Patent Publication Number: US-11025230-B2

Title: Filter that minimizes in-band noise and maximizes detection sensitivity of exponentially-modulated signals

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This Continuation-in-Part Application claims the benefit under 35 U.S.C. § 120 of application Ser. No. 15/876,910 filed on Jan. 22, 2018 which in turn is a Continuation-in-Part Application and claims the benefit under 35 U.S.C. § 120 of application Ser. No. 15/127,472 (now U.S. Pat. No. 9,941,862) filed on Sep. 20, 2016, which in turn is a U.S. National Phase Application and claims the benefit under 35 U.S.C. § 371 of International Application No. PCT/US2015/021675 filed on Mar. 20, 2015, all of which are entitled A FILTER THAT MINIMIZES IN-BAND NOISE AND MAXIMIZES DETECTION SENSITIVITY OF EXPONENTIALLY-MODULATED SIGNALS, and which in turn claims the benefit under 35 U.S.C. § 119(e) of Provisional Application Ser. No. 61/968,453 filed on Mar. 21, 2014 entitled TRANS FILTER and all of whose entire disclosures are incorporated by reference herein. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention relates generally to devices that recover, detect or demodulate signals, and more particularly, to devices that provider greater sensitivity and noise rejection for the detection of FM, Doppler radar, geological or oceanographic sonar returns and for spread spectrum communication or hybrid envelope/exponent modulation systems. 
     Conventional FM detectors/demodulators suffer from a threshold phenomenon which limits detection sensitivity of exponentially modulated signals (also referred to as “angle modulated signals”). These detectors/demodulators typically utilize diode rectifiers and matched filters to recover the baseband information signals. However, such devices introduce non-linearities, e.g., noise cross products that are the root cause of the threshold phenomenon. 
     As predicted by Claude Shannon, an FM demodulator is 1.77 dB more sensitive than a matched filter of equal bandwidth. Under this paradigm, the best that can be achieved by using the matched filter is an output signal-to-noise ratio (SNR) that is equal to the input carrier-to-noise ratio (CNR). 
     In particular, the current state-of-the-art in analog demodulators or detectors of exponentially modulated signals can be categorized into several broad classes. The first major class distinction considers the treatment of additive white Gaussian noise (AWGN). There are methods that convert or transform stationary AWGN to a parabolic noise density distribution and those that do not. Those that do convert AWGN to a parabolic distribution all have a CNR threshold limitation below which the conversion ceases. Foster-Seely, Travis and Ratio Detector types of exponential modulation demodulators, detectors or discriminators are the primary types that perform the conversion when operating at (C/KT) above the threshold limitation. See  FIGS. 1A and 1B  which depict a Travis FM discriminator and a Foster-Seeley discriminator, respectively. 
     Another general class of exponential modulation detectors utilize some form of product detection. This class of detectors do not convert AWGN to a parabolic noise power distribution. At best, they do not degrade the output detected signal-to-noise-ratio to a value worse than the input (CNR) or (C/KTB) where the input and output bands are equal. Among this type of detector is the Phase Locked Loop, the correlation detector. The Phase Locked Loop uses a voltage controlled oscillator (VCO) to provide a replica of the received signal. The phase error between the received signal and the VCO provides the signal that drives the VCO. It can have a threshold that is about 3 dB better that of the Foster-Seeley or Travis Demodulator.
     Other types of exponential modulation detectors are:
       1. Pulse Counting Discriminator. This method uses a monostable multivibrator or other pulse generator that produces a pulse of constant amplitude and width each time the composite noise and signal voltage crosses a reference value. The output pulses are low pass filtered to reject the pulse repetition rate. Fluctuation of the average value of the LP Filter output is the baseband information. This type of demodulator has a high threshold and is seldom used.   2. The FMFB utilizes negative feed-back to compress the received spectrum prior to demodulation. This technique is effective for small information bandwidths and has been used to carry up to 600 telephone channels on a single FDMFM carrier. The threshold improvement is of the order of 3 dB.   3. I/Q Demodulators. This class of demodulator requires a high degree of synchronization with the transmitted signal. The received signal is broken down into In Phase and Quadrature components. The multipliers or mixers used to perform the conversion do not transform flat input noise density to parabolic and so are limited to matched filter performance. However, there is no threshold if the band can be made small enough. Using this type of detector with a 1 Hz bandwidth the signal and noise can be sampled and stored. Multiple samples can be processed to effectively decrease the bandwidth and increase (SNR). This technique is used to detect weak Doppler RADAR returns.   
       

     Therefore, in view of the foregoing, all of these conventional demodulators fail to address the CNR threshold and, as a result, at or below this threshold the output signal is pure noise. Furthermore, because these configurations are demodulators, they do not operate as filters and consequently these demodulators cannot be cascaded. 
     Thus, there remains a need to overcome this threshold phenomenon by using filtering techniques which permit the cascading of stages thereof, that improves the SNR and which eliminates the need to utilize complex techniques to result in improved performance and design simplification. 
     All references cited herein are incorporated herein by reference in their entireties. 
     BRIEF SUMMARY OF THE INVENTION 
     A filter is disclosed that demodulates an exponentially-modulated signal, having noise in its signal band, and compresses the noise in its signal band, the filter comprises: a pair of parallel paths having a common input into which is fed the exponentially modulated signal and wherein at least one of the parallel paths comprises a time delay for delaying the exponentially-modulated signal passing therethrough, wherein each of the parallel paths comprises a respective output signal and wherein the respective output signals are delayed in time from each other by a predetermined parameter (e.g., a difference in time delays of the respective output signals that is equal to the reciprocal of twice the center frequency of the filter), wherein the parallel paths and the time delay comprise only linear components, wherein the linear components minimize a threshold (e.g., CNR threshold) that is normally present in exponentially-modulated signal demodulators; a summing network for receiving the respective output signals and summing the respective output signals to generate an output that is a function of a rate change of a carrier frequency of the exponentially-modulated signal, the output comprising impulses for abrupt changes in the carrier frequency corresponding to data transitions that form the baseband of the exponentially-modulated signal; and wherein the filter is linear time-invariant (LTI) and is operative on any modulation format of the exponentially modulated signal and generates the impulses while compressing noise in the signal band. 
     A method is disclosed for demodulating an exponentially-modulated signal, having noise in its signal band, and compressing the noise in its signal band, the method comprises: feeding the exponentially-modulated signal into a linear time-invariant (LTI) filter comprising a pair of parallel paths having a common input and wherein at least one of the parallel paths comprises a time delay for delaying the exponentially-modulated signal passing therethrough, wherein each of the parallel paths comprises a respective output signal and wherein the respective output signals are delayed in time from each other by a predetermined parameter (e.g., a difference in time delays of the respective output signals that is equal to the reciprocal of twice the center frequency of the filter), wherein the parallel paths and the time delay comprise only linear components, wherein the linear components minimize a threshold (e.g., CNR threshold) that is normally present in exponentially-modulated signal demodulators, and wherein the filter is operative on any modulation format of the exponentially-modulated signal; summing the respective output signals to generate an output that is a function of a rate change of a carrier frequency of the exponentially-modulated signal, wherein the output comprises impulses for abrupt changes in the carrier frequency corresponding to data transitions that form the baseband of the exponentially-modulated signal; and compressing noise in the signal band. 
     A system, formed of at least two filters, is disclosed that demodulates an exponentially-modulated signal, having noise in its signal band, and compresses the noise in its signal band, the system comprising: a first linear time-invariant (LTI) filter comprising: a first pair of parallel paths having a common input into which is fed the exponentially modulated signal and wherein at least one of the first parallel paths comprises a time delay for delaying the exponentially-modulated signal passing therethrough, wherein each of the first parallel paths comprises a respective output signal and wherein the respective output signals are delayed in time from each other by a predetermined parameter (e.g., a difference in time delays of the respective output signals that is equal to the reciprocal of twice the center frequency of the first filter), wherein the parallel paths and the time delay comprise only linear components, wherein the linear components minimize a threshold (e.g., CNR threshold) that is normally present in exponentially-modulated signal demodulators; a first summing network for receiving the respective output signals from the first pair of parallel paths and summing the respective output signals to generate an output that is a function of a rate change of a carrier frequency of the exponentially-modulated signal, wherein the output comprises impulses for abrupt changes in the carrier frequency corresponding to data transitions that form the baseband of the exponentially-modulated signal; and wherein the first filter is operative on any modulation format of the exponentially modulated signal and generates the impulses while compressing noise in the signal band; and a second LTI filter comprising: a second pair of parallel paths having a common input into which the impulses are fed and wherein at least one of the second parallel paths comprises a time delay for delaying the impulses passing therethrough, wherein each of the second parallel paths comprises a respective output signal and wherein the respective output signals of the second pair of parallel paths are delayed in time from each other by the predetermined parameter (e.g., a difference in time delays of the respective output signals that is equal to the reciprocal of twice the center frequency of the first filter), wherein the second pair of parallel paths and the time delay comprise only linear components, wherein the linear components minimize the threshold (e.g., CNR threshold) that is normally present in exponentially-modulated signal demodulators; and a second summing network for receiving the respective output signals from the second pair of parallel paths and summing the respective output signals to further increase amplitudes of the impulses for abrupt changes in the carrier frequency corresponding to data transitions that form the baseband of the exponentially-modulated signal while further compressing noise in the signal band. 
     A filter that demodulates an exponentially modulated signal and compresses noise in its signal band is disclosed. The filter comprises: a first frequency selective network and a second frequency selective network using only linear components and which form a frequency domain derivative operator that generates an output that is a function of a rate of change of a carrier frequency of the exponentially modulated signal at an input to said filter, and wherein the linear components minimizes a threshold that is normally present in exponentially modulated signal demodulators; wherein the first frequency selective network is tuned above a center frequency of the filter and the second frequency selective network is tuned below the center frequency of the filter, wherein the first frequency selective network and the second frequency selective network are configured in parallel and both receive the exponentially modulated signal as a first input signal, wherein the first frequency selective network generates a first output signal and the second frequency selective network generates a second output signal, and wherein the first output signal and the second output signal are 180 degrees out of phase; and wherein the summing network receives the first and second output signals and sums the first and second output signals to generate impulses for abrupt changes in the carrier frequency corresponding to data transitions that form the baseband of the exponentially modulated signal; and wherein the filter is linear time-invariant (LTI) and is operative on any modulation format of the exponentially modulated signal and generates the impulses while compressing noise in the signal band. 
     A method for demodulating an exponentially modulated signal and compressing noise in its signal band is disclosed. The method comprises: feeding the exponentially modulated signal into a linear time-invariant (LTI) filter comprising first and second frequency selective networks that use only linear components for minimizing a threshold that is normally present in exponentially modulated signal demodulators, the first frequency selective network is tuned above a center frequency of the filter and the second frequency selective network is tuned below the center frequency of the filter, and wherein the first frequency selective network and the second frequency selective network are configured in parallel and both receive the exponentially modulated signal as a first input signal, and wherein the first frequency selective network generates a first output signal and the second frequency selective network generates a second output signal, and wherein the first output signal and the second output signal are 180 degrees out of phase, wherein the filter is operative on any modulation format of the exponentially-modulated signal; summing the first and second output signals to generate impulses for abrupt changes in the carrier frequency corresponding to data transitions that form the baseband of the exponentially modulated signal, and wherein the impulses correspond to a frequency domain derivative of the exponentially modulated signal which is a function of a rate of change of the carrier frequency of the exponentially modulated signal; and compressing noise in the signal band. 
     A system, formed of at least two filters, that demodulates an exponentially modulated signal and compresses noise in its signal band is disclosed. The system comprises: a first linear time-invariant (LTI) filter comprising: a first frequency selective network and a second frequency selective network using only linear components and which form a frequency domain derivative operator that generates an output that is a function of a rate of change of a carrier frequency of the exponentially modulated signal at an input to the first filter, wherein the linear components minimizing a threshold that is normally present in exponentially modulated signal demodulators; wherein the first frequency selective network is tuned above a center frequency of the first filter and the second frequency selective network is tuned below the center frequency of the first filter, wherein the first frequency selective network and the second frequency selective network are configured in parallel and both receive the exponentially modulated signal as a first input signal, wherein the first frequency selective network generates a first output signal and the second frequency selective network generates a second output signal, and wherein the first output signal and the second output signal are 180 degrees out of phase; and wherein a first summing network for receiving the first and second output signals and summing the first and second output signals to generate impulses for abrupt changes in the carrier frequency corresponding to data transitions that form the baseband of the exponentially modulated signal; and wherein the filter is operative on any modulation format of the exponentially modulated signal and generates the impulses while compressing noise in the signal band; and a second LTI filter comprising: a third frequency selective network and a fourth frequency selective network using only linear components and which also form a frequency domain derivative operator that receive the impulses from the first filter and obtains a second derivative of the impulses, the second filter further compressing noise in the signal band and further increasing amplitudes of the impulses; and wherein the third frequency selective network is tuned above the center frequency of the first filter and the fourth frequency selective network is tuned below the center frequency of the first filter, and wherein the third frequency selective network and the fourth frequency selective network also are configured in parallel and each have outputs that are also 180 degrees out of phase and which are fed to a second summing network for generating a second derivative of the impulses. 
    
    
     
       BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS 
       Many aspects of the present disclosure can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present disclosure. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views. 
         FIG. 1A  is a prior art demodulator, viz., Travis FM discriminator along with its frequency and signal characteristics, that operates above the CNR threshold; 
         FIG. 1B  is another example of a prior art demodulator, viz., Foster-Seeley discriminator along with its frequency and signal characteristics, that operates above the CNR threshold; 
         FIG. 2  is a block diagram of the filter invention of the present application, hereinafter referred to as the “trans-filter” and also depicting a plurality of these trans-filters being cascaded for increasing noise compression and impulse amplitude where these impulses are generated at data transitions for many modulation formats; 
         FIG. 3  are respective frequency responses for the signal emanating from the upper frequency selective network, the lower frequency selective network and the signal emanating from the summer; 
         FIG. 4  depicts an exemplary analog version of the trans-filter using two low pass filters in the upper path and two high pass filters in the lower path, where R 2  and R 4  are both parts of the low pass and high pass filters and the summing network; 
         FIG. 5  is another analog version of the trans-filter using two high pass filters and two low pass filters whose 180 degrees-out-phase outputs are then fed to a summer and wherein the summer output, in certain circumstances, may be processed to extract the baseband information; 
         FIG. 6  is the amplitude vs. frequency response of the two high and low pass filters&#39; outputs; 
         FIG. 7  is a vector diagram showing the amplitude and phase of v 1  and v 2  vectors at the frequencies F 1 , F 0  and F 2  of the trans-filter corresponding to  FIGS. 5-6 ; 
         FIG. 8  is a depiction of the carrier envelope at the sum output of the trans-filter; 
         FIG. 9  is timewise depiction of the output multiplier; 
         FIG. 10  is a frequency diagram of input and output spectra of the trans-filter, showing the output of the trans-filter having a null at the center frequency even when no carrier, but only noise, is present and demonstrating proof of the linearity (absence the threshold); 
         FIG. 11  is a diagram depicting the frequency spectrum at the outputs of two (by way of example only) cascaded trans-filters, showing the absence of the threshold; 
         FIG. 12  is a block diagram of a test set up for evaluating a cascade of four (by way of example only) trans-filters and to which the following  FIGS. 13-23  pertain; 
         FIG. 13  depicts the frequency-shift keying (FSK) input signal that is high-pass-filtered and applied to a first trans-filter and wherein the signal is at a level of −60 dBm at node ND 4 ; 
         FIG. 14  depicts the trans-filter impulse output for the input signal of  FIG. 13  in accordance with the mark/space transitions at node ND 15  at an input (C/KT=−50 dB-Hz); 
         FIG. 15  is a spectrum diagram showing the input noise from the filter F 0  and the output of each trans-filter; 
         FIG. 16  is a voltage versus time measurement at the first trans-filter input and wherein the vertical scale is ±200 volts and the quantity C/KT=−60 dB-Hz at node ND 4 ; 
         FIG. 17  is a voltage versus time measurement at the second trans-filter input and wherein the vertical scale is ±200 volts and the quantity C/KT=−60 dB-Hz at node ND 5 ; 
         FIG. 18  is a voltage versus time measurement at the third trans-filter input and wherein the vertical scale is ±200 volts and the quantity C/KT=−60 dB-Hz at node ND 6 ; 
         FIG. 19  is a voltage versus time measurement at the fourth trans-filter input and wherein the vertical scale is ±200 volts and the quantity C/KT=−60 dB-Hz at node ND 9 ; 
         FIG. 20  is a voltage versus time measurement at the output of the first trans-filter, measured at node ND 15 , using a filter bank to reduce noise at baseband and wherein the impulses and noise at the quantity C/KT=−50 dB-Hz; 
         FIG. 21  is a voltage versus time measurement at the output of the second trans-filter, measured at node ND 15 , using a filter bank to reduce noise at baseband and wherein the impulses and noise at the quantity C/KT=−50 dB-Hz; 
         FIG. 22  is a voltage versus time measurement at the output of the third trans-filter, measured at node ND 15 , using a filter bank to reduce noise at baseband and wherein the impulses and noise at the quantity C/KT=−50 dB-Hz; 
         FIG. 23  is a voltage versus time measurement at the output of the fourth trans-filter, measured at node ND 15 , using a filter bank to reduce noise at baseband and wherein the impulses and noise at the quantity C/KT=−50 dB-Hz; 
         FIG. 24  is a block diagram of a digital trans-filter configuration of the present invention; 
         FIG. 25A  is a low pass filter pole-zero z-plane representation of the low pass arm of  FIG. 24 ; 
         FIG. 25B  is a high pass filter pole-zero z-plane representation of the high pass arm of  FIG. 24 ; 
         FIG. 26  is the spectral response of the digital trans-filter; 
         FIG. 27  is the phase response of the digital trans-filter; 
         FIGS. 28A-28B  are the input signal and the input noise, respectively, to the digital trans-filter; 
         FIGS. 29A-29B  are output signal and the output noise, respectively of the digital trans-filter; 
         FIG. 30  is a block diagram showing a plurality of digital trans-filters being cascaded, including the use of the first embodiment of the trans-filter being used as a noise compressor before the input signal is converted to a digital signal. 
         FIG. 31  is a block diagram of a time-domain trans-filter (TDTF); 
         FIG. 31A  is a block diagram of the TDTF where the entire delay is in only one of the paths; 
         FIGS. 32A-32C  are vector diagrams showing the amplitude and phase of v 1  and v 2  vectors at the frequencies F 1 , F 0  and F 2  of the TDTF, respectively; and 
         FIG. 33  depicts the output of the time-domain trans-filter having an output that is characteristic of a comb-band reject filter. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring now to the figures, wherein like reference numerals represent like parts throughout the several views, exemplary embodiments of the present disclosure will be described in detail. Throughout this description, various components may be identified having specific values, these values are provided as exemplary embodiments and should not be limiting of various concepts of the present invention as many comparable sizes and/or values may be implemented. 
     The trans-filter  20  minimizes in-band noise and maximizes detection sensitivity of exponentially-modulated signals  20  by eliminating the threshold phenomenon that limits detection sensitivity of exponentially modulated signals (also referred to as “angle modulated signals”). It accomplishes this by elimination of nonlinear circuit elements (e.g., diodes, transistors, non-linear magnetics, etc.) used in conventional exponential modulation detectors such as phase or frequency discriminators. As such, the trans-filter  20  is linear time-invariant (LTI). The networks used in the trans-filter  20  meet the criteria of LTI, namely, that (1) the output is linearly related to the input and (2) the output for a particular input does not change due to the presence of other signals. 
     The filter  20  is a LTI circuit that detects or demodulates a variety of different modulation formats. It differentiates the input signal and transforms in-band stationary AWGN to a parabolic noise density distribution. The outputs of two parallel frequency selective circuits with opposite amplitude vs. frequency slopes are subtracted. Stationary noise components above and below the center frequency cancel each other, resulting in the parabolic noise density distribution. The magnitude of the transfer function is a “V-shaped” slope across the bandwidth of the filter reaching zero as the center frequency. The phase of the transfer function abruptly changes by 180° at the center frequency. Rapid amplitude, phase or frequency variations in the input signal generate impulses at the trans-filter  20  output. Differentiation of the input signal extracts the baseband spectrum from the RF (radio frequency) or carrier portion of the signal. The baseband, carrier and noise spectral lines all appear at the output in their respective bands. Since all of the components that comprise the trans-filter  20  are linear, there is no multiplicative reaction between any of the spectral lines. This is the reason that there is no threshold associated with the trans-filter  20 . Since the frequency spectra of the baseband, carrier and noise all exist at the output of the trans-filter, but in their respective bands, they can be separated by judicious filtering. Because flat stationary noise at the input is transformed by the linear slope into a parabolic noise density distribution and the power of an exponentially modulated signal increases as the square of the deviation, the output SNR is increased by the well-known FM improvement equation:
 
Output SNR in  f   m   =P   S   /P   N =(3/2)( C/KTf   m )(Δ F/f   m ) 2   (Equation #1)
     where:   P S =signal power and P N =noise power;   C=input carrier signal power;   K=Boltzman&#39;s Constant;   T=Noise temperature in degrees K;   f m =highest frequency in modulated signal=B;   ΔF=frequency deviation.   Equation #1 can be rewritten as:
 
Output SNR=(3/2)( C/KTB )(Δ F/B ) 2 =(3/2)(CNR)(Δ F/B ) 2   (Equation #2)
 
where (C/KTB)=input (CNR) in the information band B. The trans-filter  20  provides FM improvement without the threshold limitation of conventional FM demodulators. This results in a more sensitive radio wave detector that can operate in noisier environments and with much weaker signals than any other currently-used devices. The sensitivity of this device is greater than that of the “matched filter” by the factor (3/2)(AF/B) 2 , known in the industry as the “FM Improvement Factor.”
   

     In contrast, the quantity C/KTB is also the optimum SNR or the best that can be achieved with a matched filter. Thus, in conventional devices/methods, the best performance is given by:
 
Output SNR matched filter =Input CNR.
 
     As will also be discussed below, a plurality of identical trans-filters  20  can be cascaded, with each one providing additional rejection of in-band noise while passing exponentially-modulated signals undiminished. For FSK (frequency-shift keying), BPSK (binary phase shift keying) and PAM (pulse amplitude modulation) and other exponentially modulated signals, cascading trans-filters produces increasingly large impulses at the signal transitions. The fundamental frequency of the transients occur at baseband and can be recovered without additional frequency conversion or synchronization. In addition, the transients, having a large peak to average ratio, are even more easily detected. Doppler and data rate information may also be obtained from the impulses, thereby simplifying the demodulation process. 
     The trans-filter  20  may be used to provide superior reception in a multitude of applications such as digital FM broadcast of voice or music, digital data, GPS, radar, sonar, medical imaging, geographical mapping, and oil/mineral exploration, by way of example only. 
     The trans-filter  20  accomplishes this by using LTI frequency or phase sensitive networks that produce outputs that maintain a 180 degree phase relationship relative to each other over the exponential modulation band. The frequency sensitive network outputs can then be summed to produce an output whose amplitude is proportional to frequency or phase deviation of the input signal. Hybrid signal modulation methods utilizing both amplitude modulation (AM) and phase modulation (PM) can also benefit from the noise rejection characteristics of the trans-filter  20 . 
     It should be noted that the term “filter” as used with regard to the trans-filter  20  is meant by Applicant to describe any implementation of the features associated with the trans-filter  20 . Therefore, the term “filter” is not limited to a discrete component design or even an analog design but also includes a solid state/integrated circuit configuration, a digital implementation formed in computer code, or any other manner of implementing the features of the trans-filter  20  as described herein. In addition, the trans-filter  20  can be a module, or a stage(s) in a larger apparatus or device such as, but not limited to, a data or communication receiver, etc. Furthermore, the term “filter” is meant to cover one or more of the trans-filters  20  if a cascade (e.g., at least two trans-filters  20  are coupled together) of these trans-filters  20  is implemented. 
     In particular, as shown in  FIG. 2 , a frequency modulated (FM) signal I, including additive white Gaussian noise (AWGN), is fed into an input  22  to the trans-filter  20 . The signal I is simultaneously fed to a frequency selective network  24 A that is tuned above the center frequency (e.g., two single high pass filters, or an even number thereof) and a frequency selective network  24 B that is tuned below the center frequency (e.g., two single pole low pass filters, or an even number thereof), both of which are linear, to generate respective slope-weighted signals  26 A and  26 B that are 180° out of phase. Network  24 A shifts the phase of FM signal  10  by +90° while network  24 B shifts the phase of FM signal  10  by −90°. As the input frequency varies (over F 0 +ΔF), the signals  26 A and  26 B (having respective vector notations, v 1  and v 2 ) remain at 180° phase relative to each other. Thus, at the center frequency (F 0 ), the signals  26 A and  26 B are equal in amplitude and 180° out of phase. See  FIGS. 3 and 6-7 . These two signals  26 A and  26 B are then fed to a summing network  27  (also linear), thereby output signal  28  having a zero amplitude at this frequency, F 0 . This accounts for the linear rejection of stationary noise density voltage that results in parabolic weighting of noise power density over the baseband. The signal deviation is undiminished and therefore the trans-filter  20  reduces only the stationary AWGN. 
     As mentioned previously, the outputs  26 A/ 26 B of the two frequency sensitive networks are summed together at the sum network  27  to produce a single output  28 . The sum output  28  has the same instantaneous frequency as the input. The instantaneous amplitude is a function of the frequency offset from the center frequency. The carrier phase at the summer output  28  reverses each time the carrier passes through the center frequency. This gives the output  28  the appearance of a Double Sideband Suppressed Carrier (DSBSC)-like waveform with a frequency modulated carrier inside the envelope. The carrier phase at the sum  28  output is shown in  FIG. 7  for a single tone analog FM carrier input. 
       FIGS. 4 and 5  provide two exemplary analog embodiments, namely,  20 A and  20 B, respectively, of the trans-filter  20  and as described previously, because the noise is compressed, the edges of the modulated signal can be easily identified. As a result, there is no need for any conventional demodulation. However, in some circumstances (e.g., in a detector for a Doppler radar, also referred to as a “correlation receiver) the baseband signal may be recovered by using a conventional demodulation stage  10 , as shown in  FIG. 5 ; in particular, the demodulation stage  10  multiplies the sum output  28  by a noiseless synchronized replica  12  of the transmitted signal. Furthermore, the multiplier  14  (e.g., product detector) is linear and produces only the sum and difference products of the inputs (see  FIG. 9 ). A low pass filter  16  ejects the carrier and the high order product. 
     As can be seen from  FIGS. 4-5 , the frequency selective network tuned above the center frequency  24 A may comprise two high pass filters, HP 1 /HP 2  while the frequency selective network tuned below the center frequency  24 B may comprise two low pass filter LP 1 /LP 2 . The respective output of these two networks are the signals  26 A/ 26 B, discussed previously. 
     It should be further noted that the LTI frequency selective networks  24 A/ 24 B may each comprise respective bandpass filters. 
     As mentioned earlier with regard to the vector diagrams ( FIG. 7 ), the output spectrum of the trans-filter  20  has a null at the center frequency, F 0 , even when no signal is present. See  FIG. 10  where M( 3 ) depicts the input noise spectrum and M( 6 ) depicts the output noise spectrum of a single trans-filter with no signal present. Cascading identical trans-filters  20 , as shown in  FIG. 2 , results in increased noise rejection multiplicatively. The limit is the intrinsic noise of the filter and summing network  27  elements used. Signal transmission through multiple trans-filters  20  is also multiplicative. The resulting distortion can be compensated for by pre-distortion in a fashion similar to pre-emphasis of audio signals in FM Broadcasting. See  FIG. 11  which illustrates the additional noise suppression provided by cascading two (by way of example only) trans-filters  20 . Thus, a key improvement provided by the trans-filter  20  is cumulative, i.e., cascading trans-filters  20  of equal bandwidth results in increased improvement of signal-to-noise (SNR) ratio. As a result, if one trans-filter  20  provides 20 dB improvement in the SNR, then two identical trans-filters  20  provide 40 dB improvement in SNR. In contrast, cascading “matched filters,” of equal bandwidth, produces no additional improvements in SNR. 
     Cascading trans-filters  20  increases noise rejection, thus increasing the SNR even more relative to a matched filter approach. This can be performed at different intermediate frequencies to avoid having too much gain at any one frequency. 
     It should be understood that any LTI networks having the properties of 180 degree-relative output phase and linear amplitude variation over the FM band under consideration would allow the cited performance to be achieved. Furthermore, it should be understood that analog representations of the trans-filter  20  of  FIGS. 4-5  are provided by way of example only and that digital numeric implementations (also referred to as an “algorithmic representation”) of the trans-filter  20  are within the broadest scope of the present invention to provide ideal performance with perfect stability. The digital numeric implementation or algorithmic representation is used to detect or demodulate exponentially modulated signals that have been converted to the digital domain by analog-to-digital converter (ADC). 
     The trans-filter  20  discriminates against stationary AWGN in the signal band (See  FIG. 10 ), thereby increasing the CNR prior to detection. Unlike any conventional band pass filter (e.g., a (matched filter), a plurality of trans-filters  20  of equal bandwidth can be cascaded, providing additional rejection of stationary AWGN in the pass band (See  FIG. 11 ). The term “signal band” or “in-band” refers to the band occupied by the transmitted signal. 
     Thus, the foregoing discloses an apparatus and method that eliminates the threshold phenomenon that limits detection sensitivity of exponentially modulated signals. The apparatus and method achieve this by the elimination of nonlinear components and modification of the frequency selective networks to produce a sloping amplitude that is proportional to frequency offset from a center frequency and passes through zero at the center frequency. The opposite sloping amplitude and 180 degree phase difference cause the noise cancellation that transforms flat AWGN to a parabolic shape. The amplitude slope with frequency and the rapid phase reversal at the crossover frequency produce large polarized impulses at the transitions for digitally modulated signals of all types, thereby making the trans-filter  20  a universal digital demodulator. Elimination of non-linear circuit elements, compression of in-band noise and the derivative action of the sloping amplitude vs. frequency characteristic together with the abrupt phase reversal at crossover, combine to produce large polarized impulses at the modulation rate (Baseband) and do not require conversion to baseband. Cascading trans-filters  20  increases the magnitude of the impulse relative to the noise and carrier leakage. 
     Trans-Filter  20  Impulse Generator/Demodulator 
     The trans-filter  20  transfer function is basically a frequency domain derivative operator. It generates an output that is a function of the rate of change of the frequency at its input. As a result, the trans-filter  20  generates impulses when the input frequency changes abruptly. This is true for all types of digital modulation, whether it be phase, frequency or even abrupt changes of amplitude such as PAM. 
     The instantaneous reversal of phase of the transfer function when the signal crosses the center frequency of the trans-filter  20  produces polarized impulses that are proportional to the instantaneous frequency change, df/dt, and its sign. For a PAM signal at the trans-filter  20  center frequency, the change in going from off to on is +F o . At the end of the pulse the change is −F o . Either of these changes generate a large enough instantaneous frequency to produce the maximum + or − output of the trans-filter  20 . For FSK signals, the output of the first trans-filter  20  is more a sine/cosine conversion rather than an impulse. The second and subsequent trans-filters  20  do produce increasingly large impulses both due to the phase reversal at center frequency and the sharpness of the transition due to the higher order derivative. 
     While the impulses are generated at the trans-filter output  28  that is centered on F o , their fundamental frequency (viz., the data rate) is at baseband. The trans-filter  20 , due to its derivative characteristic, demodulates (viz., converts to baseband) the received signal. Since there are no non-linear components in the trans-filter  20 , there is no interaction between any of the frequency components, be they signal or noise. Thus, as discussed previously, there is no threshold phenomenon. 
     The slope of the trans-filter  20  transfer function converts stationary noise power to a parabolic shape which when integrated over the transmission band relative to the modulation band yields an improvement of [10 log(3/2)+20 log(ΔF/B)] for a single unit due to noise reduction only. For two trans-filters  20 , the noise reduction improvement is [10 log(5/2)+40 log(ΔF/B)]. For N identical trans-filters  20  cascaded, the reduction in noise is [10 log((2N+1)/2)+20N log(ΔF/B)]. The increase in signal impulse voltage with each additional stage is more difficult to evaluate since it is highly dependent the form of modulation and upon rise time limitations. The data in  FIGS. 20-23  for 4 cascaded stages with a PAM input indicates an increase of approximately 3 dB in signal amplitude for each added stage. 
       FIG. 12  depicts a block diagram of a test setup  100  used to evaluate the response of a cascade of four (by way of example only) identical trans-filters  20 . An FSK signal is generated using two oscillators and a switch. The mark and space frequencies are C 1  at 105 KHz and C 2  at 95 KHz. Switching rate is 50 Hz determined by Pulse Generator S 1 . Noise is provided by noise generator N. Total noise output power is 0 dBm in a 1 MHz band that is uniform in density at −60 dBm/Hz. Signal power at input to summer A 1  is 0 dBm.  FIGS. 13-23  depict the signals and signal responses of this test setup  100 . It should be noted that with regard to the test setup  100 , the following information is pertinent:
     Carrier Power=C=0 dBM   for FSK modulation FCN=2;   Noise Power Density=−164 dBm/Hz;   For T=3,000 Deg Kelvin;   (C/KT)=−48 dB-Hz for Ps=−212 dBm;   Simulation step size=5E-7 sec; and   Simulation time=0.11 sec.   

     Noise and signal are combined by the summing network A 1 . The values of G 1  and G 2  are used to establish the (C/KT) ratio for each measurement. The value of G 1  establishes noise and ranges from 0 to 1E3 (which corresponds to 10 3 ). G 2  ranges from 0 to 1E-3 (which corresponds to 10 −3 ). RMS power meters M 1  and M 2  are provided to measure signal and noise powers to establish the (C/KT) operating point for the measurements. A high pass filter F 0  is used to attenuate any vestiges of the baseband signal to a negligible value. 
       FIG. 13  shows the FSK signal of the filter F 0  output which is fed to the first trans-filter  20 ; the signal at this point is at a level of −60 dBm.  FIG. 14  shows the output pulse resulting from the mark/space transition with respect to  FIG. 13 .  FIG. 15  is a spectrum diagram showing the input noise from the filter F 0  and the output of each trans-filter  20  (TF 1 , TF 2 , TF 3  and T 4  shown in  FIG. 12 ). The trans-filter TF 1 /TF 2 /TF 3 /TF 4  outputs do not appear parabolic because the vertical scale in  FIG. 15  is logarithmic; however, as discussed previously, each trans-filter  20  operates to transform flat noise by the linear slope relationship into a parabolic noise density distribution. 
     A series of high pass, low pass and band reject filters are provided at the output of the cascaded trans-filters  20  to attenuate noise that tends to obscure the impulses generated by the mark/space transitions. That same chain of filters is used to view the output of each trans-filter  20  (namely, TF 1 , TF 2 , TF 3  and TF 4 ) in the test circuit  100  at node ND 15 ; thus, the views of  FIGS. 20-23  depict the output of trans-filters TF 1 , TF 2 , TF 3  and TF 4 , respectively. The band reject filters contribute negligible attenuation and degradation to the impulses that emanate from the summer A 1 . 
       FIGS. 16-19  clearly depict the successive compression of the noise at the output of TF 1  (node ND 4 ), TF 2  (node ND 5 ), TF 3  (node ND 6 ) and TF 4  (node ND 9 ).  FIGS. 19-22  clearly depict the successive accentuation of the impulse outputs of each trans-filter TF 1 -TF 4  as they are viewed at node ND 15 . 
       FIGS. 24-30  are directed to a digital version of the trans-filter, hereinafter referred to as the digital trans-filter (DTF)  120  and which is also LTI. In particular,  FIG. 24  is a block diagram of the DTF  120 . The DTF  120  is a lattice filter in which one arm performs a monotonic low pass filter function, while a second arm performs a monotonic high pass filter function. These filters are designed so that cascading two filters in each arm results in a 180 degree phase shift between the two arms; as such, the amplitude responses of the two arms are exactly equal at the center of the band, i.e., at the sampling frequency (F S ) divided by four, F S /4 or also referred to as half of the Nyquist Frequency. 
       FIGS. 25A / 25 B provide the low pass filter pole-zero z-plane representation of the low pass arm and the high pass filter pole-zero z-plan representation of the high pass arm, respectively. 
     When the output of the two arms are added together at the summing network  127  of the DTF  120 , the noise completely cancels at the center of the band and is reduced throughout the band; however, the signal deviation remains the same, resulting in increased SNR. The DTF&#39;s  120  spectral response is shown in  FIG. 26 .  FIG. 27  is the phase response of the DTF  120 .  FIGS. 28A-28B  depict the signal input and the noise input, respectively, to the DTF  120 .  FIGS. 29A-29B  depict the signal output and the noise output, respectively at the DTF  120 . In particular,  FIGS. 28A-29A  depict separate processing of noise and an FSK signal with a random bitstream message and carrier frequencies 0.2 and 0.3 times F S . For best performance, these are arranged symmetrically around the trans-filter  120  null. Since the trans-filter  120  is completely linear (as well as LTI), it is valid to look at the noise and signal components separately. It can be seen that the noise level is reduced. The signal is seen to be demodulated, where each transition in the carrier frequency results in an impulse, positive for a transition from lower to higher frequency, and negative for a transition from higher to lower frequency. As previously described, the trans-filter  120  converts wideband exponential signals, in this case (by way of example only), FSK, into a set of positive and negative impulses. An output filter is used after the trans-filters  120  to remove non-impulsive energy. Since impulses have a white spectrum, this involves removing all narrowband energy prior to identifying the positive and negative impulses. This filtering step increases output SNR and removes the FM carrier frequency or frequencies. 
     As with the trans-filter  20 , the DTF  120  can be cascaded with other DTFs  120  to increase noise compression and enhance impulse amplitudes for detection of the exponentially modulated signal. 
     It should be further understood that the trans-filter  20  may also act as a pre-stage for an analog-to-digital (A/D) converter in a reconfigurable receiver to compress the noise in the analog input signal prior to the A/D conversion process. For example, as also shown in  FIG. 30 , the trans-filter  20  can compress in-band noise before the analog signal is digitized (e.g., an A/D converter). The digitized signal is then inputted into a cascade of DTFs  120 . In particular, the trans-filter  20  may be used in cases where the SNR would be adversely affected by the digitizer&#39;s quantizing noise. After digitization, one or more DTFs allow detection at improved SNR. It should be further noted that the first DTF  120  in the cascade detects the signal, whether analog or digital. As discussed previously also, in some circumstances the output signal of the final DTF  120  of the cascade can be further filtered (e.g., the low pass filter  16  as shown in  FIG. 5 ). 
     In view of the foregoing, the key features of the trans-filter  20 / 120  for digitally-modulated signals are: 
     (1) compresses noise in the signal band; 
     (2) generates impulses at data transitions for any modulation format; 
     (3) can be cascaded with other trans-filters  20 / 120  to increase noise compression and impulse amplitude; 
     (4) demodulates carrier regenerating transitions of data stream; 
     (5) experiences a latency equal to one bit period; and 
     (6) requires no precision oscillators or timing. 
     Time Domain Trans-Filter  220   
     The discussion set forth above for the trans-filter  20  and the digital trans-filter  120  can be generally termed a “frequency-domain” trans-filter  20 / 120  or FDTF. Another variation of the trans-filter  20  is a time domain trans-filter (TDTF)  220  as shown in  FIG. 31 . The TDTF  220  generates the same output as described for the trans-filter  20  or digital trans-filter  120  but the TDTF  220  is simpler, more linear (e.g., produces less distortion), is implemented more easily (e.g., it has fewer components) and can be applied over a wider range of operating frequencies. As with the trans-filter  20  and digital trans-filter  120 , the TDTF  220  also exhibits the ability to reduce in-band noise, generate polarized impulses and can also be cascaded, increasing both noise reduction and impulse enhancement as described previously. The TDTF  220  is also LTI. 
     As shown in  FIG. 31 , the TDTF  220  replaces the parallel frequency selective networks  24 A and  24 B with a delay D 1   224 A and D 2   224 B in each of the two parallel paths, thereby generating delay signals V 1  and V 2 , respectively. The criteria for the TDTF  220  is that the difference in delays, i.e., D 1 -D 2  must equal to 1/(2F 0 ). In an ideal situation, it may be possible to have the requisite delay (i.e., 1/(2F 0 )) occur in either D 1  or D 2  ( FIG. 31A ) to achieve the relative delay between the two signals V 1  and V 2 . 
     In addition, unlike in the FDTF  20 / 120  where the output amplitude of each frequency selective network signals V 1  and V 2  ( FIG. 7 ) varies with frequency, in the TDTF  220  the output amplitude of delay signals V 1  and V 2  is constant. Furthermore, as shown in  FIG. 7 , the frequency selective network signals V 1  and V 2  are always 180° degrees out of phase, whether at the operating (also referred to as the “center”) frequency, F 0 , of the filter  20 / 120  or below (F 1 ) the center frequency or above (F 2 ) the center frequency; in contrast, in the TDTF  220 , the delay signals V 1  and V 2  are only 180° degrees out of phase at the center frequency, F 0 , of the filter  220 ; elsewhere the phase difference varies. See  FIGS. 32A  (below F 0 ),  32 B (at F 0 ) and  32 C (above F 0 ). 
     Although there are numerous ways to implement the delays D 1   224 A and D 2   224 B, a preferred manner is via propagation delay based on the particular conductor, or conductor trace, length used in conventional transmission line analysis. It should be understood that whichever manner the delays  224 A and D 2   224 B are implemented, only linear components (or no components at all, other than conductor or conductor trace length) are used as with the FDTF  20 / 120 . As such, this linear component (or no component) restriction eliminates the threshold phenomenon that limits detection sensitivity of exponentially-modulated signals. 
     The delay signals V 1  and V 2  (which include the noise in the signal band) are then summed in a summer network  227  and the output signal  228  is similar to all of the foregoing discussion regarding output signal  28 . 
     The transfer function of the TDTF  220  exhibits the characteristics of a comb band reject filter ( FIG. 33 ) when the difference in time delay between the summing circuit  227  input ports is an odd multiple number of half periods of the unknown input frequency of the incoming exponentially-modulated signal I. The frequency difference between teeth in the comb, F X , is the reciprocal of the time delay between inputs to the summing circuit  227 . T X =1/F X =(D 2 −D 1 ). The frequency of the Nth tooth in the comb is given by F N =(2N−1)(F X /2), where N is any positive integer. Each of the teeth in the comb band reject filter extracts the frequency derivative of applied signals while reducing in-band noise at each tooth in the comb. Because the comb band reject filter characteristic of the TDTF  220  takes the derivative of any incoming signal I having a frequency at any tooth in the filter, this makes the TDTF  220  an ideal filter structure for rapidly determining the unknown input frequency of the incoming exponentially-modulated signal I. In particular, this filter structure can be used for rapid threat location. 
     It should be further understood that, like the FDTF  20 , the TDTF  220  can be implemented in analog or digital versions. 
     It should be further understood that the subscripts used for the frequency indications in  FIG. 33  and the corresponding text in the Specification are not connected to the subscripts used in the previous discussions. 
     Thus, as with the frequency domain trans-filter  20 / 120 , the TDTF  220  reduces in-band noise, converts exponentially-modulated signals to baseband, asynchronously generates polarized impulses at data transitions of digitally modulated signals. In addition, the TDTF  220  generates a band-reject comb filter response that extracts the frequency derivative and reduces in-band noise at each tooth in the comb. 
     In view of all of the foregoing, it should be understood that the frequency domain trans-filter  20 / 120 , the TDTF  220  can be used wherever Matched Filter/Coherent Detectors are used and operate at negative input signal-to-noise ratios to recover RADAR, SONAR, communications or data signals. 
     While the invention has been described in detail and with reference to specific examples thereof, it will be apparent to one skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope thereof.