A radio frequency signal processing system based on a single-bit frequency measurement receiver

Abstract

The present invention discloses a radio frequency signal processing system based on a single-bit frequency measurement receiver, specifically relating to the field of frequency measurement analysis, and includes a rhythm analysis module, a disturbance mapping module, a spectrum line completion module, and a path output module; the rhythm analysis module is used to convert the zero-crossing position data in the symbol polarity sequence output by the single-bit frequency measurement receiver into a symbol flip segment interval, and extract the rhythm disturbance change index to construct a continuous trend feature reflecting the frequency change trend; the disturbance mapping module is used to construct the continuous trend feature into a rhythm disturbance feature trajectory, and generate pseudo-periodic path data and a fitted frequency trend trajectory. By constructing a rhythm disturbance trajectory based on the symbol polarity sequence and introducing a rhythm structure-driven frequency interpolation reconstruction mechanism at the spectrum breakpoints, the problem of Fourier analysis failing in the frequency transition section and being unable to output a continuous frequency path under single-bit sampling conditions is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of frequency measurement and analysis, and more particularly to a radio frequency signal processing system based on a single-bit frequency measurement receiver. Background Art

[0002] In existing frequency measurement devices and spectrum analysis systems, Fourier analysis is commonly used to extract frequencies from time-domain sampled data. This relies on phase continuity and amplitude structure to establish a stable spectrum response curve to support continuous tracking of time-varying frequencies such as frequency-modulated communication signals and frequency-hopping radar signals.

[0003] However, in recent years, single-bit frequency measurement receivers have been widely introduced to meet the application requirements of low power consumption, small size, and minimalist hardware architecture. This type of receiving structure only performs a 1-bit quantization operation on the input RF signal, that is, recording its symbol polarity rather than the complete waveform, thus completely discarding the amplitude and fine phase information.

[0004] Since Fourier analysis is highly dependent on the continuous structure of time-domain signals, single-bit data will exhibit an approximately randomly alternating zero-crossing pattern in frequency mutation regions (such as frequency jump points or nonlinear frequency modulation slope breakpoints), which in turn produces an unresolvable high-frequency interference background in the spectrum analysis results, causing the frequency measurement device to be unable to form an effective spectral line in this section; therefore, in frequency measurement devices using a single-bit receiving structure, the existing Fourier analysis mechanism generally fails in the frequency transition section, ultimately forming uncompensable breakpoint defects in the spectrum, which constitutes a key limitation on the continuous measurement capability of the frequency path. Summary of the Invention

[0005] In order to overcome the above-mentioned defects of the prior art, an embodiment of the present invention provides a radio frequency signal processing system based on a single-bit frequency measurement receiver. By constructing a rhythmic perturbation trajectory based on a symbol polarity sequence and introducing a frequency interpolation reconstruction mechanism driven by a rhythmic structure at the spectrum breakpoint, the problem of Fourier analysis failing in the frequency transition section and being unable to output a continuous frequency path under single-bit sampling conditions is solved.

[0006] To achieve the above object, the present invention provides the following technical solution: a radio frequency signal processing system based on a single-bit frequency measurement receiver, comprising a rhythm analysis module, a disturbance mapping module, a spectrum line completion module and a path output module;

[0007] The rhythm analysis module is used to convert the zero-crossing position data in the symbol polarity sequence output by the single-bit frequency measurement receiver into symbol flip segment intervals and extract the rhythm disturbance change index to construct a continuous trend feature reflecting the frequency change trend;

[0008] The perturbation mapping module is used to construct continuous trend features into rhythmic perturbation feature trajectories, generate pseudo-periodic path data and fitted frequency trend trajectories, establish a pseudo-phase tensor structure reflecting frequency transition behavior, and output rhythmic path continuity as a basis for the validity of spectrum fitting;

[0009] The spectral line completion module is used to receive the Fourier spectrum response map and rhythm path continuity, identify spectrum breakpoints and extract fitting interval boundaries, perform frequency interpolation reconstruction and multi-window consistency verification, embed the reconstruction results into the fitting frequency trend trajectory, and generate a frequency continuous output sequence;

[0010] The path output module is used to calibrate the boundaries between the stable segment and the reconstruction segment of the frequency continuous output sequence, generate a structured frequency path identification sequence, and output data as the final frequency measurement result.

[0011] In a preferred embodiment, the rhythm analysis module is configured to take the symbol polarity sequence output by the single-bit frequency measurement receiver as input data, perform a sliding window scanning operation to extract zero-crossing position data within a continuous time period, construct a zero-crossing segment set from the zero-crossing position data in chronological order, and perform segment boundary recognition on the zero-crossing position data to divide the symbol flip segment interval;

[0012] Perform density statistics on the sign-flip segment intervals to obtain a sign-flip density sequence within each time window as a basic rhythm indicator. Perform adjacent window differential calculations on the basic rhythm indicator to generate a sign-flip density change sequence as a rhythm disturbance change indicator.

[0013] The rhythm disturbance change index is subjected to sliding window clustering operation to extract the continuous trend characteristics of the sign flip density change rate in the local interval.

[0014] In a preferred embodiment, the disturbance mapping module is used to construct a rhythm disturbance feature trajectory by superimposing continuous trend features in a time window manner as a symbol evolution expression within the frequency transition segment; perform a quasi-periodic estimation operation on the rhythm disturbance feature trajectory to generate a sign-flipped pseudo-periodic sequence as pseudo-periodic path data;

[0015] The pseudo-periodic path data is compared with the steady-state sign reversal density benchmark to calculate the error difference and form a fitting frequency trend trajectory. The fitting frequency trend trajectory and the rhythmic disturbance characteristic trajectory are jointly projected into the three-dimensional frequency fitting space to construct a pseudo-phase tensor structure. The pseudo-phase tensor structure is subjected to a structural stability assessment operation, and the output rhythmic path continuity is used as the validity criterion of the fitting frequency morphology.

[0016] In a preferred embodiment, the spectral line completion module is used to structurally align the rhythm path continuity obtained from the fitted frequency morphology with the original Fourier spectrum response map, and identify the fitting interval boundaries corresponding to the spectrum breakpoints; the Fourier spectrum response map is a frequency domain energy distribution result obtained by windowed Fourier transform processing based on the symbol polarity sequence;

[0017] The fitting interval boundary is used as a reconstruction constraint condition to perform frequency interpolation reconstruction of the spectrum breakpoint segment, output the breakpoint spectrum fitting segment data, and perform multi-window overlapping consistency verification on the breakpoint spectrum fitting segment data and the original sign flip density sequence to determine the rhythm structure matching situation.

[0018] The breakpoint spectrum fitting segment data that has passed consistency verification is embedded into the original fitting frequency trend trajectory to form a complete frequency continuous output sequence.

[0019] In a preferred embodiment, the path output module is used to perform boundary calibration operations on the stable segment and the reconstructed segment of the frequency continuous output sequence, output a structured frequency path identification sequence, and use the structured frequency path identification sequence as the final frequency measurement result output data to mark the rhythm disturbance compensation source corresponding to each jump segment.

[0020] In a preferred embodiment, in the rhythm analysis module, the zero crossing position data is defined as ; Define the zero-crossing segment set as ;

[0021] ;

[0022] ;

[0023] Sign-flipped fragment interval collection Expressed as:

[0024] ;

[0025] Sign flip density calculate:

[0026] ;

[0027] in:

[0028] ;

[0029] Rhythm disturbance change index Expressed as:

[0030] ;

[0031] ;

[0032] Rhythm perturbation change intensity function Expressed as:

[0033] ;

[0034] Continuous trend feature sequence obtained after sliding window clustering Expressed as:

[0035] ;

[0036] The symbol polarity sequence includes and , the symbol polarity sequence takes the value of ±1, where ±1 represents high level and low level respectively; Indicates the symbol polarity sequence in The value before the moment is the instantaneous state on the left side of the symbol polarity sequence; Indicates the symbol polarity sequence in The value after the moment is the instantaneous state of the right side of the symbol polarity sequence; is the time variable; is a set of discrete sampling moments in the continuous observation time domain; zero crossing position data Indicates all satisfaction A set of time points, indicating the time when the sign flip occurs; a set of zero-crossing segments Indicates The sliding window width is The time series set of zero-crossing points extracted within the window; for The first Zero crossing time points; is The next zero-crossing time point after that; is the lower limit of the time interval threshold; is the central time point of the sliding time window; It means to filter out a new set of elements that meet specific conditions from a set; express yes one of the; The meaning is ; represents the central time point of zero crossing; and Respectively Sampling points within the adjacent temporal neighborhood; Represents from the set Filter out the ones that meet the timing of the condition; Indicates the zero-crossing time point within the current sign-flip segment interval;

[0037] in is the segment interval between consecutive zero crossings; Indicates time interval duration; Indicates A measure of the number of sign-flip events that occur in ; the sign-flip density Indicates the current Sign reversal density index in ; rhythm disturbance change index Represents the difference in flip density between adjacent windows; is the first derivative of the flip density; is the second-order derivative of the flip density; the rhythmic perturbation intensity function Used to reflect the local oscillation and intensity of the density change rate; continuous trend feature sequence obtained after sliding window clustering Used to describe the evolutionary path of rhythmic perturbations; Indicates that the center of the sliding window is from Slide forward one window width The value of the sign flip density index calculated at the position after ; It means performing a sliding window trend clustering operation on the values of the rhythm disturbance change intensity function under all time windows, and outputting continuous time periods with the same disturbance change characteristics.

[0038] In a preferred embodiment, the disturbance mapping module further includes converting the continuous trend feature sequence Superposition to construct rhythmic perturbation characteristic trajectories , and extract the local disturbance path by dynamic rhythm projection; the rhythm disturbance feature trajectory Construct a periodic induction matrix and construct a sign-flipping pseudo-periodic sequence through the rhythmic track distance between trajectory segments ; Combined with the steady-state sign flip density benchmark , perform structural residual analysis on pseudo-periodic path data to generate fitted frequency trend trajectories ;Will and Jointly embed the frequency-disturbance coupling mapping space to construct a third-order pseudo-phase tensor based on the perturbation gauge tensor map ;Perform perturbation trajectory path consistency convolution in the tensor domain and define the rhythmic path continuity index through the perturbation frequency surface convergence behavior ;

[0039] ;

[0040] ;

[0041] ;

[0042] ;

[0043] ;

[0044] ;

[0045] ;

[0046] ;

[0047] The rhythmic perturbation characteristic trajectory Indicates The tensorial form of the internal rhythmic rate of change and acceleration; is the sliding window width; is the time window weighting function; is the continuous trend characteristic function; is the rhythm disturbance interval; represents the index offset used to time-shift the rhythmic perturbation trajectory in the track gauge calculation; is the disturbance gauge difference; For time point Rhythm disturbance characteristics at for The starting time point; for The starting time point; is the periodic induction matrix; Indicates Pseudo-periodic path value at ; Indicates traversal of all ; Indicates The rhythmic perturbation characteristic value at ; is the local sliding window half-width; For pseudo-periodic paths in time The value of for the steady-state sign-flip density reference trajectory; is the acceleration of the pseudo-periodic path; is the acceleration of the steady-state trajectory; is the rhythm gauge norm; is the gradient of the perturbation trajectory in the time dimension; is the frequency trend change rate; is the first derivative of the frequency trend; is the local sliding window tensor guidance factor, which is used to adjust the tensor contribution range; is the tensor integration window; is the second-order derivative of the tensor in the time dimension; is the gradient of the tensor with respect to the perturbation intensity; Represents the integral in the dimension of frequency change rate; is tensor multiplication; is the convolution operation.

[0048] In a preferred embodiment, in the spectrum line completion module, define for The breakpoint area set to which it belongs; definition is the fitting value after spectrum breakpoint reconstruction; definition The difference between the spectrum fitting result and the sign flip density is The structural residual integral at ;

[0049] ;

[0050] ;

[0051] ;

[0052] ;

[0053] in is the original Fourier spectrum response diagram; is the frequency variable in the frequency domain; is the curvature mutation threshold; express is a frequency point in the original Fourier spectrum response diagram; is the spectrum integration variable; Reconstruct kernel function for frequency domain; Rhythm path continuity index Mapping results in the frequency domain; is the sign-flip density; express The set of multi-window time periods mapped to; Represents the fitting frequency trend trajectory in the perturbation mapping module ; Represents the complete frequency output sequence after reconstructing the spectrum segment; For time point The corresponding frequency domain index set; is the indicator function; the threshold represents the error threshold for rhythm structure consistency verification; is the embedding kernel function from spectrum to time trajectory, which is used to transform Embedded in time .

[0054] In a preferred embodiment, in the path output module, define is the state identification value, the state identification value 0 indicates the stable stage, and the state identification value 1 indicates the reconstruction stage;

[0055] ;

[0056] in Represents the set of time points marked as stable segments; represents the set of time points marked as reconstruction segments; Represents the final structured frequency path identification sequence, the final structured frequency path identification sequence is composed of and An ordered pair of tuples.

[0057] Technical effects and advantages of the present invention:

[0058] 1. By replacing the amplitude and phase structure of traditional waveform signals with a rhythmic perturbation trajectory constructed based on symbol polarity sequences, this method enables identification of frequency transition trends even under single-bit frequency measurement reception conditions. This solves the problem of Fourier analysis being unable to resolve spectrum breakpoints at low bit rates, fundamentally restoring the continuous solvability of the frequency path.

[0059] 2. By constructing rhythmic perturbation feature trajectories and introducing pseudo-periodic fitting and perturbation track difference mechanisms, the frequency trajectory can still be reconstructed based on the structural rhythm in the presence of nonlinear perturbations or frequency hopping mutations, effectively alleviating the problem of reduced frequency recognition ability in phase loss scenarios.

[0060] 3. By designing a third-order pseudo-phase tensor structure, the frequency trend derivative, perturbation gradient, and rhythmic continuity are mapped into a unified tensor space, enhancing the system's structural understanding of complex frequency evolution patterns and providing stable spatial expression support for subsequent completion and noise filtering.

[0061] 4. By performing rhythm-constrained interpolation reconstruction on the breakpoint intervals in the Fourier spectrum response diagram and combining it with a consistency verification mechanism for sign flip density, the reconstructed spectrum segments are logically sign-source consistent, improving the rigor of the breakpoint spectrum line completion criteria and the reliability of signal reconstruction.

[0062] 5. By structurally identifying the frequency paths of the reconstructed segments and the stable segments, it is clearly marked which segments in the spectrum path originate from rhythm compensation, thus achieving visual and transparent labeling of the frequency measurement results and making the system output results structurally interpretable. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 Schematic diagram of the system module of the present invention. DETAILED DESCRIPTION

[0064] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0065] Refer to the instruction manual Figure 1 , a radio frequency signal processing system based on a single-bit frequency measurement receiver according to an embodiment of the present invention includes a rhythm analysis module, a disturbance mapping module, a spectrum line completion module and a path output module;

[0066] The rhythm analysis module is used to convert the zero-crossing position data in the symbol polarity sequence output by the single-bit frequency measurement receiver into symbol flip segment intervals and extract the rhythm disturbance change index to construct a continuous trend feature reflecting the frequency change trend;

[0067] The perturbation mapping module is used to construct continuous trend features into rhythmic perturbation feature trajectories, generate pseudo-periodic path data and fitted frequency trend trajectories, establish a pseudo-phase tensor structure reflecting frequency transition behavior, and output rhythmic path continuity as a basis for the validity of spectrum fitting;

[0068] The spectral line completion module is used to receive the Fourier spectrum response map and rhythm path continuity, identify spectrum breakpoints and extract fitting interval boundaries, perform frequency interpolation reconstruction and multi-window consistency verification, embed the reconstruction results into the fitting frequency trend trajectory, and generate a frequency continuous output sequence;

[0069] The path output module is used to calibrate the boundaries between the stable segment and the reconstruction segment of the frequency continuous output sequence, generate a structured frequency path identification sequence, and output data as the final frequency measurement result.

[0070] The rhythm analysis module is used to take the symbol polarity sequence output by the single-bit frequency measurement receiver as input data, perform a sliding window scanning operation to extract zero-crossing position data within a continuous time period, construct a zero-crossing segment set based on the zero-crossing position data in chronological order, and perform segment boundary recognition on the zero-crossing position data to divide the symbol flip segment interval;

[0071] Perform density statistics on the sign-flip segment intervals to obtain a sign-flip density sequence within each time window as a basic rhythm indicator. Perform adjacent window differential calculations on the basic rhythm indicator to generate a sign-flip density change sequence as a rhythm disturbance change indicator.

[0072] The rhythm disturbance change index is subjected to sliding window clustering operation to extract the continuous trend characteristics of the sign flip density change rate in the local interval.

[0073] The perturbation mapping module is used to construct rhythmic perturbation feature trajectories by superimposing continuous trend features in a time window manner as the symbol evolution expression within the frequency transition segment; the rhythmic perturbation feature trajectories are subjected to quasi-periodic estimation operations to generate sign-flipped pseudo-periodic sequences as pseudo-periodic path data;

[0074] The pseudo-periodic path data is compared with the steady-state sign reversal density benchmark to calculate the error difference and form a fitting frequency trend trajectory. The fitting frequency trend trajectory and the rhythmic disturbance characteristic trajectory are jointly projected into the three-dimensional frequency fitting space to construct a pseudo-phase tensor structure. The pseudo-phase tensor structure is subjected to a structural stability assessment operation, and the output rhythmic path continuity is used as the validity criterion of the fitting frequency morphology.

[0075] The spectral line completion module is used to structurally align the rhythmic path continuity obtained from the fitted frequency morphology with the original Fourier spectrum response map, and identify the fitting interval boundaries corresponding to the spectrum breakpoints; the Fourier spectrum response map is the frequency domain energy distribution result obtained by windowed Fourier transform processing based on the symbol polarity sequence;

[0076] The fitting interval boundary is used as a reconstruction constraint condition to perform frequency interpolation reconstruction of the spectrum breakpoint segment, output the breakpoint spectrum fitting segment data, and perform multi-window overlapping consistency verification on the breakpoint spectrum fitting segment data and the original sign flip density sequence to determine the rhythm structure matching situation.

[0077] The breakpoint spectrum fitting segment data that has passed consistency verification is embedded into the original fitting frequency trend trajectory to form a complete frequency continuous output sequence.

[0078] The path output module is used to perform boundary calibration operations on the stable segment and the reconstructed segment of the frequency continuous output sequence, output a structured frequency path identification sequence, and use the structured frequency path identification sequence as the final frequency measurement result output data. The rhythm disturbance compensation source corresponding to each jump segment is marked to improve the resolvability of frequency measurement processing in the transition state.

[0079] It should be noted that in the formula structure involved in this solution, dimensionless terms can serve as proportionality or structural adjustment factors. When combined with quantities with units, they only play a numerical scaling role and do not introduce new physical dimensions. Therefore, they will not change or confuse the overall unit system of expression. This combination of "dimensionless terms and units" can be understood as a composite structural expression commonly used in mathematical and physical modeling, conforming to the principle of dimensional consistency and having a clear physical interpretation basis.

[0080] Secondly, in the formula structure of this scheme, if multiple variables with different physical units are involved, including but not limited to time, mass or energy variables, their joint appearance is to express the collaborative modeling relationship of multiple physical mechanisms. Each variable can be formed into a unified structure through function mapping, ratio combination or normalization adjustment. The units and meanings are clear, and the overall expression conforms to the principle of dimensional consistency and the common formula of engineering modeling.

[0081] In this solution, any design constants, weights, adjustment factors, threshold parameters, and proportional coefficients are adjustable control parameters for different application environments. Their values depend on the target device configuration, data input characteristics, and performance optimization goals. During the implementation phase, they are set within a reasonable range through model verification, performance constraints, or engineering calibration. Although these parameters do not have unique preset values, they have clear adjustment logic and calculation paths, and are part of the deterministic setting process in engineering implementation. The purpose of such setting is to ensure that the solution is both universally adaptable, reproducible, and operable, without affecting its technical clarity and feasibility.

[0082] In the rhythm analysis module, the zero-crossing position data is defined as ; Define the zero-crossing segment set as ;

[0083] ;

[0084] ;

[0085] Sign-flipped fragment interval collection Expressed as:

[0086] ;

[0087] Sign flip density calculate:

[0088] ;

[0089] in:

[0090] ;

[0091] Rhythm disturbance change index Expressed as:

[0092] ;

[0093] ;

[0094] Rhythm perturbation change intensity function Expressed as:

[0095] ;

[0096] Continuous trend feature sequence obtained after sliding window clustering Expressed as:

[0097] ;

[0098] The symbol polarity sequence includes and , the symbol polarity sequence takes the value of ±1, where ±1 represents high level and low level respectively; Indicates the symbol polarity sequence in The value before the moment is the instantaneous state on the left side of the symbol polarity sequence; Indicates the symbol polarity sequence in The value after the moment is the instantaneous state of the right side of the symbol polarity sequence; is the time variable; is a set of discrete sampling moments in the continuous observation time domain; zero crossing position data Indicates all satisfaction A set of time points, indicating the time when the sign flip occurs; a set of zero-crossing segments Indicates The sliding window width is The time series set of zero-crossing points extracted within the window; for The first Zero crossing time points; is The next zero-crossing time point after that; is the lower limit of the time interval threshold, which is used to determine whether two adjacent zero crossing points constitute a valid sign flip segment; is the center time point of the sliding time window, in seconds; It means to filter out a new set of elements that meet specific conditions from a set; express yes one of the; The meaning is ; represents the central time point of zero crossing; and Respectively The sampling points within the adjacent minimum time neighborhood are used to determine whether the center point has a sign flip; Represents from the set Filter out the ones that meet the timing of the condition; Indicates the zero-crossing time point within the current sign flip segment interval, From the collection ,and is the first in the collection arranged in chronological order. elements, so It is the actual zero-crossing time point that is tested one by one during the integration process, which can be understood logically as follows: ;

[0099] in The segment interval between consecutive zero crossings is the minimum interval in which the symbol polarity remains unchanged, and the unit is seconds; Indicates time interval The duration of , in seconds; Indicates A measure of the number of sign-flip events that occur in , modeled using a unit impulse function; sign-flip density Indicates the current The symbol reversal density index in the symbol reversal density index represents the reversal intensity per unit time; the rhythm disturbance change index Represents the flip density difference between adjacent windows, which is used to capture rhythm mutations; is the first derivative of the reversal density, which represents the rate of density change; is the second-order derivative of the flip density, which indicates the trend of the change rate; the rhythmic perturbation change intensity function Used to reflect the local oscillation and intensity of the density change rate; continuous trend feature sequence obtained after sliding window clustering Used to describe the evolutionary path of rhythmic perturbations; Indicates that the center of the sliding window is from Slide forward one window width The value of the sign flip density index calculated at the position after ; Indicates that a sliding window trend clustering operation is performed on the values of the rhythm disturbance change intensity function under all time windows, and the continuous time periods with the same disturbance change characteristics are output to construct a continuous trend feature sequence .

[0100] The perturbation mapping module also includes the continuous trend feature sequence Superposition to construct rhythmic perturbation characteristic trajectories , and extract the local disturbance path by dynamic rhythm projection; the rhythm disturbance feature trajectory Construct a periodic induction matrix and construct a sign-flipping pseudo-periodic sequence through the rhythmic track distance between trajectory segments ; Combined with the steady-state sign flip density benchmark , perform structural residual analysis on pseudo-periodic path data to generate fitted frequency trend trajectories ;Will and Jointly embed the frequency-disturbance coupling mapping space to construct a third-order pseudo-phase tensor based on the perturbation gauge tensor map ;Perform perturbation trajectory path consistency convolution in the tensor domain and define the rhythmic path continuity index through the perturbation frequency surface convergence behavior ;

[0101] ;

[0102] ;

[0103] ;

[0104] ;

[0105] ;

[0106] ;

[0107] ;

[0108] ;

[0109] The rhythmic perturbation characteristic trajectory Indicates The tensorial form of the internal rhythmic rate of change and acceleration; is the center time point of the sliding time window, in seconds; is the sliding window width; is the time window weighting function, which is used to weight the time points The disturbance contribution of is a continuous trend characteristic function, which represents the sequence of sign reversal density change rates; is the first derivative of the continuous trend, indicating the instantaneous rate of change of the rhythmic disturbance; is the second-order derivative of the continuous trend, indicating the changing trend of the rhythmic perturbation rate; is the rhythm disturbance interval; represents the index offset used to time-shift the rhythmic perturbation trajectory in the track gauge calculation; is the disturbance gauge difference; For time point Rhythm disturbance characteristics at for The starting time point; for The starting time point; is the periodic induction matrix; Indicates The pseudo-periodic path value at ; Indicates traversal of all ; Indicates The rhythmic perturbation characteristic value at ; is the local sliding window half-width, in seconds; For pseudo-periodic paths in time The value of is the steady-state sign-flip density reference trajectory, which comes from the non-transition segment; is the acceleration of the pseudo-periodic path; is the acceleration of the steady-state trajectory; is the rhythmic track norm, which indicates the disturbance trajectory in Gradient strength; is the gradient of the perturbation trajectory in the time dimension; represents the two-norm; is the frequency trend change rate, which indicates the changing speed of the frequency fitting trajectory in the time dimension; is the first derivative of the frequency trend; is the local sliding window tensor guidance factor, which is used to adjust the tensor contribution range; the rhythm path continuity index Used to measure the consistency of the tensor structure under the frequency transition state; is the tensor integration window; is the second-order derivative of the tensor in the time dimension, indicating the trend of time structure change; is the gradient of the tensor with respect to the perturbation intensity; Represents the integral in the dimension of frequency change rate; is tensor multiplication; is the convolution operation.

[0110] In the line completion module, define for The breakpoint area set to which it belongs; definition is the fitting value after spectrum breakpoint reconstruction; definition The difference between the spectrum fitting result and the sign flip density is The structural residual integral at ;

[0111] ;

[0112] ;

[0113] ;

[0114] ;

[0115] in is the original Fourier spectrum response diagram. In the above formula, the original Fourier spectrum response diagram is expressed in Frequency domain energy distribution; is the frequency variable in the frequency domain, the unit is Hz; is the curvature mutation threshold, which is used to identify spectrum breakpoints; express is a frequency point in the original Fourier spectrum response diagram; is the spectrum integration variable, which represents the frequency points in the reconstruction neighborhood; is the frequency domain reconstruction kernel function, which is used to weight the neighborhood spectrum reconstruction; Rhythm path continuity index Mapping results in the frequency domain; is the sign-flip density; express The set of multi-window time periods mapped to; is the center time point of the sliding time window, in seconds; Represents the fitting frequency trend trajectory in the perturbation mapping module , that is, fitting frequency trend trajectory The expression from the perturbation mapping module input to the spectrum completion module; Represents the complete frequency output sequence after reconstructing the spectrum segment; For time point Corresponding frequency domain index set, time point The corresponding frequency domain index set is used to map the spectrum embedding range; is the indicator function. The indicator function in the above formula means that if Less than threshold , then the value is 1; the threshold represents the error threshold for rhythm structure consistency verification; is the embedding kernel function from spectrum to time trajectory, which is used to transform Embedded in time .

[0116] In the path output module, define is the state identification value, the state identification value 0 indicates the stable stage, and the state identification value 1 indicates the reconstruction stage;

[0117] ;

[0118] in Represents the set of time points marked as stable segments; represents the set of time points marked as reconstruction segments; Represents the final structured frequency path identification sequence, the final structured frequency path identification sequence is composed of and An ordered pair of tuples.

[0119] It should be noted that this solution addresses the problem of spectrum discontinuity defects caused by the inability of existing frequency measurement devices to effectively perform Fourier spectrum analysis after introducing a single-bit receiving structure. Because single-bit frequency measurement receivers only retain symbol polarity information, their output does not include amplitude and continuous phase. This makes it impossible for traditional Fourier analysis, which relies on phase continuity and waveform details, to operate stably in frequency transition sections. Key information such as frequency jump points is easily lost or broken in the spectrum diagram, resulting in the inability to form a continuous frequency trajectory, which seriously restricts the accuracy and integrity of high-sensitivity RF signal analysis.

[0120] To overcome these issues, this approach employs a multi-stage processing mechanism to reconstruct the spectral structure based on the characteristics of symbol polarity sequences. Its primary logic is to reconstruct a "traceable frequency evolution path" from "unresolvable low-dimensional information in the spectrum." Specifically, a rhythm parsing module is used to convert the temporal distribution of symbol flipping behavior in the symbol polarity sequence into a flipping density sequence in a continuous time window. The trend characteristics of the flipping density over time are then extracted. The extracted trend information does not rely on amplitude, but rather on the flipping rhythm of the symbols, constructing an intermediate representation that reflects the dynamic characteristics of frequency changes.

[0121] On this basis, the perturbation mapping module reconstructs the rhythmic coherence interrupted by the perturbation structure during the frequency transition process by constructing rhythmic perturbation characteristic trajectories and performing pseudo-periodic fitting. The periodic induction matrix mechanism introduced in this process is not based on the classical periodic function modeling, but judges the pseudo-periodic behavior through the structural similarity between rhythmic trajectories, thereby forming a frequency trend expression that does not depend on the original frequency value but can reflect the trajectory coherence. By constructing a third-order tensor structure including perturbation velocity, perturbation gradient and trend derivative, a three-dimensional space-frequency-perturbation coupling model of the frequency transition segment can be formed. The generated rhythmic path continuity index represents the degree of coherence of the structure in the time domain.

[0122] To achieve complete completion of the spectral structure, the spectral line completion module receives the aforementioned rhythm path continuity and maps it to the frequency domain, aligning it with the original Fourier spectrum response diagram; the original spectrum is the frequency domain energy result obtained by windowed Fourier transform of the polarity sequence. Although it is itself limited by data quantization loss, it still has a usable frequency response in the non-transition segment; therefore, by performing frequency interpolation reconstruction on the frequency range corresponding to the rhythm structure breakpoints and verifying the consistency of the reconstruction results with the original sign flip density sequence, the spectrum breakpoint segments can be effectively completed while ensuring the rationality of the completed area in terms of rhythmic logic; the resulting frequency continuous output sequence includes the original information retention area and the reconstructed compensation segment;

[0123] Based on the above-mentioned continuous frequency output sequence, the path output module further performs boundary calibration operations for the jumping segments and stable segments to generate a structured frequency path identification sequence. In this process, the scheme does not use the frequency numerical value as the identification basis, but instead labels the frequency state of each time period as a stable segment or a rhythm compensation segment based on its formation method (original or reconstructed). This structured representation ultimately forms frequency measurement result data that can be directly read by downstream systems. It has complete path, source traceability and structural transparency, and is suitable for scenarios with high requirements for continuity and resilience in tasks such as frequency hopping signal detection and broadband signal spectrum analysis.

[0124] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A radio frequency signal processing system based on a single-bit frequency measurement receiver, comprising a rhythm analysis module, a disturbance mapping module, a spectrum line completion module, and a path output module, characterized in that: The rhythm analysis module is used to convert the zero-crossing position data in the symbol polarity sequence output by the single-bit frequency measurement receiver into symbol flip segment intervals and extract the rhythm disturbance change index to construct a continuous trend feature reflecting the frequency change trend; The perturbation mapping module is used to construct continuous trend features into rhythmic perturbation feature trajectories, generate pseudo-periodic path data and fitted frequency trend trajectories, establish a pseudo-phase tensor structure reflecting frequency transition behavior, and output rhythmic path continuity as a basis for the validity of spectrum fitting; The spectral line completion module is used to receive the Fourier spectrum response map and rhythm path continuity, identify spectrum breakpoints and extract fitting interval boundaries, perform frequency interpolation reconstruction and multi-window consistency verification, embed the reconstruction results into the fitting frequency trend trajectory, and generate a frequency continuous output sequence; The path output module is used to calibrate the boundaries between the stable segment and the reconstruction segment of the frequency continuous output sequence, generate a structured frequency path identification sequence, and output data as the final frequency measurement result.

2. The radio frequency signal processing system based on a single-bit frequency measurement receiver according to claim 1, characterized in that: The rhythm analysis module is used to take the symbol polarity sequence output by the single-bit frequency measurement receiver as input data, perform a sliding window scanning operation to extract zero-crossing position data within a continuous time period, construct a zero-crossing segment set based on the zero-crossing position data in chronological order, and perform segment boundary recognition on the zero-crossing position data to divide the symbol flip segment interval; Perform density statistics on the sign-flip segment intervals to obtain a sign-flip density sequence within each time window as a basic rhythm indicator. Perform adjacent window differential calculations on the basic rhythm indicator to generate a sign-flip density change sequence as a rhythm disturbance change indicator. The rhythm disturbance change index is subjected to sliding window clustering operation to extract the continuous trend characteristics of the sign flip density change rate in the local interval.

3. The radio frequency signal processing system based on a single-bit frequency measurement receiver according to claim 2, characterized in that: The perturbation mapping module is used to construct rhythmic perturbation feature trajectories by superimposing continuous trend features in a time window manner as the symbol evolution expression within the frequency transition segment; the rhythmic perturbation feature trajectories are subjected to quasi-periodic estimation operations to generate sign-flipped pseudo-periodic sequences as pseudo-periodic path data; The pseudo-periodic path data is compared with the steady-state sign reversal density benchmark to calculate the error difference and form a fitting frequency trend trajectory. The fitting frequency trend trajectory and the rhythmic disturbance characteristic trajectory are jointly projected into the three-dimensional frequency fitting space to construct a pseudo-phase tensor structure. The pseudo-phase tensor structure is subjected to a structural stability assessment operation, and the output rhythmic path continuity is used as the validity criterion of the fitting frequency morphology.

4. The radio frequency signal processing system based on a single-bit frequency measurement receiver according to claim 3, characterized in that: The spectral line completion module is used to structurally align the rhythmic path continuity obtained from the fitted frequency morphology with the original Fourier spectrum response map, and identify the fitting interval boundaries corresponding to the spectrum breakpoints; the Fourier spectrum response map is the frequency domain energy distribution result obtained by windowed Fourier transform processing based on the symbol polarity sequence; The fitting interval boundary is used as a reconstruction constraint condition to perform frequency interpolation reconstruction of the spectrum breakpoint segment, output the breakpoint spectrum fitting segment data, and perform multi-window overlapping consistency verification on the breakpoint spectrum fitting segment data and the original sign flip density sequence to determine the rhythm structure matching situation. The breakpoint spectrum fitting segment data that has passed consistency verification is embedded into the original fitting frequency trend trajectory to form a complete frequency continuous output sequence.

5. The radio frequency signal processing system based on a single-bit frequency measurement receiver according to claim 4, characterized in that: The path output module is used to perform boundary calibration operations on the stable segment and the reconstructed segment of the frequency continuous output sequence, output a structured frequency path identification sequence, and use the structured frequency path identification sequence as the final frequency measurement result output data to mark the rhythm disturbance compensation source corresponding to each jump segment.

6. The radio frequency signal processing system based on a single-bit frequency measurement receiver according to claim 5, characterized in that: In the rhythm analysis module, the zero-crossing position data is defined as ; Define the zero-crossing segment set as ; ； ； Sign-flipped fragment interval collection Expressed as: ； Sign flip density calculate: ； in: ； Rhythm disturbance change index Expressed as: ； ； Rhythm perturbation change intensity function Expressed as: ； Continuous trend feature sequence obtained after sliding window clustering Expressed as: ； The symbol polarity sequence includes and , the symbol polarity sequence takes values of ±1, where ±1 represents high level and low level respectively; Indicates the symbol polarity sequence in The value before the moment is the instantaneous state on the left side of the symbol polarity sequence; Indicates the symbol polarity sequence in The value after the moment is the instantaneous state of the right side of the symbol polarity sequence; is the time variable; is a set of discrete sampling moments in the continuous observation time domain; zero crossing position data Indicates all satisfaction A set of time points, indicating the time when the sign flip occurs; a set of zero-crossing segments Indicates The sliding window width is The time series set of zero-crossing points extracted within the window; for The first Zero crossing time points; is The next zero-crossing time point after that; is the lower limit of the time interval threshold; is the central time point of the sliding time window; It means to filter out a new set of elements that meet specific conditions from a certain set; express yes one of the; The meaning is ; represents the central time point of zero crossing; and Respectively Sampling points within the adjacent temporal neighborhood; Represents from the set Filter out the ones that meet the timing of the condition; Indicates the zero-crossing time point within the current sign-flip segment interval; in is the segment interval between consecutive zero crossings; Indicates time interval duration; Indicates A measure of the number of sign-flip events that occur in ; the sign-flip density Indicates the current Sign reversal density index in ; rhythm disturbance change index Represents the difference in flip density between adjacent windows; is the first derivative of the flip density; is the second-order derivative of the flip density; the rhythmic perturbation intensity function Used to reflect the local oscillation and intensity of the density change rate; continuous trend feature sequence obtained after sliding window clustering Used to describe the evolutionary path of rhythmic perturbations; Indicates that the center of the sliding window is from Slide forward one window width The value of the sign flip density index calculated at the position after ; It means performing a sliding window trend clustering operation on the values of the rhythm disturbance change intensity function under all time windows, and outputting continuous time periods with the same disturbance change characteristics.

7. The radio frequency signal processing system based on a single-bit frequency measurement receiver according to claim 6, characterized in that: The perturbation mapping module also includes the continuous trend feature sequence Superposition to construct rhythmic perturbation characteristic trajectories , and extract the local disturbance path by dynamic rhythm projection; the rhythm disturbance feature trajectory Construct a periodic induction matrix and construct a sign-flipping pseudo-periodic sequence through the rhythmic track distance between trajectory segments ; Combined with the steady-state sign flip density benchmark , perform structural residual analysis on pseudo-periodic path data to generate fitted frequency trend trajectories ;Will and Jointly embed the frequency-disturbance coupling mapping space to construct a third-order pseudo-phase tensor based on the perturbation gauge tensor map ;Perform perturbation trajectory path consistency convolution in the tensor domain and define the rhythmic path continuity index through the perturbation frequency surface convergence behavior ; ； ； ； ； ； ； ； ； The rhythmic perturbation characteristic trajectory Indicates The tensorial form of the internal rhythmic rate of change and acceleration; is the sliding window width; is the time window weighting function; is the continuous trend characteristic function; is the rhythm disturbance interval; represents the index offset used to time-shift the rhythmic perturbation trajectory in the track gauge calculation; is the disturbance gauge difference; For time point Rhythm disturbance characteristics at for The starting time point; for The starting time point; is the periodic induction matrix; Indicates The pseudo-periodic path value at ; Indicates traversal of all ; Indicates The rhythmic perturbation characteristic value at ; is the local sliding window half-width; For pseudo-periodic paths in time The value of for the steady-state sign-flip density reference trajectory; is the acceleration of the pseudo-periodic path; is the acceleration of the steady-state trajectory; is the rhythm gauge norm; is the gradient of the perturbation trajectory in the time dimension; is the frequency trend change rate; is the first derivative of the frequency trend; is the local sliding window tensor guidance factor, which is used to adjust the tensor contribution range; is the tensor integration window; is the second-order derivative of the tensor in the time dimension; is the gradient of the tensor with respect to the perturbation intensity; Represents the integral in the dimension of frequency change rate; is tensor multiplication; is the convolution operation.

8. The radio frequency signal processing system based on a single-bit frequency measurement receiver according to claim 7, characterized in that: In the line completion module, define for The breakpoint area set to which it belongs; definition is the fitting value after spectrum breakpoint reconstruction; definition The difference between the spectrum fitting result and the sign flip density is The structural residual integral at ; ； ； ； ； in is the original Fourier spectrum response diagram; is the frequency variable in the frequency domain; is the curvature mutation threshold; express is a frequency point in the original Fourier spectrum response diagram; is the spectrum integration variable; Reconstruct kernel function for frequency domain; Rhythm path continuity index Mapping results in the frequency domain; is the sign-flip density; express The set of multi-window time periods mapped to; Represents the fitting frequency trend trajectory in the perturbation mapping module ; Represents the complete frequency output sequence after reconstructing the spectrum segment; For time point The corresponding frequency domain index set; is the indicator function; the threshold represents the error threshold for rhythm structure consistency verification; is the embedding kernel function from spectrum to time trajectory, which is used to transform Embedded in time .

9. The radio frequency signal processing system based on a single-bit frequency measurement receiver according to claim 8, characterized in that: In the path output module, define is the state identification value, the state identification value 0 indicates the stable stage, and the state identification value 1 indicates the reconstruction stage; ； in Represents the set of time points marked as stable segments; represents the set of time points marked as reconstruction segments; Represents the final structured frequency path identification sequence, the final structured frequency path identification sequence is composed of and An ordered pair of tuples.

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