FIELD OF INVENTION 
     This invention relates to the generation of multiple frequencies, and more particularly to the utilization of a minimum number of base frequencies or tones, in order to generate a large number of spectrally pure preselected frequencies. 
     BACKGROUND OF THE INVENTION 
     It will be appreciated that in air defense systems, an incoming missile is counter-measured through the utilization of an interceptor missile, which is guided towards the incoming missile through attitude control and millimeter wave radar techniques. In order to be able to intercept an incoming missile with current attitude adjusting technology, it is important to be able to transmit millimeter radar signals in hundreds of frequency channels so that the frequency can be hopped amongst channels to avoid jamming. Moreover, it is important that these frequencies be selectable and available through a switching system in which the transmit frequency can be set rapidly. 
     In the past, master frequency generators have been employed utilizing a large number of base frequencies or tones in order to be able to synthesize the required channel. In one application, as many as 16 tones were necessary in order to generate the required frequencies with the required spectral purity. In addition to generating the 16 tones, multipliers, dividers, and mixers were combined to provide the large number of frequencies required. For instance, in one application, 100 channels are needed to be generated. The result of such a master frequency generator was that the number of parts necessary was excessive, which both added weight and resulted in high power consumption in an application, which because of its intended use, must be extremely lightweight and extremely parsimonious in its power consumption. 
     In general, for interceptor missiles, it is the kinetic energy of the missile that takes out the incoming missile, as opposed to explosives that utilize proximity fuses to be able to accomplish the task. Thus, it is desirable to minimize the mass of the components in the missile to be able to maximize the velocity. This is because the energy in the collision is proportional to the square of the velocity. The number of components also obviously adds considerably to the cost of the entire system, such that any system that can minimize the parts count is desirable. 
     In the interceptor missile application, as mentioned before, it is a requirement to generate hundreds of channel frequencies and to be able to hop between frequencies to avoid jamming. Secondly, channels permit profiling the incoming missile as to its attitude or orientation, as well as its physical characteristics, to determine the most lethal point of impact, and this requires hundreds of channels. 
     SUMMARY OF THE INVENTION 
     In order to accomplish the generation of hundreds of channels with high accuracy, low phase noise, low spurious content and fast switching, in one embodiment, five base frequencies or tones are generated, with a relationship between the tones being f 0 +/−⅛f 0  and +/−{fraction (1/16)}f 0 . After much research into the various tradeoffs between different synthesizer techniques, a solution was found which permits utilization of only five tones to generate hundreds of channels with a master frequency generator utilizing one half the parts count previously thought necessary. 
     In one embodiment, one first determines the desired step size between the multiple frequencies to be generated, which is usually a system requirement. With a fixed configuration of dividers and mixers designed to permit generation of a predetermined number of different frequencies with the above step size, then one can specify the center tone as being the step size x, a number reflecting the one over the base tone spacing (i.e. 16), multiplied by a number determined by the specific configuration. In one embodiment, for a circuit which can generate 160 different frequencies, the center tone is step size×16×128, where the basic step size is the tone spacing divided by 128, and where the tone spacing is defined as {fraction (1/16)} of the center tone. 
     Thus, setting the tone spacing=F c /16=128×step size, F c =16×128×step size. Having specified the center or base tone, one can generate the other four tones based on the above +/−⅛f 0  and +/−{fraction (1/16)}f 0  relationship. 
     In one example, with three mixers and four dividers, and with selected dividers providing a divide-by-4 or a divide-by-8 function, it can be shown that 160 different frequencies can be generated from five tones, with the frequency generated            f   agility     =         41   128          F   A       +       K   4          (         N   1     /   1     +       N   2     /   2     +       N   3     /   8     +       N   4     /   32       )           ,                          
     where F A  is the lowest tone, where K is the tone spacing, and where N is either 0 or an integer. 
     It will be appreciated that in the past, the simplest way of generating multiple frequencies was to utilize a phase locked oscillator at the output frequency. This technique was, however, found to be woefully short of being able to generate the frequencies without considerable phase and spurious noises and a slow switching speed. 
     It will also be appreciated that there are an infinite number of solutions that can be tried in order to accommodate the number of frequencies to be generated with the minimum number of tones. There are also an infinite number of combinations of multipliers, dividers, mixers and oscillators to be able to achieve the desired result. It is noted that one prior art master frequency generator has a parts count of 328 components. These components are mixers, filters, KA amplifiers, microwave amplifiers, dividers, regulators, cables and a Doppler VCO. In contradistinction to the prior master frequency generator in the subject system, in one embodiment only 155 components need be utilized. 
     In the preferred embodiment, a fixed oscillator is used in combination with dividers and mixers to generate the five basic tones. These five basic tones are then combined in three additional mixers to generate the hundreds of frequencies required for the above-mentioned channels. The combining circuit in one embodiment includes divide-down circuits, which in combination with the mixers, minimizes spurs by up-conversion, expansion and divide-down steps to provide the required spectral purity. 
     In summary, a system is provided for generating multiple frequencies in a specified frequency band, with a specified step size between frequencies, in which the spectral purity of the frequencies is assured. The switching speed between frequencies is very fast, limited only by the speed of the switches used. In one embodiment, only five tones are generated as the base for the rest of the synthesis, in which the relationship of the five tones is f 0 +/−⅛f 0  and +/−{fraction (1/16)}f 0 . The subject system in one embodiment, utilizes a channel synthesizer and a doppler offset synthesizer which may be utilized in air defense systems for generating the transmit channels to be able to permit a missile seeker to transmit a signal at the appropriate frequency. In one embodiment, spectral purity is achieved by providing a number of stages of up converting, expanding, and dividing down of an input signal. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     These and other features of the Subject Invention will be better understood taken in connection with the Drawings, in conjunction with the Detailed Description of which; 
     FIG. 1 is a diagrammatic illustration of an incoming and interceptor missile scenario, in which a radar at the interceptor missile illuminates the incoming missile and analyzes the returns therefrom; 
     FIG. 2 is a block diagram of a system for generating multiple frequencies in which a master oscillator is coupled to a master frequency generator, which generates the frequencies required with the required spectral purity, low phase noise and low spurious content through the utilization of only five tones; 
     FIG. 3 is a block diagram of the subject master frequency generator, illustrating the generation of the five tones, and the supplying of the five tones by a synthesizer which generates a number of channels to provide an RF output at hundreds of different selectable frequencies; 
     FIG. 4 is an expanded block diagram of the master frequency generator of FIG. 3, illustrating the distribution of the five different frequencies from a base frequency generation unit to the channel synthesizer; 
     FIG. 5 is a schematic diagram of a prior art master frequency generator, illustrating the number of components necessary to provide for the multiple frequency output; 
     FIG. 6 is a schematic diagram of the channel synthesizer of FIG. 5; 
     FIG. 7 is a schematic diagram illustrating the Doppler offset synthesizer of FIG. 4, illustrating the selectability of the various frequencies utilizing the five tones generated by the master frequency generator of FIG. 4, as well as the upconversion, expansion, and division stages, which reduce the spurious content; 
     FIG. 8 is a diagrammatic illustration of the algorithm utilized in the generation of the five tones, in which a fixed frequency oscillator has its center frequency f 0  varied by +/−⅛f 0  and +/−{fraction (1/16)}f 0 ; 
     FIG. 9 is a schematic diagram of the utilization of an oscillator having its output mixed with a divided down version of the oscillator signal to provide a new frequency that is a combination of the two, but having a spurious content no closer than the highest common divider between the input frequencies; 
     FIG. 10 is a graph showing permissible spurious levels as a function of offset frequencies in the system of FIG. 8; 
     FIG. 11 is a schematic diagram of one embodiment of the subject invention in which numerous frequencies are generated through the utilization of 3 mixers and 4 dividers, in which the dividers either divide the incoming signal by 4 or 8; 
     FIG. 12 is a series of equations for specifying the frequency generated by the circuit of FIG. 11, in which all mixers are configured to output the upper side band; 
     FIG. 13 is a series of equations illustrating the step size and the minimum and maximum frequencies obtainable as an output from the circuit of FIG. 11; 
     FIG. 14 is a table for one specific example of the output frequencies derivable from the circuit of FIG. 11, indicating a minimum and maximum frequency for a given size step; 
     FIG. 15 is a schematic diagram of the system of FIG. 11 in which one of the mixers provides as an output to the lower side band; 
     FIG. 16 is an equation specifying the frequencies available as the output of the circuit of FIG. 15; 
     FIG. 17 is a table illustrating an example of the frequency range of the circuit of FIG. 15 given a 2.5 MHz step size, and one of the mixers of the FIG. 15 outputting the lower side band; 
     FIG. 18 is a schematic diagram of the circuit of FIG. 11, in which two of the mixers output only lower side bands; 
     FIG. 19 is an equation describing the frequencies available from the circuit of FIG. 18; 
     FIG. 20 is a table illustrating the frequency range of frequencies available from the circuit of FIG. 18 in which two of the mixers produce lower side bands, and in which the step size is maintained at 2.5 MHz; 
     FIG. 21 is a schematic diagram of the circuit of FIG. 11, in which all mixers provide the lower side band as an output thereof; 
     FIG. 22 is an equation describing the frequencies available from the circuit of FIG. 21; 
     FIG. 23 is a table describing the frequency range of the circuit of FIG. 21, with all mixers outputting lower side bands, and with the step size being 2.5 MHz; 
     FIG. 24 is a table of possible frequencies for the circuits of FIGS. 11,  15 ,  18  and  19 , in which is the given example, 160 different frequencies are available having a range between 727.5 MHz and 1,832.5 MHz; 
     FIG. 25 is a block diagram for the generic case, in which a base frequency is multiplied by an integer and mixed with the output of the circuit of a frequency agility circuit, the output of which is again multiplied by an integer, and mixed with a fine tuning frequency to provide a number of different frequencies modified by a number of different fine tuning steps; 
     FIG. 26 is an equation specifying the output frequency of the circuit of FIG. 25; and, 
     FIG. 27 is a table showing the generation of a number of frequencies generated through the utilization of various multipliers and mixers. 
    
    
     DETAILED DESCRIPTION 
     Referring now to FIG. 1, in one interceptor-type scenario, an incoming missile  10  is to be intercepted by an interceptor missile  12 , which determines the position of the incoming missile through the utilization of signals illuminating the target. As illustrated, a transmitter  14  emits radiation  16  towards the missile and detects reflected radiation  18 , whereupon attitude adjustment apparatus within missile  12  steers the interceptor missile towards the incoming missile. 
     As mentioned hereinbefore, it is only with difficulty that the exact position or trajectory of the incoming missile can be ascertained to the point that a collision between two missiles traveling at a high rate of velocity can be made to occur. In the above scenario, it is important to be able to switch the output of transmitter  14  to one of a variety of different frequencies to generate the aforementioned channels to take into account such things as countermeasure radiation, which must be taken into account in terms of shifting the channel in which the transmitted radiation lies, to avoid jamming radiation. Additionally, as mentioned above, projecting radiation in a number of different channels permits profiling the incoming missile so as to assure the most effective hit. 
     Referring now to FIG. 2, in general, a master oscillator  20  is utilized to provide a fixed frequency, which is then processed by a master frequency generator  22  so as to provide transmitter  14  of FIG. 1 with the required frequency. In general, it is important to be able to provide that transmitter  14  emit radiation at a number of selectable frequencies for the above mentioned channel selection. Typically, the number of channels utilized in such a situation is in the hundreds. 
     As mentioned above, it is somewhat a daunting task to be able to generate hundreds of frequencies through the utilization of traditional master frequency generators. In the past, a master frequency generator oftentimes needs to generate sixteen different tones in order to provide the frequencies required not only for the transmitter, but also for the receiver and the further processing of the received signals. 
     Referring now to FIG. 3, in the subject system master frequency generator  22  provides at its output, five tones, here illustrated at  30 , which are utilized by a channel synthesizer  32 . The five tones are quite simply generated by multiplying the fixed frequency f 0  by +/−⅛f 0  and +/−{fraction ( 1 / 16 )}f 0 . It is a unique finding of this invention that all the required frequencies for a seeker can be generated with just 5 tones, and more particularly, tones with the indicated relationships, e.g. A=C+⅛C; B=C+{fraction (1/16)}C; D=C−{fraction (1/16)}C; and E=C−⅛C. 
     In one embodiment, the tones are generated by providing a divide-by-8 divider  36 , followed by a divide-by-2 divider  38 , the outputs of which are applied to a combiner  40 , which then feeds the IF port of a two-input port mixer  42 . The first of the inputs is the direct output of oscillator  20 , namely f 0 , whereas the second input is from combiner  40 . 
     In one embodiment, combiner  40  can be conceived as a diplexer fed backwards, or a reverse Wilkinson combiner. The purpose of the combiner is merely to provide an output which is divided down by ⅛ and ½. Mixer  42  provides the +/−⅛ and +/−{fraction (1/16)} multiplier for f 0 . Mixers in general operate to provide the sum and difference of two input signals. In the illustrated case there are actually three different frequencies being multiplied, thereby to provide four different tones. The fifth tone is merely the f 0  fixed frequency. The output of mixer  42 , as well as the fixed frequency output of oscillator  20 , is provided to a quadraplexer  44 , the purpose of which is to provide four separate and distinct frequency tones or outputs from the input signals. The fifth tone is f 0 . Quadraplexers in general are well known, and have been described as filter banks or channelizers, the purpose of which is to provide frequency separation for an input signal. 
     As illustrated, the five tones are used in various combinations for channel synthesizer  32 , with the outputs of synthesizer  32  going to mixer  50  in an up-converter  54 . This unit up-converts the channel frequency through the utilization of a multiplier  56 , which multiplies the fixed frequency from oscillator  20  by a predetermined integer. The output of mixer  50  is then itself multiplied by an integer at multiplier  58 . Channel selection is provided by frequency controller  60 . 
     Referring now to FIG. 4 in which like reference characters specify like elements, as will be seen, master oscillator  20  provides an input to up converter and Doppler combiner  54 , with its output also utilized for base frequency generator  66  utilizing the elements of FIG.  3 . It will be appreciated that the five tones in this case are designated A, B, C, D and E, where A=C+⅛C; B=C+{fraction (1/16)}C; D=C−{fraction (1/16)}C and E=C−⅛C. These frequencies are applied to a distribution unit  70 , which selectively provides either A, B, C or D to channel synthesizer  32 , which includes a mixer  74  having its other input the output of divider  72 . The other input to IF mixer  78  is either the A or E tones which are divided down by divider  80  and provided to a mixer  82 , the other input of which is the tone B, C, D or E. The output of mixer  78  is divided down by a divider  84 , with the output thereof being provided to mixer  50  of the combiner. Channel synthesizer unit  32  is capable of providing hundreds of different frequencies which are switched by distribution unit  70 , which switches between the various frequencies. 
     An algorithm for switching among A, B, C, D and E tones to achieve a particular frequency is described in connection with FIGS. 11-25 hereinafter. 
     Most importantly, because of the upconversion, expansion and divide-down provided by channel synthesizer  32 , spurs are reduced, which increases the spectral purity of the signal. 
     It will be appreciated that distribution unit  70  switches the A, B, C, D, or E inputs one at a time to channel synthesizer  32 , with unit  70  performing a full axis matrix switch function. 
     In summary, the output of quadraplexer  44 , along with the base frequency fo is selectively switched over lines  90 ,  92 ,  94  and  96 , such that at any given time, either A, B, C, or D is supplied over line  90 , A, B, C or D is supplied over line  92 , A or E is supplied over line  94 , and B, C, D or E is supplied over line  96 . 
     As to the Doppler offset synthesis, it will be appreciated that the output of distribution unit  70  is in one instance B, C, D, or E supplied over line  100 ; B, C, D, or E supplied over line  102 ; C supplied over line  104 ; and E supplied over line  106 . A divider  105  is provided to divide-down the signal over line  104 . A divider  108  is provided to divide down the signal over line  100 , whereas a divider  110  is provided to divide-down the signal over line  102 . It will be appreciated that B is provided over line  112  as illustrated. 
     The divided down or original signals from lines  100 ,  102 ,  104 ,  106  and  112  are provided to Doppler offset synthesizer  34 . This synthesizer requires a number of signals. First, distribution unit  70  provides a clock signal by dividing down the signal C over line  113  by divider  114 , and further dividing it down by divider  116  such that this clock signal is provided to a direct digital synthesizer  118  in synthesizer  34 , with synthesizer  118  being conventional in nature. The output of the direct digital synthesizer is upconverted by the mixer  120 , with the divided-down signal over line  100 , with the output of mixer  120  being divided at divider  122  to eliminate spurs. The divided down output is then provided to another upconvert mixer  124 , which is provided with a divided down signal over line  102 . The output of mixer  124  is again divided down by a divider  126  for further spurious signal rejection. The divided down output is provided to a mixer  128 , which is provided with the divided down signal over line  104 . The output of mixer  128  is provided to a mixer  130 , which is provided with signal E over line  106 . The output of mixer  130  is divided down by a divider  132  for further spurious signal rejection. The output of divider  132  is applied to a mixer  134  having as its input signal, the signal provided over line  112 . The output of mixer  134  is then provided to mixer  52  for providing the large number of spurious-free frequencies. 
     The purpose of the direct digital synthesizer  118  is to be able to generate a large number of discreet frequencies. In order to achieve spectral purity for these frequencies, a number of stages of spur rejection are provided. In each stage, an input signal is upconverted and expanded by the associated mixer. After upconverting and expansion, the signal is divided back down for spurious improvement characteristic purposes. After a number of such stages, in one embodiment, an overall divided ratio of 64 is provided. This achieves a 36 dB improvement in the spurious performance of direct digital synthesizer  18 . It will be appreciated that direct digital synthesizer  18  used alone, has significant spurious components. By utilization of the upconvert expansion and divide chain, one can reduce the level of spurious signals to an acceptable level. 
     It will be appreciated that frequencies useable for the remainder of the seeker can also be generated from the outputs of distribution unit  70 . For instance, the B tone delivered over  140  may be divided down by divider  142 , which may itself be divided down by a divider  144  or a divider  146 , to provide two different local oscillator reference frequencies. Likewise, the E tone which may be provided over line  150  can be provided to one input of mixer  152 , the other input being the output of divider  114 , such that a third local oscillator reference frequency can be generated for use otherwise in the seeker. It will be appreciated that these particular frequencies are not switched, but are conveniently available from distribution unit  70  for other purposes. 
     Referring now to FIG. 5, in the prior art, in one embodiment, a master frequency generator  200  was composed of six mixers  206  and a number of band pass filters utilized throughout this unit, with one of the band pass filters being shown at  208 . Also shown are local oscillators  214 , one of which had 4 parts, one of which had 3 parts, and one of which had  6  parts. In one embodiment, phase locked oscillator  210  had 5 parts, for a total of at least 25 parts for this portion of the master frequency generator. S band channel synthesizer  202  had 19 parts, whereas the millimeter wave circuit upconverter has a multiplier  216 , an upconverter mixer  218 , and an upconverter mixer  220 , the output of which is applied to an upconverter mixer  222  for a parts count of 8 parts, including 5 parts for the local oscillator. 
     Referring now to FIG. 6, the S band channel synthesizer has 19 parts associated with it, there being a number of dividers  224 , a number of mixers  226 , a diplexer  228 , and a single-pole double-throw switch  230 . As a result, the sum total of all of the parts necessary for this master frequency generator grew to 328 parts, including Doppler offset circuits not described here. 
     What will be readily apparent is that the prior art master frequency generators were indeed complex, having to generate numbers of different basic tones, and having a large number of processing elements to provide the required outputs. 
     Referring now to FIG. 7, what is shown is that Doppler offset synthesizer  34  of the subject system has only 12 parts, rather than the 25 parts associated with the prior synthesizer. 
     Referring now to FIG. 8, what is shown is that by taking the fixed frequency output fo and designating it as C, one can provide five different tones in which five fixed tones are generated by adding to the fixed frequency C+⅛C, +{fraction (1/16)}C, −{fraction (1/16)}C, and −⅛C. It is this arrangement of tones that permits the multiple frequency generation with the required low phase noise, low spurious content characteristic. 
     In terms of the spectral purity requirements, for the frequencies to be used by a seeker, and referring now to FIG. 9, as is common, an IF can be conceived of as a mixer  250  which is provided with a fixed frequency as from oscillator  20 , and at its other input a divided down rendition of the fixed frequency as provided by divider  252 . This schematic characterizes a basic IF stage, which is to have a low spurious content. The requirement is that the spurious frequencies must be separated from the desired output frequency by a minimum distance that is established by the divided-by number which is the highest common divider of the system. Here, this divider is illustrated by reference character  252 . This sets the minimum spacing of a spur from the fixed frequency, with the requirement being that the spur be no closer than {fraction (1/16)}f 0  if the divide-by number is 16. 
     Referring to FIG. 10, what is shown here is a graph in which the center frequency of the IF of FIG. 9 is shown at  254 , with the spurious requirement characteristic being shown by curve  256 . Here it will be noted that there are to be no spurs within the closest offset region, here defined by points  258  and  260  on curve  256 . 
     It is a characteristic of the subject system through the utilization of only five tones and the spurious frequency reduction system of the channel synthesizer, that the output of the subject master frequency generator can generate hundreds of frequencies with a small parts count, and with the required spectral purity. 
     Algorithms for Frequency Generation 
     Referring now to FIG. 11, one topology for the generation of the multiple frequencies is illustrated in which the topology permits modulo  32  counting. Modulo  32  counting in general relies on base  2  dividers such as illustrated in FIG.  11 . In this figure, a divider  300  is a divide-by-8 divider, divider  302  is a divide-by-4 divider, divider  304  is a divide-by-8 divider, and divider  306  is a divide-by-4 divider. When the frequency spacing is K, the step size is {fraction (K/128+L )}, whereby the modulo  32  counting system is, in effect, a modulo  128  counting system due to the formula illustrated in FIG. 12, which will be discussed hereinafter. 
     It will be appreciated that in FIG. 11, tones A, B, C, D and E are applied to a mixer  308 , having its other input a divide-down version of tones A and E. It will be noted that mixer  308  utilizes only the upper side band. This is also true for mixer  310 , which has as its input tones A, B, C, and D, and the same tones divided-down by 4 as illustrated. Mixer  312  mixes the outputs of mixer  308  and mixer  310 , which is divided-down by divider  304 , with mixer  312  also utilizing only the upper side band. The output of mixer  312  is divided-down by divider  306 , such that the circuit can output  160  frequencies in one embodiment. This output is called F agility , which is switchable between multiple frequencies. The F agility  output carries reference character  314 . 
     Referring now to FIG. 12, the number of frequencies available at output  314  is such that if F 1  is either A, B, C, D or E and if F 2  is A or E; and F 3  is A, B, C or D, and if F 4  is A, B, C, D then F agility  is the sum of the weighted F 1 , F 2 , F 3  and F 4  signals noted in this figure. Noting that F 1 =F A +N 1 ×K where N 1 =0, 1, 2, 3, 4; and where F 2 =F A +N 2 ×4×K where N 2 =0, 1; and where F 3  is F A +N 3 ×K, where N 3 =0, 1, 2, 3; and where F 4 =F A +N 4 ×K and N 4 =0, 1, 2, 3, it can be shown that F agility ={fraction (41/128)}F A +{fraction (K/4+L )}(N 1 /1+N 2 /2+N 3 /8+N 4 /32). 
     What this means is that given a basic starting frequency and a predetermined step size, there is a maximum and minimum frequency achievable by the circuit of FIG. 11, in which the frequency steps are {fraction (K/128+L )}, and in which the lowest frequency that can be generated is {fraction (41/128)}F A . 
     Note, the maximum frequency generatable is in this case, the lowest frequency+{fraction (320/4)}(4+{fraction (31/32)}). In the indicated example, given a frequency step of 2.5 MHz, and given an F C  of 5,120 MHz derived from multiplying step size×128×16, then having defined F C  as the center frequency above and below which +/−⅛F C  and +/−{fraction (1/16)}F C  are added, one can then generate or derive K=128 times the step size (2.5 MHz) or 320 MHz, and can define F A  as =5,120 MHz−⅛F C  or 4,480 MHz. Moreover, the minimum frequency generated is{fraction (41/128)}×F A , where {fraction (41/128)}=¼(1+⅛+⅛+{fraction (1/32)}). The maximum frequency is given by Fmax agility =Fmin agility +{fraction (320/4)}(4+{fraction (31/32)}) Note, 4+{fraction (31/32)} represents the total number of 32 nds  that one is counting, which is {fraction (159/32)}. Thus, 160 frequencies are generated by 159 steps. 
     The result in this case is that the maximum frequency generatable with these step sizes is 1,832.5 MHz, whereas the minimum frequency is 1,435 MHz. 
     By a parity of reasoning, referring now to FIG. 15, by simply selecting the lower side band as that which is output by mixer  312 , one has a frequency output at output  314  of F agility =F A /4(1−{fraction (1/32)})+{fraction (K/4+L )}(N 1 +N 2 /2−N 3 /8−N 4 /32), as shown in FIG.  16 . 
     In the above example, referring now to FIG. 17, the minimum frequency obtainable is 1,047.5 MHz, whereas the maximum frequency available is 1,445 MHz, with 160 different frequencies being obtainable. These different frequencies are different from the frequencies derivable by the circuit of FIG.  11 . 
     Referring now to FIG. 18, assuming that mixer  308  outputs only its lower side band, with mixer  312  also outputting its lower side band, it can be seen, referring to FIG. 19, that the frequency=F A /4(1−⅛−⅛−{fraction (1/32)})+{fraction (K/4+L )}(N1−N 2 /2−N 3 /8−N 4 /32). This means that the lowest possible frequency obtainable with this topology is 727.5 MHz, whereas the highest frequency in this case is 1,125 MHz. 
     Finally, as illustrated in FIG. 21, assuming all of the mixers output only the lower side band, then the frequency as illustrated at FIG. 22 is given by F A /4(1−{fraction (7/32)})+{fraction (K/4+L )}(N−N 2 /2−N 3 /8+N 4 /32), where the minimum frequency is 805 MHz, whereas the maximum frequency is 1,202.5 MHz, as illustrated in FIG.  23 . 
     What will be seen is that there is an overlap. This overlap is illustrated in the Table of FIG. 24, and illustrates the provision of continuous coverage in 2.5 MHz steps from 727.5 MHz to 1,832.5 MHz. 
     What will be appreciated is that each of these 160 frequencies from each of the circuits, are generatable over a significant frequency band in 2.5 MHz steps. Should fine tuning of these frequencies be desired, then as illustrated in FIG. 25, they can be mixed with finer frequency offsets such as that available from a Doppler generator, with the output of the Doppler generator applied to mixer  320 . It can be shown that the number of fine-tuned offsets, rather than having steps at 2.5 MHz, can be of a fractional hertz resolution due to the use of standard digital synthesizers. 
     As illustrated in FIG.  25  and most generally, a base frequency F i , here illustrated at  322 , can be any of the five tones A, B, C, D or E. Rather than selecting C as the center tone, it will be appreciated that any one of the five tones can be selected as F i . The output from the base tone generator is multiplied at  324  by an integer N s  in this example. The output from the circuit of FIG. 10, for instance output  314 , is applied to one input of mixer  326 , which outputs both upper and lower side bands. The output of the mixer is applied to a multiplier  328 , here-designated N T , the output of which is applied to mixer  320 . 
     Referring now to FIG. 26, it will be seen that the output frequency is [F i ×N s +/−F agility ]×N T +/−F Doppler . Assuming that the multiplier for multiplier  324  is 3, and the multiplier for multiplier  328  is 2, and assuming that F i =4,480, 4,800, 5,120 and 5,760 MHz, and assuming a range of 727.5 MHz to 1,832.5 MHz, and assuming an F Doppler  of between 3,200 MHz and 5,760 MHz, then as illustrated in the Table of FIG. 27, where N s  is either 2, 3, or 4, continuous frequency coverage exceeding 20 to 40 GHz is possible. This frequency range is accomplished through the utilization of multipliers  324  and  328 , as well as mixers  326  and  320 . 
     Note that any frequency range can be obtained by simply scaling the basic five tones by factors of 2, i.e., 5,120/2. By doing so, one obtains a 10-20 GHz frequency coverage at a 1.25 MHz step size. The ability to scale the base frequencies is facilitated by having octave coverage at the output. What this means is that for every frequency doubling, the output frequency coverage will double, and the step size will double. 
     In summary, what has been provided is a convenient five-tone system for being able to generate hundreds and hundreds of frequencies throughout a wide band. It is the five tones plus the particular topology or architecture of dividers and mixers which permits the utilization of only five tones to provide this wide frequency coverage. 
     With respect to spurious rejection, it will be appreciated that at critical nodes in the circuit of FIG. 11 there is an approximate 8 to 1 frequency relationship between the input to a mixer at the IF port and the LO port thereof. For those mixers which have only a 4 to 1 ratio, the inputs to these mixers are such that whatever spurs are generated are corrected by a divider downstream of the mixer, which in essence provides an approximate 8 to 1 ratio. Note that the spurs generated at the output of mixer  310  are corrected by approximately 30 dB, due to the divide-by-8 divider  304  and the divide-by-4 divider  306 , in which the spurious content is reduced by 20 times the log of the division ratio. In this case, the division ratio is 32, or 4 times 8. 
     It will be noted that it is the tone spacing that sets the spurs at particular offsets, and it is the mixers that generate the inter-modulation spurs. However, the spurs produced by the mixers are reduced by the dividers. In essence, in the subject invention, there is an upconversion, expansion, and divide-down, which eliminates the spurs or at least reduces the spurious content. 
     Having now described a few embodiments of the invention, and some modifications and variations thereto, it should be apparent to those skilled in the art that the foregoing is merely illustrative and not limiting, having been presented by the way of example only. Numerous modifications and other embodiments are within the scope of one of ordinary skill in the art and are contemplated as falling within the scope of the invention as limited only by the appended claims and equivalents thereto.
A system is provided for generating multiple frequencies in a specified frequency band, with a specified step size between frequencies, in which the spectral purity of the frequencies is assured. The switching speed between frequencies is very fast, limited only by the speed of the switches used. In one embodiment, only five tones are generated as the base for the rest of the synthesis, in which the relationship of the five tones is f 0 +/- 1/8 f 0 and +/-{fraction (1/16)}f 0. The subject system in one embodiment, utilizes a channel synthesizer and a doppler offset synthesizer which may be utilized in air defense systems for generating the transmit channels to be able to permit a missile seeker to transmit a signal at the appropriate frequency. In one embodiment, spectral purity is achieved by providing a number of stages of up converting, expanding, and dividing down of an input signal.