.3310         120            0.1970                 165                    0.0663                         210                            0.0251                                 255                                    0.0413                                         300                                            0.1648                                                 345                                                    0.367031  -0.3596  76    -0.1904         121            -0.0002                 166                    -0.1424                         211                            0.1559                                 256                                    -0.0161                                         301                                            0.2606                                                 346                                                    0.410832  -0.2610  77    -0.0173         122            -0.2097                 167                    -0.2973                         212                            0.2239                                 257                                    -0.0536                                         302                                            0.3421                                                 347                                                    0.418933  -0.1148  78    0.1690         123            -0.3590                 168                    -0.3643                         213                            0.1887                                 258                                    -0.0858                                         303                                            0.3960                                                 348                                                    0.378134  0.0648  79    0.3120         124            -0.4078                 169                    -0.2894                         214                            0.0855                                 259                                    -0.1400                                         304                                            0.4189                                                 349                                                    0.305935  0.2065  80    0.4082         125            -0.3412                 170                    -0.1157                         215                            -0.0369                                 260                                    -0.1932                                         305                                            0.4082                                                 350                                                    0.180336  0.3373  81    0.3867         126            -0.1846                 171                    0.0871                         216                            -0.1417                                 261                                    -0.2437                                         306                                            0.3738                                                 351                                                    0.031237  0.4082  82    0.2915         127            0.0255                 172                    0.2640                         217                            -0.1717                                 262                                    -0.2930                                         307                                            0.3008                                                 352                                                    -0.121138  0.4082  83    0.1316         128            0.2122                 173                    0.3424                         218                            -0.1099                                 263                                    -0.3328                                         308                                            0.2068                                                 353                                                    -0.234939  0.3334  84    -0.0686         129            0.3430                 174                    0.2908                         219                            -0.0006                                 264                                    -0.3436                                         309                                            0.0975                                                 354                                                    -0.332140  0.1922  85    -0.2594         130            0.3652                 175                    0.1266                         220                            0.1301                                 265                                    -0.3322                                         310                                            0.0096                                                 355                                                    -0.375241  0.0277  86    -0.3827         131            0.2746                 176                    -0.0813                         211                            0.2072                                 266                                    -0.2899                                         311                                            -0.0981                                                 356                                                    -0.347442  -0.1524  87    -0.4295         132            0.1053                 177                    -0.2519                         222                            0.2285                                 267                                    -0.2362                                         312                                            -0.1875                                                 357                                                    -0.287443  -0.2968  88    -0.3796         133            -0.1035                 178                    -0.3221                         223                            0.1508                                 268                                    -0.1844                                         313                                            -0.2684                                                 358                                                    -0.197044  -0.3963  89    -0.2444         134            -0.2753                 179                    -0.2640                         224                            0.0235                                 269                                    -0.1244                                         314                                            -0.3319                                                 359                                                    -0.0985                                                 360                                                    0.0000__________________________________________________________________________