International Telemetering Conference Proceedings / October 13-16, 1986 / Riviera Hotel, Las Vegas, Nevada / A digital frequency discriminator (DFD) of the delay-correlator type is described. The device is shown to have an instantaneous frequency measurement capability on very short pulses. The theoretical performance of the DFD in a noisy background is derived and shown to compare favorably with measured results.

Nonlinear control is an important subject drawing much attention. When a nonlinear system undergoes route-to-chaos, its response is naturally bounded in the time-domain while in the meantime becoming unstably broadband in the frequency-domain. Control scheme facilitated either in the time- or frequency-domain alone is insufficient in controlling route-to-chaos, where the corresponding response deteriorates in the time and frequency domains simultaneously. It is necessary to facilitate nonlinear control in both the time and frequency domains without obscuring or misinterpreting the true dynamics. The objective of the dissertation is to formulate a novel nonlinear control theory that addresses the fundamental characteristics inherent of all nonlinear systems undergoing route-to-chaos, one that requires no linearization or closed-form solution so that the genuine underlying features of the system being considered are preserved. The theory developed herein is able to identify the dynamic state of the system in real-time and restrain time-varying spectrum from becoming broadband. Applications of the theory are demonstrated using several engineering examples including the control of a non-stationary Duffing oscillator, a 1-DOF time-delayed milling model, a 2-DOF micro-milling system, unsynchronized chaotic circuits, and a friction-excited vibrating disk. Not subject to all the mathematical constraint conditions and assumptions upon which common nonlinear control theories are based and derived, the novel theory has its philosophical basis established in the simultaneous time-frequency control, on-line system identification, and feedforward adaptive control. It adopts multi-rate control, hence enabling control over nonstationary, nonlinear response with increasing bandwidth ? a physical condition oftentimes fails the contemporary control theories. The applicability of the theory to complex multi-input-multi-output (MIMO) systems without resorting to mathematical manipulation and extensive computation is demonstrated through the multi-variable control of a micro-milling system. The research is of a broad impact on the control of a wide range of nonlinear and chaotic systems. The implications of the nonlinear time-frequency control theory in cutting, micro-machining, communication security, and the mitigation of friction-induced vibrations are both significant and immediate.

Time-frequency analysis for non-linear and non-stationary signals is extraordinarily challenging. To capture the changes in these types of signals, it is necessary for the analysis methods to be local, adaptive and stable. In recent years, decomposition based analysis methods were developed by different researchers to deal with non-linear and non-stationary signals. These methods share the feature that a signal is decomposed into finite number of components on which the time-frequency analysis can be applied. Differences lie in the strategies to extract these components: by iteration or by optimization. However, considering the requirements of being local, adaptive and stable, neither of these decompositions are perfectly satisfactory. Motivated to find a local, adaptive and stable decomposition of a signal, this thesis presents Adaptive Local Iterative Filtering (ALIF) algorithm. The adaptivity is obtained having the filter lengths being determined by the signal itself. The locality is ensured by the filter we designed based on a PDE model. The stability of this algorithm is shown and the convergence is proved. Moreover, we also propose a local definition for the instantaneous frequency in order to achieve a completely local analysis for non-linear and non-stationary signals. Examples show that this decomposition really helps in both simulated data analysis and real world application.

An emerging diagnostic tool for detecting heart and physiological conditions is heart rate variability (HRV). Copious research continuously discovers relationships between heart rate variability metrics and physiological functions and cardiac health. The first step in calculating HRV metrics is calculating heart rate. Heart rate is typically calculated using the interval between R peaks in an EKG signal. Consequently, heart rate measurements rely on the presence of distinctive R peaks and the accurate detection of them. The study is motivated by the drawbacks associated with using R peaks to calculate instantaneous heart rate. In this study we present an alternative method (that does not rely on R peaks) based on the concept of instantaneous frequency to estimate heart rate from electrocardiogram (EKG) signals. The EKG signal is filtered to extract constituent frequency components that correlate with the instantaneous heart rate. The filtered signal is then fed into an algorithm that outputs a signal that shows the variation of the instantaneous heart rate with time. This output signal contains noise due to the behavior of the algorithm at zero crossings of the filtered EKG signal. Two methods for filtering the output signal are also presented in the study. The proposed method was able to successfully estimate the instantaneous heart rate and allowed the subsequent calculation of frequency domain HRV metrics. This method potentially provides more information for HRV analysis and addresses the drawbacks associated with methods based on R peak detection. / Master of Science / Heart disease is the leading cause of death in America accounting for about 20% of all deaths. Consequently, both the public and the medical community are engrossed in cardiovascular health, research that enables early detection of heart disease and novel treatments for cardiac conditions. An emerging diagnostic tool for detecting heart and physiological conditions is heart rate variability (HRV). Copious research continuously discovers relationships between heart rate variability metrics and physiological functions and cardiac health. The first step in calculating HRV metrics is calculating heart rate. With the rise in popularity and improvement of wearable technologies, it has become easier than ever to collect data and perform diagnostics, often in real time. As such the need for robust methods and algorithms to perform these calculations are ever more important. The study is motivated by drawbacks associated with the conventional method used to calculate heart rate from electrocardiogram signals. In this study we present a more robust method to calculate heart rate from EKG signals allowing more accurate HRV metrics to be calculated. In this study we present an alternative method based on the concept of instantaneous frequency to estimate heart rate from electrocardiogram (EKG) signals. We identify the shortcomings of the conventional method of estimating heart rate and discuss the strengths and weaknesses of the alternative method introduced. We then calculate and compare the HRV metrics calculated from the proposed method and the conventional method. The method presented also has the potential to be used on other signals that measure the heart's activity such as Photoplethysmography signals (PPG) allowing it to be used on wearable devices. We hope that the information provided, and the findings presented in this study will be utilized by the medical community and researchers for future research related to heart rate variability.

Any periodic signal can be decomposed into a sum of oscillating functions. Traditionally, cosine and sine segments have been used to represent a single period of the periodic signal (Fourier Series). In more general cases, each of these functions can be represented by a set of spectral parameters such as its amplitude, frequency, phase, and the variability of its instantaneous spectral components. The accuracy of these parameters depends on several processing variables such as resolution, noise level, and bias of the algorithm used. This thesis presents some background of existing frequency estimation techniques and proposes a new technique for estimating the instantaneous frequency of signals using short sinusoid-like basis functions. Furthermore, it also shows that the proposed algorithm can be implemented in a popular embedded DSPmicroprocessor for practical use. This algorithm can also be implemented using more complex features on more resourceful processing processors in order to improve estimation accuracy

Excessive vibrations continue to be a major hurdle in improving machining efficiency and achieving stable high speed cutting. To overcome detrimental vibrations, an enhanced understanding of the underlying nonlinear dynamics is required. Cutting instability is commonly studied through modeling and analysis which incorporates linearization that obscures the true nonlinear characteristics of the system which are prominent at high speeds. Thus to enhance cutting dynamics knowledge, a comprehensive nonlinear turning model that includes tool-workpiece interaction is experimentally validated using a commercial laser vibrometer to capture tool and workpiece vibrations. A procedure is developed to use instantaneous frequency for experimental time-frequency analysis and is shown to thoroughly characterize the underlying dynamics and identify chatter. For the tests performed, chatter is associated with changing spectral components and bifurcations which provides a view of the underlying dynamics not experimentally observed before. Validation of the turning model revealed that the underlying dynamics observed experimentally are accurately captured, and the coupled tool-workpiece chatter vibrations are simulated. The stability diagram shows an increase in the chatter-free limit as the spindle speed increases until 1500rpm where it begins to level out. At high speeds the workpiece dominates the dynamics, and excessive workpiece vibrations create another stability limit to consider. Thus, workpiece dynamics should not be neglected in analyses for the design of machine tools and robust control laws. The chip formation mechanisms and high speeds make micro-milling highly non-linear and capable of producing broadband frequencies that negatively affect the tool. A nonlinear dynamic micro-milling model is developed to study the effect of parameters on tool performance through spectral analysis using instantaneous frequency. A lumped mass-spring-damper system is assumed for modeling the tool, and a slip-line force mechanism is adopted. The effective rake angle, helical angle, and instantaneous chip thickness are accounted for. The model produced the high frequency force components seen experimentally in literature. It is found that increasing the helical angle decreased the forces, and an increase in system stiffness improved the dynamic response. Also, dynamic instability had the largest effect on tool performance with the spindle speed being the most critical parameter.

With the rapid and ongoing developments in telecommunication and electronic warfare technology, faster and more flexible systems are in demand. Wideband signal processing is thus needed to implement such systems. Microwave photonics has been introduced as a tool for achieving such ultra broadband signal processing. Instantaneous Frequency Measurement (IFM) receivers play an important role in electronic warfare. They have been developed as a means of obtaining a rapid indication of the presence of a threat and to roughly identify the frequency of the threat signals. They also have the advantages of low-cost, compactness and moderate to good sorting capability in an interference-free environment. The main limitation of the traditional RF IFM receivers is constrained bandwidth. Microwave Photonic IFMs have been considered, but the main disadvantages of photonic realization of the recent IFM receiver is cost. This work aims to propose and demonstrate low-cost photonic IFM receivers with a broad frequency measurement range. The proposed methods are based on the use of photonic mixing to down-convert the RF modulated optical signals to DC. In a RADAR warning receiver, usually a bank of IFMs is required. Increasing the numbers of IFMs requires an increase in the number of photo-detectors. Thus if low-frequency, low-cost detectors can be used, then the net system cost will be reduced significantly. The concept is proven and the issues arising are analyzed. In the proof of concept system, measurement of the RF frequency required advance knowledge of the RF power. Secondly, the use of co-axial RF cables as delay elements limited the bandwidth and increased bulk. Using a photonic hybrid approach to achieve orthogonal measurements was demonstrated as a means of dentifying both RF frequency and power simultaneously and independently. Employing all optical mixing removed the need for co-axial RF cables delays using non-linear optical devices such as Semiconductor Optical Amplifier (SOA) and Highly Non-Linear Fiber (HLNF). The last investigation is to improve the sensitivity of the implemented IFM system. The sensitivity of the implemented system is characterized first and a lock-in technique is employed to improve the sensitivity of the system. The final system achieves a sensitivity of -41 dBm which is comparable with the traditional RF IFM receivers.

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In this paper, a new concept for ultrasonic indoor positioning based on instantaneous frequency of ultrasonic signals is presented. Nonlinear phase characteristics of ultrasonic transducers introduce a frequency deviation in ultrasonic signals. By sweeping at very fast rates, a large spike in the deviation is introduced. The artefacts observable in instantaneous frequency estimations are highly localized and present an opportunity for accurate frequency detection. In order to be useful, the artefacts need to take place within the pulse and have sufficient magnitude for accurate processing. The system consists of a transducer transmitter and receiver pair, which have a center frequency of 40kHz and a bandwidth of 460Hz. In order to incorporate more transmitters, a time-division multiple access (TDMA) scheme is applied to ensure orthogonality of signals. The concept includes four ultrasonic transmitters and a single receiver, which can uniquely identify each transmitter by a distinct signal sweep. Linear chirp signals are used to form narrow pulses and ensure no interference in the TDMA scheme. The received signal is amplified and passed through a phase-locked loop (PLL) to detect the chirp signals. Accurate instantaneous frequency detection can be done on the voltage-controlled oscillator (VCO) of the PLL, which has a narrower bandwidth than the overall signal sweep. The instantaneous frequency estimation methods are largely explored in this work and consider two methods: the Hilbert transform and a zero-crossings method. This work highlights some of the advantages and disadvantages of both methods. Time of flight (ToF) in this system can ultimately be obtained by considering the instantaneous frequency estimations and the time for one particular frequency to be transmitted and received.

Research in damage detection and structural health monitoring in engineering systems during their service life has received increasing attention because of its importance and benefits in maintenance and rehabilitation of structure. Though the concept of vibration-based damage detection has been in existence for decades, and several procedures have been proposed to date, its practical applications remain limited, considering the increased utilization of sensors to measure structural response at multiple points. In this thesis, use of acceleration response of the structure as a method of global damage detection is explored using instantaneous frequency and stiffness degradation methods. Instantaneous frequency was estimated using continuous wavelet transform of measured acceleration response of the structure subjected to ground motion. Complex Morlet Wavelet was used in the time-frequency analysis due to its ability to provide sufficient resolution in both time and frequency domains. This ability is important in analyzing nonstationary signals like earthquake response of structure containing sharp changes in the signal. The second method, called the stiffness degradation analysis, is based on estimating the time-varying stiffness. This estimation is done by fitting a moving least-square line to the force-displacement loop for the duration of the ground motion.A four-story shear building is used as the model structure for numerical analysis. Two damage scenarios are considered: single damage instant and multiple damage instants. Both scenarios assume that the damage occurs at a single location. In the numerical simulations, damage was modeled as a reduction in the stiffness of the first floor, and accelerations were computed at floor levels using state-space model. The two methods were compared in terms of their damage detection ability and it was shown that both methods can be used in detecting damage and the time at which the damage occurs. These methods can later be extended by simultaneously considering the correlations of responses at all floor levels. This extension may enable locating the damage and quantifying the severity of the damage.