Chirp Function Research Articles

Log-polar transform-based wavelet-modified maximum average correlation height filter for distortion invariance in a hybrid digital-optical correlator

We discuss and implement a log-polar transform-based distortion-invariant filter for automatic target recognition applications. The log-polar transform is a known space-invariant image representation used in several image vision systems to eliminate the effects of scale and rotation in an image. For in-plane rotation invariance and scale invariance, a log-polar transform-based filter was synthesized. In cases of in-plane rotation invariance, peaks shift horizontally, and in cases of scale invariance, peaks shift vertically. To achieve out-of-plane rotation invariance, log-polar images were used to train the wavelet-modified maximum average correlation height (WaveMACH) filter. The designed filters were implemented in the hybrid digital-optical correlation scheme. It was observed that, for a certain range of rotation and scale differences, the correlation signals merge with the strong dc. To solve this problem a shift was introduced in the log-polar image of the target. The use of a chirp function for dc removal has also been discussed. Correlation peak height and peak-to-sidelobe ratio have been calculated as metrics of goodness of the log-polar transform-based WaveMACH filter. Experimental results are presented.

Wavelet-modified maximum average correlation height filter for out-of-plane rotation invariance

In this paper, we implement a wavelet-modified maximum average correlation height (WaveMACH) filter for recognition of 0–360° out-of-plane rotated targets employing hybrid digital–optical correlator architecture. A chirp function is used with the synthesized WaveMACH filter, which focuses the correlation signals in three different planes, thereby providing the choice of recording a single correlation peak at a particular plane. Signal-to-noise ratio and peak-to-sidelobe ratio have been calculated as metrics of goodness of the proposed WaveMACH filter.

Hybrid digital-optical correlation employing a chirp-encoded simulated-annealing-based rotation-invariant and distortion-tolerant filter

The simulated annealing (SA) algorithm based on entropy optimization is a technique of synthesizing distortion-invariant matched filters capable of discriminating very similar images. The synthesis of rotation-invariant filters using modified SA-based filter equations and their tolerance to distortions are studied. The filters are trained with true class images rotated in-plane at 3 degrees intervals between 0 degrees and 360 degrees . A total of seven filters are required over the whole range for both CCD or thermal images. Optical correlation in a hybrid digital-optical correlator results in an unwanted zero-order dc along with two first-order (+/-1) correlation peaks. A chirp function multiplied with the filter separates out the three peaks to three different planes, and only one peak in focus is captured in a camera. The performance of the modified SA-based filter has been studied in comparison to the conventional SA filter as well as with other filters.

On the minimax optimality of block thresholded wavelet estimators with long memory data

We consider the estimation of non-parametric regression function with long memory data and investigate the asymptotic rates of convergence of wavelet estimators based on block thresholding. We show that the estimators achieve optimal minimax convergence rates over a large class of functions that involve many irregularities of a wide variety of types, including chirp and Doppler functions, and jump discontinuities. Therefore, in the presence of long memory noise, wavelet estimators still provide extensive adaptivity to many irregularities of large function classes.

Analytical and numerical analysis of linear optical systems

The numerical calculation of the Fresnel transform (FST) presents significant challenges due to the high sampling rate associated with the chirp function in the kernel. The development of an efficient algorithm is further complicated by the fact that the output extent of the FST is dependent on the propagation distance. In this paper, we implement a recently proposed technique for efficiently calculating the FST in which we apply the Wigner distribution function and the space bandwidth product to identify suitable sampling rates. This method is shown to be suitable for all propagation distances. Our method can also be applied to describe the effect of a thin lens modeled as a chirp modulation transform (CMT). Combining our results for the FST and the CMT, we numerically calculate the light distribution at the output of both Cai-Wang and Lohmann Type-I optical fractional Fourier transform (OFRT) systems. Analytic solutions for the OFRT of rectangular window and circular apertures are presented. The analytical solutions are compared to experimental data and to numerical results for equivalent cases. Finally the numerical method is applied to examine the effect that apertured lenses, in the OFRT system, have on the output distribution.

Wavelet-modified maximum average correlation height filter for rotation invariance that uses chirp encoding in a hybrid digital-optical correlator

We discuss and implement a wavelet-modified maximum average correlation height (MACH) filter for 0 degrees -360 degrees in-plane rotations in a hybrid digital-optical correlator. Use of a wavelet transform improves the performance of the MACH filter by reducing the number of filters that are required to identify a target rotated at any angle between 0 degrees and 360 degrees in-plane rotations and enhances the autocorrelation peak intensity significantly. The output of a hybrid digital-optical correlator contains two autocorrelation peaks and a strong dc. Using a chirp function with the wavelet-modified MACH filter, the correlation signals are focused in three different planes. Thus placing a peak-capturing CCD camera at a particular plane, only one autocorrelation peak is recorded, discarding the strong dc and other autocorrelation peaks. A signal-to-noise ratio has been calculated as a metric of goodness of the proposed wavelet-modified MACH filter.

Waveguide damage detection by the matching pursuit approach employing the dispersion-based chirp functions

If the wave mode used in guided wave non-destructive inspection is dispersive, reflected pulses from damaged parts may be significantly distorted due to wave dispersion. The main concern, in this case, is how to detect the reflected pulses in noisy signals, and to extract meaningful damage information from the detected pulses. However, current signal processing techniques used for guided wave inspection do not account for pulse dispersion, so the extracted information is often not so accurate. The objective of this study is to develop an efficient technique to deal with dispersed pulses for guided-wave nondestructive evaluation. Our idea is to model dispersed pulses by chirp functions of special form that can simulate up to quadratically varying group delay. To determine the parameters of the chirp functions approximating dispersed, reflected pulses, an adaptive matching pursuit algorithm is employed. Once the characterizing parameters are found, the damage location and extent can be estimated. The proposed method is tested with experimentally measured signals of longitudinal waves in a circular cylinder.

Application of fractional Fourier transform on spatial filtering

Starting from the relationship between the Wigner transformation and the fractional Fourier transform (FRFT), we apply the FRFT to the spatial filtering. In the process of filtering, the noise can be simulated as the chirp functions or their linear combination, which can be filtered at the corresponding fractional planes, and also the actual positions can be exactly obtained. Some numerical simulations prove its possibility.

Enhancing mass sensitivity of SAW delay line sensors by chirping transducers

The paper proposes a new device design for enhancing the mass sensitivity of SAW delay line oscillator sensors. Considering implicit dependence of the phase condition of oscillation on SAW velocity and delay path length it is theoretically shown that a chirped delay line can either reduce or enhance the mass sensitivity depending upon the characteristics of the chirp function. It is found that a linear FM up-chirp always reduces the mass sensitivity. The linear FM down-chirp devices with commonly implemented chirp parameters for matched filtering applications also reduce the mass sensitivity, though they offer the possibility of enhanced sensitivity through steep chirp slope implementation. A nonlinear chirp consisted of sum of linear and sinusoidal terms is proposed for practical implementation of SAW dispersive delay lines that can dramatically enhance the mass sensitivity of SAW chemical sensors.

유도 초음파 이용 결함 진단을 위한 정합추적 기법

For successful guided-wave damage inspection, the appropriate signal processing of measured wave signals is very important. The objective of this paper is to introduce an efficient signal processing technique especially suitable for the guided-waves used for damage detection. The key idea of this technique is to model guided-waves by chirp functions of special form considering the dispersion phenomenon. To determine the parameter of the chirp functions simulating guided-waves, the matching pursuit algorithm is employed. The damage information in waveguides can be extracted by pulse-characterizing parameters. The effectiveness of present method is checked with the guided wave-based damage inspection.

Range of plasma filaments created in air by a multi-terawatt femtosecond laser

The propagation of a multi-terawatt femtosecond laser pulse in air is studied as a function of initial chirp. The chirp conditions for optimising air ionisation at long distance are presented. Ionisation channels are observed over a distance reaching 400 m.

Electronic and vibrational population transfer in diatomic molecules as a function of chirp for different pulse bandwidths

We study the dynamics of two-photon nonresonant electronic excitation of diatomic molecules driven by chirped pulses. While the majority of the experimental results address the role of the chirp for fixed pulse bandwidth, we analyze the possibility of selective excitation for fixed time, as a function of the pulse bandwidth, depending on the sign of the chirp. With strong picosecond pulses and positive chirp it is shown that the dynamics always prepare the molecule in the ground vibrational level of the excited electronic state. The robustness of the dynamics inherits the properties of an effective Landau–Zener crossing. For negative chirp the final state is very sensitive to the specific pulse bandwidth. The dynamics of the system follow a complex convoluted behavior, and the final state alternates between low vibrational levels of the excited electronic state and excited vibrational levels of the ground potential, which become increasingly more excited with increasing bandwidth. The final electronic populations follow a double-period oscillatory behavior. We present a model based on sequential independent crossings which correlates the long-oscillation period with changes in the final vibrational state selected. We show that the short-oscillation period is related with nonadiabatic effects that give rise to fast dynamic Rabi flipping between the electronic states, providing only information of the field–molecule effective coupling. Although the short-oscillation period partially masks the expected results of the final populations, we show that it is still possible to retrieve information from the long-oscillation period regarding the frequencies of the electronic potentials. In order to do so, or in order to control the outcome of the dynamics, it is necessary to perform experiments scanning very different pulse bandwidths, and we propose a possible experimental implementation. All the numerical results of the paper are calculated for a model of the Na2 dimer.

A closed-form wideband direction-of-arrival estimation with chirplet-based adaptive signal decomposition algorithm

The Direction-Of-Arrival (DOA) estimation with Coherent Signal Subspace (CSS) is not easy to extend from narrowband to wideband case. Time-frequency analysis is a powerful technique to deal with time-variant or non-stationary signal. Its combination with CSS explores a new field in signal processing, especially the wideband DOA estimation. The chirp function is one of the most fundamental functions in nature. Many nature events can be modeled as chirplet function, such as radar system or seismic exploring. Hence, the chirplet-based signal decomposition has attracted great attention in the area of signal processing. In this paper, the closed-form wideband DOA estimation with algorithm of chirplet-based adaptive signal decomposition is developed. With only three testing values, the delay of signals arriving at different elements can be acquired through a closed-form solution, then the DOA of sources can be got. Compared with Maximum Likelihood (ML), this novel approach has very low complexity. Its robust performance is demonstrated with numerical simulations.

2R regeneration based on dispersion-imbalanced loop mirror and its applications in WDM systems

2R regeneration based on dispersion-imbalanced loop mirror is investigated including the characteristics of transfer function, output extinction ratio, initial chirp, predispersion, and WDM signals transfer functions. Theoretical results show that the input peak power is a critical parameter for the dispersion-imbalanced loop mirror (DILM) and furthermore, to guarantee the multiwavelength operation of the DILM, limitations due to accumulated dispersion and dispersion slope have to be considered. Our experiment demonstrates that 6/spl times/10 Gb/s WDM signals can be successfully regenerated by a novel 2R regenerator based on a DILM consisting of a single mode fiber (SMF) and a highly nonlinear dispersion-shifted fiber (DSF) after WDM transmission over 40 km SMF of the WDM signals.

A fast refinement for adaptive Gaussian chirplet decomposition

The chirp function is one of the most fundamental functions in nature. Many natural events, for example, most signals encountered in seismology and the signals in radar systems, can be modeled as the superposition of short-lived chirp functions. Hence, the chirp-based signal representation, such as the Gaussian chirplet decomposition, has been an active research area in the field of signal processing. A main challenge of the Gaussian chirplet decomposition is that Gaussian chirplets do not form an orthogonal basis. A promising solution is to employ adaptive type signal decomposition schemes, such as the matching pursuit. The general underlying theory of the matching pursuit method has been well accepted, but the numerical implementation, in terms of computational speed and accuracy, of the adaptive Gaussian chirplet decomposition remains an open research topic. We present a fast refinement algorithm to search for optimal Gaussian chirplets. With a coarse dictionary, the resulting adaptive Gaussian chirplet decomposition is not only fast but is also more accurate than other known adaptive schemes. The effectiveness of the algorithm introduced is demonstrated by numerical simulations.

Characterization of diffraction patterns directly from in-line holograms with the fractional Fourier transform.

We show that the fractional Fourier transform is a suitable mechanism with which to analyze the diffraction patterns produced by a one-dimensional object because its intensity distribution is partially described by a linear chirp function. The three-dimensional location and the diameter of a fiber can be determined, provided that the optimal fractional order is selected. The effect of compaction of the intensity distribution in the fractional Fourier domain is discussed. A few experimental results are presented.

Multiple-order adaptive dispersion compensation using polynomially-chirped grating devices

Devices such as the planar arrayed-waveguide grating or the distributed Bragg reflector (AWG and DBR, respectively) are assuming increasing importance in the areas of fibre point-to-point communication and networking. In the particular context of dense wavelength-division multiplexing (DWDM), these devices play a well-established role as wavelength-selective elements. More recently, chirped variants have found use as dispersion compensators, offering wideband reduction of both basic and higher-order departures from constant group delay. However, up to the present time, the existence of a systematic approach to higher-order dispersion compensation has not been recognised. Additionally, we have identified a comprehensive isomorphism between AWG and DBR devices that allows the design characteristics of the former transverse geometry to be mapped on to the latter longitudinal structure. Here, we present a systematic study of these important passive optical grating-based devices which considers, firstly, analytic solutions for 2nd-order dispersion compensation (DC), and then 3rd- and 4th-order dispersion compensators with 100 GHz bandwidth. We then review optimisation strategies for DC, 3 dB bandwidth, and passband dispersion ripple, as determined by device chirp, apodisation, coupling strength and polyphase transfer function superposition. We conclude with a preliminary discussion of grating parametric sensitivity as evidenced by Monte Carlo analysis.

Dispersive-scan measurement of the fast component of the third-order nonlinearity of bulk materials and waveguides

A new, simple method to measure the nonlinear refraction and absorption of bulk material and waveguides is proposed. The method relies on the evolution of the intensity and width of femtosecond-pulse spectra, owing to self-phase modulation, as a function of variable chirp and stretching introduced at the input.

Quantum Control of Population Transfer in Green Fluorescent Protein by Using Chirped Femtosecond Pulses

We demonstrate that the methods of quantum control can be applied successfully to very large molecules in room temperature liquid solution. Chirped femtosecond pulses are used to excite a green fluorescent protein mutant in both buffered aqueous solution and solid acrylamide gel. At high energy densities, the fluorescence shows a strong chirp dependence, with positively chirped pulses transferring almost 50% more population to the excited state than negatively chirped pulses. By measuring the photobleaching rate in the gel as a function of pulse chirp, we find that the data are consistent with the bleaching of the protein being due to a thermal mechanism rather than to an excited-state photoreaction.

Quantum control of the yield of a chemical reaction

Order of magnitude enhancement in the concerted elimination pathway leading to I2 product formation in the photodissociation reaction of CH2I2 by the use of positively chirped 312 nm femtosecond laser pulses is demonstrated. The maximum yield is found for chirps of 2400 fs2 while the minimum is found near −500 fs2. Multiphoton excitation with 624 nm pulses results in the opposite effect, where the maximum yield is found near −500 fs2. The enhancement as a function of chirp is found to depend on the wavelength and intensity of the laser pulses. These results offer new experimental evidence for quantum control of chemical reactions.