Sinusoidal Frequency Modulation Research Articles

Noise mechanism clarification in external-modulation Brillouin optical correlation-domain reflectometry with double-sideband modulator

Brillouin optical correlation-domain reflectometry (BOCDR) allows for relatively high spatial resolution and random accessibility with single-end light injection into the sensing fiber. Typically, BOCDR relies on directly modulating the laser diode’s driving current, which facilitates sinusoidal frequency modulation for distributed sensing but also introduces unintended power modulation that can degrade performance. To address these power variations, external-modulation BOCDR using a double-sideband modulator has been developed. However, this method generates substantial noise, overpowering the Brillouin signal and impeding accurate strain and temperature measurements. This study clarifies the previously unexplained noise mechanisms and suggests system design optimizations to mitigate their impact.

A High Frequency Vibration Compensation Approach for Ultra-High Resolution SAR Imaging Based on Sinusoidal Frequency Modulation Fourier-Bessel Transform

A High Frequency Vibration Compensation Approach for Ultra-High Resolution SAR Imaging Based on Sinusoidal Frequency Modulation Fourier-Bessel Transform

Pulsed Active Sonar Using Generalized Sinusoidal Frequency Modulation for High-Speed Underwater Target Detection and Tracking

Pulsed Active Sonar Using Generalized Sinusoidal Frequency Modulation for High-Speed Underwater Target Detection and Tracking

Theoretical and experimental study of inversion of spectral absorption function using experimental data of laser absorption spectrum with slow scanning and fast modulation of wavelength

Based on the tested data of laser absorption spectra, a matrix slicing method is proposed to invert the absorption function of spectral lines by using the two parameters of laser modulation frequency and laser scanning range as well as transmitted wave signal and reference wave signal under the condition of slow uniform scanning wavelength and fast periodic modulation wavelength. When the modulation is single frequency sinusoidal modulation, an accurate contour of the spectral line absorption function can be obtained by using the matrix data consisting of the values of the transmitted wave signal by the reference wave signal through the minimum value of two slice integrals with the interval of half modulation period, and the amplitude of modulation can be estimated. When the fast modulation of the wavelength is distorted to the multi-frequency superposition modulation, the absorption function is also formed by using the complementarity of multiple slices. The method above is utilized for investigating a real absorption function inversion process involving multiple overlapping absorption lines in the range of the scanning wavelengths. Moreover, the scanning range of laser wavelength can be calibrated by the interval parameters of several spectral lines in the scanning wavelength range. The absorption function of CO at 4300.700 cm<sup>–1</sup> and CO<sub>2</sub> at 6336 cm<sup>–1</sup> are successfully obtained by using this matrix slice method for experimental verification.

Maintenance method of signal coherence in lidar and experimental validation.

According to the self-heterodyne signal obtained by lidar under different fiber delay times, the model of the local oscillator signal was established, and the maintenance method of signal coherence in lidar based on the digital delay was improved by using multiple sinusoidal frequency modulation components. An imaging detection experiment was carried out at a distance of 5.4 km. The coherence of the lidar signal was maintained by combining the transmitting reference channel correction method and the local oscillator reference channel compensation method, accompanied by the use of a phase spectrum to analyze the improvement effect. The processing results of the echo signal showed that the method could remove the high-order phase errors that cannot be compensated by the phase gradient autofocus algorithm and improve the signal coherence, which could be used for the detection and imaging of long-range targets.

Adaptive transmit waveform design for active cognitive sonar using multi-tone sinusoidal frequency modulation

Cognitive sonar systems leverage information gathered from earlier sensing interactions with the acoustic environment to adapt its system parameters for optimal performance. Of the many system parameters, an active cognitive sonar system could adapt, the acoustic signal projected into the medium, also known as the transmit waveform, has a profound impact on system performance as many of the physical characteristics of the acoustic environment are contained in the return echo signal. This research examines utilizing multi-tone sinusoidal frequency modulated (MTSFM) waveforms as an adaptive transmit waveform model for use in active cognitive sonar systems. The MTSFM waveform’s frequency and phase modulation functions are composed of a finite set of weighted sinusoidal harmonics. The weights for each harmonic are utilized as a discrete set of design coefficients. Adjusting these coefficients results in constant amplitude, spectrally compact FM waveforms that possess a wide variety of performance characteristics, which in the past required a diverse set of waveform types to achieve. The adaptability of the MTSFM waveform model enables a cognitive sonar system to generate waveforms that are finely tuned for the novel scenarios and environments that it may encounter.

An improved local oscillator modulation of modulated sampling scheme for multiple mono-pulse radar signals reconstruction

The modulated sampling scheme can intercept noncooperative signals distributed in a wide frequency band by using a single receiving channel, which is an efficient architecture in many radar and communication applications. The modulated sampling scheme employs a non-uniform sample pulse train to fold the intercepted signal prior to quantization/digitization by using a local oscillator (LO) that contains a certain modulation type. Since the mono-pulse radar signals are widely used in many radar systems, the modulated sampling scheme will receive the multiple mono-pulse radar signals simultaneously in dense signal environment, and the folded outputs of the modulated sampling scheme may meet frequency aliasing. Thus, it is necessary to investigate the reconstruction of the multiple mono-pulse signals intercepted by the modulated sampling scheme in the frequency aliasing situation. In this paper, based on the orthogonal matching pursuit algorithm, the LO modulation type of the modulated sampling scheme is analyzed to achieve a better reconstruction performance of the multiple mono-pulse signals. The drawback of the typical LO using sinusoidal frequency modulation to reconstruct multiple mono-pulse signals is investigated firstly. Then, an improved LO using periodic linear frequency modulation is proposed, and its effectiveness to reconstruct multiple mono-pulse signals is analyzed. Furthermore, the parameter setting criterion of the improved LO modulation is given, and the comparison using other modulation types is discussed. Finally, several simulations are conducted to prove our analysis and the improved LO modulation can reconstruct multiple mono-pulse signals under the frequency aliasing condition.

SQUARE-WAVE FREQUENCY MODULATION IN MICROWAVE SPECTROSCOPY

Subject and Purpose. The frequency modulation (FM)combined with lock-in detection, the technique which is used in microwave spectroscopy for enhancing the sensitivity of measurements, as well as the effects due to standing wavesinthe measuring absorption cell can lead to distortions in the spectral line shapes observed. To ensure the highest possible accuracy derivable from the experimental data, these distortions needto be taken into account. A way of improving theaccuracy is to approximate to the experimental line contour with a theoretical line shape that would account for the observable distortion effects.The relevant literature sources suggest examples of theoretical expressions for the line shape in the case of a sinusoidal frequency modulation. This work has been aimed at derivingsimilar expressions for the case of a square-wave frequency modulation that shall allow increasing the accuracy of measurements. Methods and Methodology.The square-wave-FM signalsare obtained with the aid of a direct digital frequency synthesizer thatcan provide switching between two frequencies known to a high accuracy. This technical solution permits generating FM signals with precisely specified parameters. Results. A closed-form expression has been suggested, based on numerically evaluated line shape derivatives, whichallows taking into considerationthe basic types of distortions encountered in the spectral line records. The cases that have been considered concern a variety of experimental conditions, including sub-Doppler measurements with Lamb-dip observations. Conclusions. The approach that has been proposed allows one to properly take into account the distortions of spectral line shapes resulting from the use of a square-wave-FM signal, as well as those due to standing wave effects in the spectrometer cell. As has been found, application of this approach to experimental spectra with a variety of modulation parameters permits reducing the errors of frequency determination to ±0.001MHz, provided the signal-to-noise ratios are reasonably high.

Frequency response measurement of electro-optic phase modulators using the time-frequency analysis method

We propose a novel method for the frequency response measurement of electro-optic phase modulators by time-frequency analyzing the instantaneous frequency of a sinusoidal frequency-modulated (SFM) signal. The SFM signal is generated by a frequency-shifting loop (FSL) in which the electro-optic phase modulator under test generates a dual-sideband frequency shift per roundtrip. And the bandwidth of the generated SFM signal is dozens of times of the input radio-frequency (RF), which makes it a precise method to measure the frequency response of electro-optic phase modulators at lower cutoff frequencies. Based on the previously proposed time-delayed interference model [H. Yang et al., J. Lightwave Technol. 39, 3112 (2021)10.1109/JLT.2021.3059875], we establish the relationship between the “peak-to-peak” frequency of the SFM waveforms and the modulation index of the phase modulators. And a short-time Fourier transformation (STFT) is adopted to characterize the time-frequency properties of output waveforms. Experimental results are well supported by the simple theoretical model. Finally, the accuracy of the half-wave voltage measurement is discussed.

Electrochemical Frequency Modulation: New Approach and Revision of Previous Model

A careful evaluation of the earlier model (1–2) for electrochemical frequency modulation (EFM) involving two sinusoidal applied potentials for the determination of corrosion parameters shows an algebraic error. Although the missing term in the original derivation appears to be insignificant, it is found that errors involved in corrosion current determination, and especially in evaluation of the Tafel slopes can be very significant, which is of consequence because of the rising popularity of this technique. The magnitude of error is found to be a function of the inherent corrosion characteristics (anodic and cathodic Tafel slopes) of the corroding material as well as the applied peak potential of the modulation. A corrected model with detailed steps showing the appropriate math is presented. In addition, using the experimental data available in the literature, the errors involved in estimating the corrosion parameters by the earlier EFM model of Bosch et al. (1–2) are evaluated. The corrected corrosion current and the Tafel slopes can be recovered from the incorrect model without the benefit of the harmonic currents, as shown in this paper. An analysis is also presented for the case of only one applied sinusoidal frequency modulation, which offers several advantages over the multiple frequency modulation.

Double-pass consistency for amplitude- and frequency-modulation detection in normal-hearing listeners.

Amplitude modulation (AM) and frequency modulation (FM) provide crucial auditory information. If FM is encoded as AM, it should be possible to give a unified account of AM and FM perception both in terms of response consistency and performance. These two aspects of behavior were estimated for normal-hearing participants using a constant-stimuli, forced-choice detection task repeated twice with the same stimuli (double pass). Sinusoidal AM or FM with rates of 2 or 20 Hz were applied to a 500-Hz pure-tone carrier and presented at detection threshold. All stimuli were masked by a modulation noise. Percent agreement of responses across passes and percent-correct detection for the two passes were used to estimate consistency and performance, respectively. These data were simulated using a model implementing peripheral processes, a central modulation filterbank, an additive internal noise, and a template-matching device. Different levels of internal noise were required to reproduce AM and FM data, but a single level could account for the 2- and 20-Hz AM data. As for FM, two levels of internal noise were needed to account for detection at slow and fast rates. Finally, the level of internal noise yielding best predictions increased with the level of the modulation-noise masker. Overall, these results suggest that different sources of internal variability are involved for AM and FM detection at low audio frequencies.

Experimental Results of Underwater Acoustic Communication with Nonlinear Frequency Modulation Waveform.

In this paper, we propose underwater acoustic (UWA) communications using a generalized sinusoidal frequency modulation (GSFM) waveform, which has a distinct ambiguity function (AF) and correlation function characteristic. For these reasons, it is more robust in multipath channels than the conventional chirp spread spectrum (CSS) with a linear frequency modulation (LFM) waveform. Four types of GSFM waveforms that are orthogonal to each other are applied for each symbol in the proposed method. To evaluate the performance of the proposed method, we compared the performances of the proposed method and conventional method by conducting diverse experiments: simulations, lake trials and sea trials. In the simulation results, the proposed method shows better performance than the conventional method. The lake trial was conducted with a distance of 300~400 m between the transmitter and receiver. As a result of the experiment, the average bit error rate (BER) of the proposed method is and that of the conventional method is , which shows that the proposed method is superior to the conventional method. The sea trial was conducted at a distance of approximately 20 km between the transmitter and receiver at a depth of 1500 m, and the receiver was composed of 16 vertical line arrays (VLAs) with a hydrophone. The proposed method had a BER of in one channel and was error free in the other.

Underwater acoustic communication using nonlinear frequency modulation waveform with low side-lobe characteristics

In fluctuating underwater acoustic (UWA) communication, reducing the interference caused by multi-path propagation is important to get better performance. For this reason, Chirp Spread Spectrum (CSS), which has insensitive Doppler effect and having effective bandwidth, using Linear Frequency Modulation (LFM) waveform was used in UWA communication before. But LFM waveform has high auto-correlation function sidelobes it becomes interference and gets worse performance in reverberation environment. This presentation proposes an UWA communication using Generalized Sinusoidal Frequency Modulation (GSFM) waveform which is generalized form of sinusoidal FM. GSFM waveform usually attains much higher spectral efficiency and lower peak-to-average power ratio than LFM while maintaining same bandwidth and pulse duration. GSFM waveform has various types and we use two GSFM pulses that is a Forward type in time-frequency domain and a time reversing type of Forward type in this presentation. Each type represents binary values '0' and '1', respectively. Each of pulses occupy same band of frequency and each of GSFM pulses have nearly orthogonality. Simulation results in various underwater channel environments with noise will be presented. A Bellhop-based underwater channel model is used for simulation. The proposed method will be analyzed compared to the conventional CSS method with LFM waveform.

Sinusoidal Frequency-Modulated Waveforms Generated by a Phase-Modulated Frequency-Shifting Loop

We theoretically and experimentally investigate a phase-modulated frequency-shifting loop (PM-FSL) that includes an electro-optic phase modulator (EOPM) and a gain element, and is seeded by a single-frequency laser. By slightly detuning the modulation frequency of the EOPM off an integer multiple of the fundamental loop frequency, we generate an output waveform that exhibits a series of pulse doublets modulated at radio frequency (RF). We prove that the series consists of sinusoidal frequency-modulated (SFM) pulse doublets whose repetition rate and bandwidth are easily reconfigurable. We report the generation of the SFM waveforms with bandwidth above 7 GHz (limited by the detection bandwidth) by simply tuning the input RF tone over a span of a few kHz in the vicinity of 14.58 MHz (the round-trip frequency). The system is modeled using a time-delayed interference model that accounts for the modulation function of the EOPM, the loop delay time, and the detuning parameter. The model explains the formation of SFM pulse doublets and effectively reproduces all the experimental waveforms. This well-defined waveform may find applications in RF-optical signal processing and radar systems.

A High Frequency Vibration Compensation Approach For Terahertz SAR Based on Sinusoidal Frequency Modulation Fourier Transform

In this paper, a vibration estimation method for terahertz synthetic aperture radar (THz SAR) is proposed based on the sinusoidal frequency modulation Fourier transform (SFMFT), which directly operates on the phase term of the signal. Small high frequency vibration of the platform will introduce nonlinear phase modulation in radar echoes. To improve the potential of the method for vibration with multiple vibration frequencies, SFMFT is used to extract the vibration spectrum of the platform. When the vibration amplitude exceeds a certain threshold, the phase ambiguity will occur. To improve the range of estimable vibration amplitude, a method based on the conjugate cancellation of the phase errors with sub-band decomposition is introduced to reconstruct a signal with a longer equivalent wavelength. Then the accurate phase errors caused by the platform vibration can be estimated by performing SFMFT on the composite signal. The simulations prove that the proposed method is superior to the time-frequency (TF) analysis methods and can improve the range of estimable vibration amplitude.

Доплеровский скаттерометр трехсантиметрового диапазона с полным поляризационным зондированием.

The paper describes an experimental model of an X-band multi-polarization Doppler scatterometer developed at the IAP RAS with one antenna for receiving and transmitting, two generators with sinusoidal frequency modulation, slightly differing in frequency, and rigidly synchronized with each other. At the output of each of the two mixers, the co-polarizations are simultaneously distinguished in two quadratures at the beats and the cross-polarizations at the difference frequency. After filtering and synchronous detection, Doppler frequencies are obtained at all polarizations, which are then recorded on a computer for further processing. Experimental results obtained in the wind-wave channel of the large thermally stratified basin of the IAP RAS are presented.

Sinusoidal FM patterns of fault-related vibration signals for planetary gearbox fault detection under non-stationary conditions

Vibration signals related to planetary gearbox faults under non-stationary conditions will be equipped with sinusoidal modulation laws in their amplitude modulation (AM) and frequency modulation (FM) modes. Extracting fault features implied in the AM and FM modes is the key issue to detect inner gear faults occurring in planetary gearboxes. However, there exist few signal analysis approaches that are able to track the fast oscillating nature implied in the fault-induced sinusoidal FM patterns. To address such a challenging issue, this paper conducts a detailed study on sinusoidal FM patterns of the fault-related vibration signal model and proposes a novel method to extract them successfully. To be specific, the proposed method firstly separates the AM and FM modes via Hilbert transform to avoid their mutual interference. The intrinsic modulation features implied in the AM and FM modes can then be separately extracted by a developed signal decomposition method named iterative-joint chirp mode decomposition (I-JCMD) with a composite mode optimization scheme. Compared with the existing fault detection techniques, the proposed method is not only able to avoid the complicated sideband analysis but also identify the fast and time-varying oscillating nature of the FM mode with a high accuracy. The performance of our method is finally verified by three simulated cases and four groups of real vibration signals related to four types of sun gear faults occurring in a planetary gearbox test-rig, which also reveals a potential scaling relation between load strength and the oscillating coefficient of the FM mode.

Adaptive Transmit Waveform Design Using Multitone Sinusoidal Frequency Modulation

This paper presents an adaptive waveform design method using Multi-Tone Sinusoidal Frequency Modulation (MTSFM). The MTSFM waveform's modulation function is represented as a finite Fourier series expansion. The Fourier coefficients are utilized as a discrete set of design parameters that may be modified to adapt the waveform's properties. The MTSFM's design parameters are adjusted to shape the spectrum, Auto-Correlation Function (ACF), and Ambiguity Function (AF) shapes of the waveform. The MTSFM waveform model naturally possesses the constant envelope and spectrally compact waveforms that make it well suited for transmission on practical radar/sonar transmitters which utilize high power amplifiers. The MTSFM has an exact mathematical definition for its time-series using Generalized Bessel Functions which allow for deriving closed-form analytical expressions for its spectrum, AF, and ACF. These expressions allow for establishing well-defined optimization problems that finely tune the MTSFM's properties. This adaptive waveform design model is demonstrated by optimizing MTSFM waveforms that initially possess a "thumbtack-like" AF shape. The resulting optimized designs possess substantially improved sidelobe levels over specified regions in the range-Doppler plane without increasing the Time-Bandwidth Product (TBP) that the initialized waveforms possessed. Simulations additionally demonstrate that the optimized thumbtack-like MTSFM waveforms are competitive with thumbtack-like phase-coded waveforms derived from design algorithms available in the published literature.

Parameter Estimation for Sinusoidal Frequency-Modulated Signals Using Phase Modulation

In this letter, we propose a novel estimator for the phase parameters of sinusoidal frequency-modulated (SFM) signals. First, we developed a simple function to perform phase modulation on the original SFM signal to obtain a new modulated signal. Second, we derived the amplitude spectrum (AS) of the modulated signal and proved that the AS exhibited peaks periodically. Third, we obtained the parameter estimation of SFM signals by locating the AS peaks. Finally, the estimates were refined to reduce bias. The simulation results show that the proposed technique has a lower signal-to-noise ratio threshold than the existing methods.

Rotor Blades Micro-Doppler Feature Analysis and Extraction of Small Unmanned Rotorcraft

In this article, the micro-Doppler feature analysis and extraction of small unmanned rotorcraft (SUR) is considered. To be specific, the radar returns from the rotor blades are first modeled as sinusoidal frequency-modulated (SFM) signals. Then, the Gabor transform is utilized to obtain the time-frequency distribution (TFD). In order to solve the problem of limited TF analysis resolutions, high carrier frequency of radar is employed for the sake of separating different sinusoidal curves from TFD. After that, the Hough-Radon transform (HRT) is introduced to detect the sinusoidal curves from the TFD. Finally, based on the relationship between the SFM signal and the rotating blade, the micro-Doppler parameters which can reflect the threat level of the SUR to a large extend are estimated. Compared with other existing methods, the proposed method presents the relationships between the carrier frequency and the rotating blade parameters and it can be employed to extract the micro-Doppler feature of SUR with multiple rotor hubs. Simulation results demonstrate the effectiveness of the proposed micro-Doppler feature extraction method.