Abstract:
A system for recovering a signal of interest from a complex signal is provided. The system includes a plurality of different oscillators. Each of the plurality of oscillators is configured to facilitate improving a signal-to-noise ratio of an input complex signal by adjusting an oscillation frequency of each of the plurality of oscillators based on an input frequency of interest of the input complex signal.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
       [0001]     This application is related to co-pending United States patent application having Ser. No. 10/846,183, titled “Frequency Rectification System: Apparatus and Method”, and filed on May 14, 2004. 
     
    
     BACKGROUND OF THE INVENTION  
       [0002]     This invention relates generally to systems and methods for distinguishing a frequency of interest from noise and more particularly to systems and methods for recovering a signal of interest from a complex signal.  
         [0003]     Electric machines, such as motors, are used for a wide variety of applications including but not limited to closing or opening electric switches, and/or providing power to electrical appliances. Knowing the frequency of interest with which such electrical machines operate facilitates accurately determining whether a machine is malfunctioning. However, because of surrounding noise, it may be difficult to determine the frequency of interest. Moreover, in some instances, the frequency of interest cannot be easily separated from the noise when the frequency of interest is indistinguishable from the noise.  
         [0004]     To facilitate determining the frequency of interest of a machine, at least some applications use a filter to narrow a range of frequencies of operation of the machine to a band of frequencies that includes the frequency of interest. After the operations frequency range is narrowed, the frequency of interest may then be detected from within the frequency band. However, when the signal of interest is indistinguishable from the noise, all spectrum peaks may represent frequencies of the noise rather than the frequency of interest. Selecting one of the spectrum peaks may produce random results, rather than the frequency of interest. Thus, it is difficult to distinguish the frequency of interest from within the frequency band.  
       BRIEF DESCRIPTION OF THE INVENTION  
       [0005]     In one aspect, a system for recovering a signal of interest from a complex signal is provided. The system includes a plurality of different oscillators. Each of the plurality of oscillators is configured to facilitate improving a signal-to-noise ratio of an input complex signal by adjusting an oscillation frequency of each of the plurality of oscillators based on an input frequency of interest of the input complex signal.  
         [0006]     In another aspect, a system for recovering a signal of interest from a complex signal is provided. The system includes a signal transducer configured to convert a machine output signal having a first form to generate an analog sensed signal, an analog-to-digital converter configured to convert the analog sensed signal to an input complex signal, and a plurality of different oscillators. Each of the plurality of oscillators is configured to facilitate improving a signal-to-noise ratio of an input complex signal by adjusting an oscillation frequency of each of the plurality of oscillators based on an input frequency of interest of the input complex signal.  
         [0007]     In a further aspect, a method for recovering a signal of interest from a complex signal is provided. The method includes receiving an input complex signal, and improving, by each of a plurality of oscillators of different types, a signal-to-noise ratio of the input complex signal, wherein improving the signal-to-noise ratio is performed by adjusting an oscillation frequency of the oscillator based on an input frequency of interest of the input complex signal.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0008]      FIG. 1  is an exemplary embodiment of a system that may be used to recover a signal of interest from a complex signal.  
         [0009]      FIG. 2  is an exemplary embodiment of a computer which may be used with the system of  FIG. 1 .  
         [0010]      FIG. 3  is a flowchart of an exemplary method for recovering a signal of interest from a complex signal.  
         [0011]      FIG. 4  is an alternative embodiment of a system that may be used to recover a signal of interest from a complex signal.  
         [0012]      FIG. 5  is a graphical representation of an exemplary input signal provided to the system of  FIGS. 1 and 4 .  
         [0013]      FIG. 6  is a graphical representation of an exemplary noise signal detected with the system of  FIGS. 1 and 4 .  
         [0014]      FIG. 7  is a graphical representation of an exemplary output signal used with the system of  FIGS. 1 and 4 .  
         [0015]      FIG. 8  is a graphical representation of an alternative exemplary input signal that may be used with the system of  FIGS. 1 and 4 .  
         [0016]      FIG. 9  is a graphical representation of an alternative exemplary noise signal that may be detected with the system of  FIGS. 1 and 4 .  
         [0017]      FIG. 10  is a graphical representation of an alternative exemplary output signal that may be used with the system of  FIGS. 1 and 4 .  
         [0018]      FIG. 11  is a graphical representation of a further exemplary input signal that may be used with the system of  FIGS. 1 and 4 .  
         [0019]      FIG. 12  is a graphical representation of a further exemplary noise signal that may be detected with the system of  FIGS. 1 and 4 .  
         [0020]      FIG. 13  is a graphical representation of a further exemplary output signal that may be used with the system of  FIGS. 1 and 4 .  
         [0021]      FIG. 14  is an exemplary embodiment of a rotator which may be used with the system shown in the  FIG. 4 .  
         [0022]      FIG. 15  is an exemplary embodiment of a Van der Pol oscillator. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0023]      FIG. 1  is an exemplary embodiment of a system  10  for recovering a signal of interest from a complex signal. System  10  includes a machine  12 , a transducer  14 , an analog-to-digital (A/D) converter  16 , an oscillator  18 , a transform device  20 , and an output device  22 . In an alternative embodiment, oscillator  18  includes transform device  20  and output device  22 . Machine  12  may represent but is not limited to being a rotor shaft of an electric motor and/or a casing of a turbine. Transducer  14  may represent but is not limited to an electromagnetic sensor that senses a change in electromagnetic signals. Such signal changes are generated by an oscillation, such as a rotation, of machine  12 .  
         [0024]     Oscillator  18  may include a voltage-controlled oscillator (VCO), a rotator, or alternatively any other component that adjusts an oscillation frequency of oscillator  18  to be approximately equal an input frequency of interest of an input complex signal provided to the oscillator. In an alternative embodiment, oscillator  18  is not a Van der Pol oscillator. Transform device  20  may represent a Fourier transform device that converts a signal from a time domain to a frequency domain. For example, in one embodiment, the Fourier transform device is a Fast Fourier transform device. Output device  22  may include a display, such as a cathode ray tube.  
         [0025]     Transducer  14  generates a field, such as an electromagnetic field, around machine  12 . Machine  12  oscillates, such as, rotates, within the electric magnetic field and changes the field to generate a machine output signal  24 . Transducer  14  senses machine output signal  24  and converts signal  24  into an analog sensed signal  26  that has a form suitable for reception by A/D converter  16 . For example, in the exemplary embodiment, transducer  14  receives an electromagnetic signal output from machine  12  and converts the electromagnetic signal into an electrical signal. A/D converter  16  receives analog sensed signal  26  and converts signal  26  from an analog form to a digital form. A/D converter  16  outputs an input complex signal  28  that includes an input signal of interest and an input noise signal, such as white noise. The input signal of interest has an input frequency of interest, which may be indistinguishable from the input noise signal and may be constant. An example of the input frequency of interest is a natural frequency of oscillation of machine  12 . The natural frequency may be displayed on a label on machine  12 .  
         [0026]     Oscillator  18  receives input complex signal  28  and adjusts a plurality of operating parameters of oscillator  18  to be approximately equal the oscillation frequency with the input frequency of interest of signal  28 . Alternatively, upon receipt of input complex signal  28 , oscillator  18  adjusts a single operating parameter, such as the oscillation frequency, of oscillator  18  to be approximately equal the oscillation frequency of input frequency of interest of signal  28 . Oscillator  18  continues to adjust operating parameters until the oscillation frequency is approximately equal to an input frequency of interest of signal  28 .  
         [0027]     Over time, oscillator  18  synchronizes the oscillation frequency with an input frequency of interest of input complex signal  28 . Moreover, the impact of the input noise signal on the oscillation frequency lessens and self-eliminates over time. More specifically, the input noise signal changes the oscillation frequency in a positive direction for some time and in a negative direction for the remaining time. Oscillator  18  outputs an output complex signal  30  having an output signal of interest and an output noise signal. Signal  30  has a higher signal-to-noise ratio than input complex signal  28  and as such, the output signal of interest is distinguishable from the output noise signal. Moreover, the output signal of interest has an output frequency of interest, which represents the oscillation frequency.  
         [0028]     Transform device  20  receives output complex signal  30  and transforms signal  30  from the time domain to the frequency domain. In one embodiment, transform device  20  applies a Fourier transform or alternatively a Fast Fourier transform to transform output complex signal  30  from the time domain to the frequency domain. Transform device  20  outputs a frequency domain signal  32  to output device  22  which displays frequency domain signal  32 .  
         [0029]     An operator views output device  22  and determines whether machine  12  is oscillating properly, such as, within a pre-determined frequency range, or alternatively within a variance of a pre-determined frequency. When machine  12  is not oscillating properly, the operator takes measures, such as, calls a repair center, to improve the operation of machine  12 . For example, machine  12  may be determined to be not oscillating properly when machine  12  oscillates with a frequency that is outside the pre-determined frequency range or alternatively is outside the variance.  
         [0030]      FIG. 2  is an exemplary embodiment of a computer  50 , which is an example of oscillator  18  and which may be used with system  10  of  FIG. 1 . Computer  50  includes a processor  52 , a memory  54 , an input device  56 , and output device  22 . As used herein, the term computer is not limited to just those integrated circuits referred to in the art as a computer, but broadly refers to a processor, a microcontroller, a microcomputer, a programmable logic controller, an application specific integrated circuit, and other programmable circuits, and these terms are used interchangeably herein. Memory  54  may include, but it not limited to, a computer-readable medium, such as a floppy disk, a random access memory, a compact disc—read only memory (CD-ROM), a magneto-optical disk (MOD), and/or a digital versatile disc (DVD). Input device  56  may represent, but is not limited to, a mouse, a keyboard, and/or a scanner.  
         [0031]     Processor  52  receives input complex signal  28  from A/D converter  16  and processes the signal  28 . Processor  52  processes signal  28  by adjusting a plurality of operating parameters to approximately equal the oscillation frequency with an input frequency of interest of signal  28 . Processor  52  retrieves the operating parameters from memory  54  via a memory signal  58 . The operator operates input device  56  to provide the operating parameters to processor  52  via an input signal  60 . Optionally, the operator may adjust the processor operating parameters to approximately equal the oscillation frequency with the input frequency of interest of input complex signal  28 . Processor  52  generates output complex signal  30  by processing input complex signal  28 .  
         [0032]     Processor  52  converts output complex signal  30  from the time domain to the frequency domain, and then outputs frequency domain signal  32 . Processor  52  determines, based on frequency domain signal  32 , whether the oscillation frequency approximately equals an input frequency of interest of signal  28 . When the oscillation frequency is not approximately equal to the input frequency of signal  28 , processor  52  re-adjusts the operating parameters to approximately equal the oscillation frequency with the input frequency of interest of signal  28 .  
         [0033]      FIG. 3  is a flowchart illustrating an exemplary method  70  for recovering a signal of interest from a complex signal. Method  70  includes receiving  72  input complex signal. Method  70  also includes processing  74  an input complex signal by adjusting the processor operating parameters to approximately equal the oscillation frequency with an input frequency of interest of the input complex signal. Method  70  also includes generating  76 , the output complex signal, by processing the input complex signal. In doing so, a determination  78  is made whether the oscillation frequency approximately equals an input frequency of interest of the input complex signal. The operating parameters of processor are then re-adjusted to be approximately equal the oscillation frequency with an input frequency of interest of the input complex signal when the determination  78  indicates that the oscillation frequency is not approximately equal to the input frequency of interest. The method  70  is repeated when another input complex signal  28  is received.  
         [0034]      FIG. 4  is an exemplary embodiment of a system  90  that may be used to recover a signal of interest from a complex signal.  FIGS. 5-13  illustrate graphs representing exemplary signals that may be communicated within system  90 . System  90  includes a rotator  92 , which is an example of oscillator  18 . System  90  further includes a first multiplier  94 , an adder  96 , a second multiplier  98 , a trigonometric function device  100 , a clock signal generator  102 , a plurality of switches  104  and  106 , and a plurality of terminals  108 ,  110 ,  112 , and  114 . Clock signal generator  102  may include a quartz crystal. Trigonometric function device  100  executes a trigonometric function, such as a sin function and a cosine function. Each of mutipliers  94  and  98  may include an amplifier.  
         [0035]     Clock signal generator  102  oscillates to generate a clock signal  116 . Multiplier receives clock signal  116 , determines a frequency of the clock signal, multiplies the frequency with a constant, such as, for example, 0.95, and outputs a multiplied clock signal  118 . Trigonometric function device  100  receives multiplied clock signal  118  and performs the trigonometric function on signal  118  to generate an input clock signal of interest  120 . An example of the input clock signal of interest  120  is displayed in graphs  140  and  142  of  FIG. 5 , graphs  150  and  152  of  FIG. 8 , and graphs  160  and  162  of  FIG. 11 .  
         [0036]     Graph  140  illustrates an example of an exemplary input clock signal of interest  120  in the time domain and graph  142  illustrates an example of an exemplary signal of interest  120  in the frequency domain. Graph  150  displays an example of an exemplary input clock signal of interest  120  in the time domain and graph  152  shows an example of an exemplary signal of interest  120  in the frequency domain. Graph  160  shows an example of an exemplary input clock signal of interest  120  in the time domain and graph  162  shows an example of an exemplary signal of interest  120  in the frequency domain. In graphs  140 ,  150  and  160 , the amplitudes of each input clock signal of interest  120  are plotted on the y-axis and time t, measured in seconds, is plotted on the x-axis. In graphs  142 ,  152  and  162 , the amplitudes of each input clock signal of interest  120  are plotted on the y-axis and the frequency of signal of interest  120 , measured in radians/second, are plotted on the x-axis. In each of graphs  140 ,  150 , and  160 , each input clock signal of interest  120  has an amplitude of 1, a frequency of approximately 0.95 radians/second, and is a sinusoidal signal.  
         [0037]     Referring again to  FIG. 4 , multiplier  94  receives a rotation noise signal  170 . Rotation noise signal  170  represents noise from which input clock signal of interest  120  is indistinguishable. An example of rotation noise signal  170  is shown in graphs  172  and  174  of  FIG. 6 , graphs  182  and  184  of  FIG. 9 , and graphs  192  and  194  of  FIG. 12 .  
         [0038]     Graph  172  illustrates an example of an exemplary rotation noise signal  170  in the time domain and graph  174  illustrates an example of an exemplary signal  170  in the frequency domain. Graph  182  displays an example of an exemplary rotation noise signal  170  in the time domain and graph  184  shows an example of an exemplary signal  170  in the frequency domain. Graph  192  shows an example of an exemplary rotation noise signal  170  in the time domain and graph  194  shows an example of an exemplary signal  170  in the frequency domain. In graphs  172 ,  182 , and  192 , the amplitudes of rotation noise signal  170  are plotted on the y-axis and time t, measured in seconds, is plotted on the x-axis. In graphs  174 ,  184  and  194 , amplitudes of each rotation noise signal  170  are plotted on the y-axis and frequencies of signal  170 , measured in radians/second, are plotted on the x-axis. Referring again to  FIG. 4 , multiplier  94  multiplies rotation noise signal  170  with a factor to generate a multiplied rotation noise signal  200 . As an example, multiplier  94  multiplies rotation noise signal  170  by amplifying signal  170 . An example of the factor includes a constant, such as one, two, or three.  
         [0039]     Adder  96  adds multiplied rotation noise signal  200  with input clock signal of interest  120  to generate an input complex rotation signal  202 . Rotator receives  92  an input signal  204  having an amplitude of zero and/or does not receive input complex rotation signal  202 . More specifically, rotator  92  receives input signal  204  when switch  106  is connected to terminal  114 , and rotates to output an output complex rotation signal  206  including an output rotation noise signal and an output rotation signal of interest. Moreover, when input signal  204  is received, rotator  92  rotates with a rotation frequency, which is adjusted prior to receiving input signal  204 . More specifically, the rotation frequency is adjusted to approximately equal an input frequency of interest of signal  120 . Operating parameters of rotator  92  are adjusted to be approximately equal the rotation frequency of the input frequency of interest of signal  120 .  
         [0040]     Graphs  140  and  142  illustrate an exemplary input clock signal of interest  120  when switch  206  is connected to terminal  114 , and graphs  172  and  174  represent an example of rotation noise signal  170  when switch  106  is connected to terminal  114 . Graph  220 , shown in  FIG. 7  represents an exemplary of output complex rotation signal  206  in the time domain when switch  106  is connected to terminal  114 , and graph  222  represents an exemplary output complex rotation signal  206  in the frequency domain when switch  106  is connected to terminal  114 . In graph  220 , the amplitudes of output complex rotation signal  206  are plotted on the y-axis and time t, measured in seconds, is plotted on the x-axis. In graph  220 , the amplitudes of output complex rotation signal  206  are plotted on the y-axis and frequencies of signal  206 , measured in radians/second, are plotted on the x-axis. In graph  222 , an output rotation frequency of interest, which is evident as a major component in the graph, of output complex rotation signal  206  is 1 radian/second, which is the rotation frequency of rotator  92 .  
         [0041]     When switch  104  is connected to terminal  110 , multiplier  94  receives input signal  204  having an amplitude of zero and outputs multiplied rotation noise signal  200  having an amplitude of zero. When multiplied rotation noise signal  200  is received, adder  96  adds signal  200  and input clock signal of interest  120  to generate input complex rotation signal  202 . Input complex rotation signal  202  is the same as input clock signal of interest  120  when multiplied rotation noise signal  200  has an amplitude of zero. When input complex rotation signal  202  is received, rotator  92  adjusts operating parameters to approximately equal the rotation frequency with an input frequency of interest of input clock signal of interest  120 , and generates output complex rotation signal  206 . Rotator  92  receives input complex rotation signal  202  when switch  106  is connected to terminal  112 . Graphs  152  and  154  illustrate an example of an exemplary input clock signal of interest  120  when switch  104  is connected to terminal  110  and switch  106  is connected to terminal  112 , and graphs  182  and  184  represent an example of an exemplary rotation noise signal  170  when switch  104  is connected to terminal  110  and switch  106  is connected to terminal  112 . Graph  232  of  FIG. 10  represents an example of an exemplary output complex rotation signal  206  in the time domain when switch  104  is connected to terminal  110  and switch  106  is connected to terminal  112 , and a graph  234  represents an example of an exemplary signal  206  in the frequency domain when switch  104  is connected to terminal  110  and switch  106  is connected to terminal  112 . In graph  232 , the amplitudes of output complex rotation signal  206  are plotted on the y-axis and time t, measured in seconds, is plotted on the x-axis. In graph  234 , the amplitudes of output complex rotation signal  206  are plotted on the y-axis and frequencies of signal  206 , measured in radians/second, are plotted on the x-axis. In graph  234 , an output rotation frequency of interest, which is evident as a major component in the graph, of output complex rotation signal  206  is approximately 0.95 radians/second.  
         [0042]     When switch  104  is connected to terminal  108 , multiplier  94  receives rotation noise signal  170  and multiplies signal  170  with the factor to generate multiplied rotation noise signal  200 . Adder  96  adds multiplied rotation noise signal  200  to input clock signal of interest  120  and outputs input complex rotation signal  202 . Rotator  92  receives input complex rotation signal  202 , adjusts operating parameters of rotator  92  to approximately equal the rotation frequency with an input frequency of interest of input clock signal of interest  120 , and generates output complex rotation signal  206 . Rotator  92  receives input complex rotation signal  202  when switch  106  is connected to terminal  112 . Graphs  160  and  162  illustrate an example of an exemplary input clock signal of interest  120  when switch  106  is connected to terminal  112  and switch  104  is connected to terminal  108 , and graphs  192  and  194  illustrate an example of an exemplary rotation noise signal  170  when switch  106  is connected to terminal  112  and switch  104  is connected to terminal  108 . Graph  242  of  FIG. 13  illustrates an example of an exemplary output complex rotation signal  206  in the time domain when switch  106  is connected to terminal  112  and switch  104  is connected to terminal  108 , and a graph  244  displays an example of an exemplary signal  206  in the frequency domain when switch  106  is connected to terminal  112  and switch  104  is connected to terminal  108 . In graph  242 , the amplitudes of output complex rotation signal  206  are plotted on the y-axis and time t, measured in seconds, is plotted on the x-axis. In graph  244 , the amplitudes of output complex rotation signal  206  are plotted on the y-axis and frequencies of the output complex rotation signal, measured in radians/second, are plotted on the x-axis. In graph  244 , an output rotation frequency of interest, which is evident as a major component in the graph, of output complex rotation signal  206  is approximately 0.95 radians/second.  
         [0043]      FIG. 14  is an exemplary embodiment of rotator  92  that may be used with system  90  of  FIG. 4 . Rotator  92  includes a plurality of integrators  260  and  262 , trigonometric function device  100 , a static moment multiplier  264 , a multiplier  266 , a plurality of adders  268  and  270 , a negative damping multiplier  272 , and an inverse inertia multiplier  274 . Each of adder  268  and multiplier  266  may represent a modulator. Each of static moment multiplier  264 , negative damping multiplier  272 , and inverse inertia multiplier  274  may include an amplifier.  
         [0044]     When input complex rotation signal  202  is received, multiplier  266  multiplies signal  202  by a static moment multiplier output signal  282  to output a multiplier output signal  284 . Adder  268  receives multiplier output signal  284  and a negative damping multiplier output signal  286 , and adds signal  284  and signal  286  to generate an adder output signal  288 . When adder output signal  288  is received, inverse inertia multiplier  274  multiplies signal  288  with an inverse 1/I of inertia I of rotator  92  to generate an inverse inertia multiplier output signal  290 . Integrator  260  receives inverse inertia multiplier output signal  290 , integrates signal  290  over time t to generate an integrator output signal  292 . When integrator output signal  292  is received, adder  270  adds signal  292  to a negative value  294  of the rotation frequency f of rotator  92 , and outputs an adder output signal  296 . Negative damping multiplier  272  receives adder output signal  296 , multiplies signal  296  by a negative value of a damping D of rotator  92 , and generates negative damping multiplier output signal  286 . When integrator output signal  292  is received, integrator  262  integrates signal  292  over time t to generate an integrator output signal  298 . Trigonometric function device  100  receives integrator output signal  298  and executes the trigonometric function on signal  298  to generate output complex rotation signal  206 . When output complex rotation signal  206  is received, static moment multiplier  264  multiplies signal  206  with a static moment w of rotator  92  to output static moment multiplier output signal  282 .  
         [0045]     In the exemplary embodiment, rotator  92  is represented by 
 
 I*d ( du/dt )/ dt+D *( du/dt−f )= w* sin( u )*input complex rotation signal  202    (1) 
 
 wherein ‘*’ represents multiplication, sin(u) is output complex rotation signal  206 , d/dt represents a derivative with respect to time t, and u is an angular variable output, such as a rotation, of rotator  92 . Operating parameters of rotator  92  include I, D, f, and w. An example of I=1, D=1, f=1, w=0.5. When an input frequency of interest of input clock signal of interest  120  is 0.95 radians/second, f is selected to be 1 radian/second, which is approximately equal to 0.95 radians/second. As another example, when an input frequency of interest of input clock signal of interest  120  is 0.95 radians/second, f is selected from a range between 0.90 radians/second and I radian/second and f is approximately equal to 0.95 radians/second. When input complex rotation signal  202  is received by rotator  92 , the rotator adjusts operating parameters of the rotator so that the rotation frequency is approximately equal to an input frequency of interest of input clock signal of interest  120 . When input complex rotation signal  202  is input signal  204  with an amplitude of zero, equation (1) becomes 
 
 I*d ( du/dt )/ dt+D *( du/dt−f )=0   (2) 
 
         [0046]     It is noted that a terminal  314  includes a switch that connects integrator output signal  292  to integrator  262  at one time t and connects integrator output signal  292  to adder  272  at another time t.  
         [0047]      FIG. 15  is an exemplary embodiment of an exemplary oscillator  320 , known as a Van der Pol oscillator. Van der Pol oscillator  320  includes integrators  260  and  262 , an output signal and amplitude device  322 , a stiffness multiplier  324 , a multiplier  326 , a damping multiplier  328 , adder  268 , an adder  330 , and a negative inverse mass multiplier  332 . Each of stiffness multiplier  324 , negative inverse mass multiplier  332 , and damping multiplier  328  may represent an amplifier. Multiplier  326  may include a modulator.  
         [0048]     When an input Van der Pol complex signal  340  and an adder output signal  342  are received, adder  330  adds signal  340  and signal  342  to generate an adder output signal  344 . Negative inverse multiplier  332  receives adder output signal  344  and multiplies signal  344  with a negative value of an inverse (1/M) of a mass M of Van der Pol oscillator  340  to output a negative inverse mass multiplier signal  346 . When negative inverse mass multiplier signal  346  is received, integrator  260  integrates signal  346  over time t to output an integrator output signal  348 . Integrator  262  receives integrator output signal  348  and integrates signal  348  over time t to output an output Van der Pol complex signal  350 . When output Van der Pol complex signal  350  is received, output signal and amplitude device  322  multiplies signal  350  by signal  350  raised to a power x to generate a first result, multiplies an amplitude A of signal  350  with the amplitude A raised to the power x to generate a second result, and subtracts the second result from the first result to output an output signal  352 . It is noted that x is an integer.  
         [0049]     Multiplier  326  receives output signal  352  and integrator output signal  348 , and multiplies signal  352  with signal  348  to output a multiplier output signal  354 . When multiplier output signal  354  is received, damping multiplier  328  multiplies signal  354  with a damping D v  of Van der Pol oscillator  320  to generate a damping multiplier output signal  356 . Stiffness multiplier  324  receives output Van der Pol complex signal  350  and multiplies signal  350  by a stiffness K of Van der Pol oscillator  320  to generate a stiffness multiplier output signal  360 . When damping multiplier output signal  356  and stiffness multiplier output signal  360  are received, adder  268  adds signal  356  and signal  360  to generate adder output signal  342 .  
         [0050]     In the exemplary embodiment, Van der Pol oscillator  320  is represented by 
 
 M*d ( dv/dt )/ dt−Dv *(0.25* A*A−v*v )* dv/dt+K*v =input Van der Pol oscillator complex signal  340    (3) 
 
         [0051]     where v is output Van der Pol complex signal  350 , ‘*’ represents multiplication, and d/dt represents a derivative with respect to time t. When input Van der Pol oscillator complex signal  340  has an amplitude of zero, equation (3) becomes 
 
 M*d ( dv/dt )/ dt−Dv *(0.25 *A*A−v*v )* dv/dt+K*v= 0   (4) 
 
         [0052]     It is noted that a terminal  420  includes a switch that connects integrator output signal  348  to multiplier  326  at one time t and connects integrator output signal  348  to integrator  262  at another time t. It is also noted that a terminal  422  includes a switch that connects output Van der Pol complex signal  350  to stiffness multiplier  324  at one time t and connects signal  350  to output signal and amplitude device  322  at another time t.  
         [0053]     Technical effects of the systems and methods for recovering a signal of interest from a complex signal include receiving input complex signal  28  in which the input noise signal cannot be distinguished from the input signal of interest, adjusting the oscillation frequency of oscillator  18  to approximately equal an input frequency of interest of signal  28 , and outputting output complex signal  30 . A display of output complex signal  30  shows the oscillation frequency that is approximately equal to an input frequency of interest of input complex signal  28 . It is noted that an input frequency of interest of input complex signal  28  is the same as an input frequency of interest of the input signal of interest of signal  28 . It is also noted that an input frequency of interest of input clock signal of interest  120  is the same as an input frequency of interest of input complex rotation signal  202 .  
         [0054]     While the invention has been described in terms of various specific embodiments, those skilled in the art will recognize that the invention can be practiced with modification within the spirit and scope of the claims.