Spectral Peak Location Research Articles

An ultra-precise Fast Fourier Transform

The Fast Fourier Transform (FFT) is a cornerstone of digital signal processing, generating a computationally efficient estimate of the frequency content of a time series. Its limitations include: (1) information is only provided at discrete frequency steps, so further calculation, for example interpolation, may be required to obtain improved estimates of peak frequencies and amplitudes; (2) ‘energy’ from spectral peaks may ‘leak’ into adjacent frequencies, potentially causing lower amplitude peaks to be distorted or hidden; (3) the FFT is a discrete time approximation of continuous time mathematics. A new FFT calculation addresses each of these issues through the use of two windowing functions, derived from Prism Signal Processing. Separate FFT results are obtained by applying each windowing function to the data set. Calculations based on the two FFT results yields high precision estimates of spectral peak location (frequency) amplitude and phase while suppressing spectral leakage.

Ultra-simplified diffraction-based computational spectrometer

Miniaturizing spectrometers for compact and cost-effective mobile platforms is a major challenge in current spectroscopy research, where conventional spectrometers are impractical due to their bulky footprint. Existing miniaturized designs primarily rely on precalibrated response functions of nanophotonic structures to encode spectral information captured in a snapshot by detector arrays. Accurate spectrum reconstruction is achieved through computational techniques, but this requires precise component design, high-precision fabrication, and calibration. We propose an ultra-simplified computational spectrometer that employs a one-to-broadband diffraction decomposition strategy facilitated by a numerical regularized transform that depends only on the spectrum of the diffracted radiation. The key feature of our design is the use of a simple, arbitrarily shaped pinhole as the partial disperser, eliminating the need for complex encoding designs and full spectrum calibration. Our spectrometer achieves a reconstructed spectral peak location accuracy of better than 1 nm over a 200 nm bandwidth and excellent resolution for peaks separated by 3 nm in a bimodal spectrum, all within a compact footprint of under half an inch. Notably, our approach also reveals a breakthrough in broadband coherent diffractive imaging without requiring any prior knowledge of the broadband illumination spectrum, assumptions of non-dispersive specimens, or correction for detector quantum efficiency.

An ultra-precise Fast Fourier Transform

The Fast Fourier Transform (FFT) is a cornerstone of digital signal processing, generating a computationally efficient estimate of the frequency content of a time series. Its limitations include: (1) information is only provided at discrete frequency steps, so further calculation, for example interpolation, may be required to obtain improved estimates of peak frequencies, amplitudes and phases; (2) ‘energy’ from spectral peaks may ‘leak’ into adjacent frequencies, potentially causing lower amplitude peaks to be distorted or hidden; (3) the FFT is a discrete time approximation of continuous time mathematics. A new FFT calculation addresses each of these issues through the use of two windowing functions, derived from Prism Signal Processing. Separate FFT results are obtained by applying each windowing function to the data set. Calculations based on the two FFT results yields high precision estimates of spectral peak location (frequency), amplitude and phase while suppressing spectral leakage.

Refining a deep learning-based formant tracker using linear prediction methods

In this study, formant tracking is investigated by refining the formants tracked by an existing data-driven tracker, DeepFormants, using the formants estimated in a model-driven manner by linear prediction (LP)-based methods. As LP-based formant estimation methods, conventional covariance analysis (LP-COV) and the recently proposed quasi-closed phase forward–backward (QCP-FB) analysis are used. In the proposed refinement approach, the contours of the three lowest formants are first predicted by the data-driven DeepFormants tracker, and the predicted formants are replaced frame-wise with local spectral peaks shown by the model-driven LP-based methods. The refinement procedure can be plugged into the DeepFormants tracker with no need for any new data learning. Two refined DeepFormants trackers were compared with the original DeepFormants and with five known traditional trackers using the popular vocal tract resonance (VTR) corpus. The results indicated that the data-driven DeepFormants trackers outperformed the conventional trackers and that the best performance was obtained by refining the formants predicted by DeepFormants using QCP-FB analysis. In addition, by tracking formants using VTR speech that was corrupted by additive noise, the study showed that the refined DeepFormants trackers were more resilient to noise than the reference trackers. In general, these results suggest that LP-based model-driven approaches, which have traditionally been used in formant estimation, can be combined with a modern data-driven tracker easily with no further training to improve the tracker’s performance.

An ultra-precise fast fourier transform

<h2>Abstract</h2> The Fast Fourier Transform (FFT) is a cornerstone of digital signal processing, generating a computationally efficient estimate of the frequency content of a time series. Its limitations include: (1) information is only provided at discrete frequency steps, so further calculation, for example interpolation, is often used to obtain improved estimates of peak frequencies and amplitudes; (2) ‘energy' from spectral peaks may ‘leak' into adjacent frequencies, potentially causing lower amplitude peaks to be distorted or hidden; (3) the FFT, like many other DSP algorithms, is a discrete time approximation of continuous time mathematics. This paper describes a new FFT calculation which uses two windowing functions, derived from Prism Signal Processing. Separate FFT results are obtained from each windowing function applied to the data set. Calculations based on the two FFT results yields high precision estimates of spectral peak location (frequency), amplitude and phase. This technique addresses FFT limitations as follows: (1) spectral peak parameters are calculated directly, unrestricted by FFT frequency step discretization; (2) the windowing functions have narrowband characteristics which attenuate and localize spectral leakage; (3) the windowing functions incorporate a Romberg Integration mechanism to overcome the discrete/continuous time approximation.

An Efficient CS-Based Spectral Peak Search Method.

Spectral peak search is an essential part of the frequency domain parametric method. In this paper, a spectral peak search algorithm employing the principle of compressed sensing (CS) is proposed to rapidly estimate the spectral peaks. The algorithm adopts fast Fourier transform (FFT) with a few points to obtain the coarsely estimated spectral peak positions, and then only three small-scale inner products are iteratively calculated by increasing the input sequence length to rapidly refine the estimated positions. Compared with the conventional methods, this algorithm can directly capture the exact locations of spectral peaks without acquiring the entire spectrum. In addition, the proposed algorithm can be easily integrated into the existing frequency domain interpolation methods to accurately determine the spectral peak positions, and if so, only 30% of inner product operations of the original algorithms are required. Theoretical analysis and numerical results show that this algorithm yields accurate results with low complexity for analyzing both one-dimensional and two-dimensional signals.

Ultra-high resolution particle size measurement based on scattering spectrum analysis-simulation and experiment.

This paper focuses on the properties of light scattering spectra from a spherical particle and their application for particle size measurement. The influence of particle size and scattering angle on the scattering spectra are investigated and simulated. An ultra-resolution particle dimension measurement method was proposed based on detecting the peak of scattering spectra. An accurate spectral peak location strategy based on the spectral shape features is adopted to reduce the spectra peak positioning error caused by dispersion. The size of smaller particle is measured by locating a wide scattering spectral peak at a larger scattering angle to achieve higher measurement sensitivity, while the size of larger particle is measured by locating a narrow scattering spectral peak at a smaller angle to achieve a larger measurement range. If the spectral resolution of the spectrometer is 0.8 nm, the particle size resolution of 1.1 nm and 8.3 nm are achieved for measured particles with sizes ranging from 0.25µm to 1µm and measured particles with sizes ranging from 1µm to 10µm, respectively. And if the spectrometer with picometer resolution is used, the particle size resolution is expected to be on the order of picometers.

An Advanced Frequency Estimation Algorithm Based on Analytic Compensation of Effects of Dominant Harmonic in Power Systems

This paper proposes an advanced frequency estimation algorithm, where the interference effect of harmonic is effectively compensated by proposing and using a new ‘harmonics interference decomposition model’. In the decomposition model, the interference effect of harmonic is represented as the sum of the two separated components, i.e., a deviation bias and an oscillatory disturbance, where the deviation bias is modeled to include only the uncoupled amplitude parameter terms and the oscillatory disturbance is modeled to exclusively include all the phase parameter coupled terms in representing a power spectral peak location. The separation and the independent compensation of the two interfering parameters significantly reduce the nonlinearity associated difficulties in deriving analytic compensation equations. Frequency estimation performance of the proposed algorithm is verified through computer simulations with diverse patterns of power system signals. The proposed algorithm’s excellent estimation accuracy and rapid convergence performance are confirmed by comparing the simulation results with those of other representative algorithms.

Research of chromatic spectral peak location on confocal point sensors

Chromatic confocal point sensors are used to measure the high-precision surface distance, and it’s based on the theory of chromatic dispersion and encodes the distance between the measure surface and chromatic lens. By accurately measuring the wavelength value, it indirectly calculates the distance to object surface. The accuracy of the sensor depends on the chromatic range of the lens and the resolution of the spectrograph. In this paper, the algorithm of spectral peak positioning can effectively filter kinds of noise, such as spectrometer and light source. The spectral data signal peak is extracted by Gaussian fitting method. In practice, the wavelength position can be stably detected effectively.

Characterization of zirconium oxides part I: Raman mapping and spectral feature analysis

Abstract Raman mapping of sectioned zirconium cladding oxides was performed to analyze different spectral features before and after breakaway, as well as between zirconium and its alloys Zr-2.65Nb, Zry-3, and Zry-4. Oxide phase composition, or percent tetragonality, was defined to compare tetragonal to monoclinic zirconia. Percent tetragonality was spatially mapped to support distinction of zirconia phase distribution. A tetragonal-rich layer was seen at the metal/oxide interface, while post-breakaway samples exhibited increased amount of tetragonal phase in the bulk of their oxides. Spatial mapping of spectral peak location and half-width at half-maximum was accomplished to distinguish differences in stability mechanisms of tetragonal-rich zirconia phase. Shifts in monoclinic peak positions provided mapping of relative stress state, supporting the differences in stabilization of tetragonal phase near the metal/oxide interface and tetragonal phase in the bulk of the oxide. Tetragonal phase near the metal/oxide interface is stabilized through support of oxygen sub-stoichiometry and compressive stress. Tetragonal phase observed in the bulk of the oxide is stabilized through oxygen sub-stoichiometry, void of compressive stress. A linear trend between percent tetragonality and stress state was determined. This resulted in a connection between mechanism of tetragonal to monoclinic phase transformation and a cladding's ability to resist oxidation and breakaway. Poor performing samples displayed greater stress gradients, driven by lattice mismatch at the metal/oxide interface, as well as between tetragonal and monoclinic phase boundaries. Tetragonal phase at the metal/oxide interface for superior performing samples have reduced epitaxial growth of tetragonal grains, lowering compressive stress gradients and provided more resistant inner-oxide layers. With increased utility of Raman spectroscopy for characterizing zirconium cladding materials, different degradation mechanisms can be further understood.

Label-free fluorescent discrimination and detection of epinephrine and dopamine based on bioinspired in situ copolymers and excitation wavelength switch

A simple and label-free fluorescence turn-on method is proposed for the discrimination and detection of epinephrine (Ep) and dopamine (DA) via polyethyleneimine (PEI)-initiated in situ copolymerization and excitation wavelength switch. The PEI solution in the presence of Ep, DA and the mixture of Ep and DA are denoted as PEp-PEI, PDA-PEI and MEp+DA, respectively. In this study, PEI aqueous solution medium initiates the auto-oxidization of Ep and DA and the bioinspired copolymerization. These resultant copolymers emit yellow-green fluorescence color with a fluorescence emission maximum at 515 nm. Interestingly, these fluorescent copolymers exhibit distinct different excitation spectra, although Ep and DA are structurally very similar. PDA-PEI exhibits only one excitation peak at 385 nm, and PEp-PEI shows dual-excitation mode with two significant excitation peaks at 328 nm and 405 nm, respectively. MEp+DA also shows dual-excitation mode with two excitation peaks at 330 nm and 395 nm, respectively. Thus, individual Ep, DA, and their mixture can be discriminated based on the different excitation spectral shapes and peak locations of PEp-PEI, PDA-PEI and MEp+DA. Furthermore, the quantitative analysis of Ep and DA in mixture can also be achieved by switching excitation wavelength between 330 and 395 nm and monitoring the fluorescence emission intensity of MEp+DA at 515 nm. The fluorescence intensity of MEp+DA only related to the concentration of Ep when excited at 330 nm. Moreover, the concentration of DA can also be calculated by subtracting the fluorescence intensity of PEp-PEI from the total fluorescence intensity when excited at 395 nm. The resultant method has been used to simultaneously detect Ep and DA in human urine samples. The proposed fluorescence system is facile, eco-friendly, low-cost, and time-saving, and also provides a new and simple path for discriminating analogues.

Imaging Spatial Variations of Optical Bandgaps in Perovskite Solar Cells

AbstractA fast, nondestructive, camera‐based method to capture optical bandgap images of perovskite solar cells (PSCs) with micrometer‐scale spatial resolution is developed. This imaging technique utilizes well‐defined and relatively symmetrical band‐to‐band luminescence spectra emitted from perovskite materials, whose spectral peak locations coincide with absorption thresholds and thus represent their optical bandgaps. The technique is employed to capture relative variations in optical bandgaps across various PSCs, and to resolve optical bandgap inhomogeneity within the same device due to material degradation and impurities. Degradation and impurities are found to both cause optical bandgap shifts inside the materials. The results are confirmed with micro‐photoluminescence spectroscopy scans. The excellent agreement between the two techniques opens opportunities for this imaging concept to become a quantified, high spatial resolution, large‐area characterization tool of PSCs. This development continues to strengthen the high value of luminescence imaging for the research and development of this photovoltaic technology.

Production of word-initial fricatives of Mandarin Chinese in prelingually deafened children with cochlear implants

Purpose: This study examined the production of fricatives by prelingually deafened Mandarin-speaking children with cochlear implants (CIs).Method: Fourteen cochlear implant (CI) children (2.9–8.3 years old) and 60 age-matched normal-hearing (NH) children were recorded producing a list of 13 Mandarin words with four fricatives, /f, s, ɕ, ʂ/, occurring at the syllable-initial position evoked with a picture-naming task. Two phonetically-trained native Mandarin speakers transcribed the fricative productions. Acoustic analysis was conducted to examine acoustic measures including duration, normalised amplitude, spectral peak location and four spectral moments.Result: The CI children showed much lower accuracy rates and more diverse error patterns on all four fricatives than their NH peers. Among these four fricatives, both CI and NH children showed the highest rate of mispronunciation of /s/. The acoustic results showed that the speech of the CI children differed from the NH children in spectral peak location, normalised amplitude, spectral mean and spectral skewness. In addition, the fricatives produced by the CI children showed less distinctive patterns of acoustic measures relative to the NH children.Conclusion: In general, these results indicate that the CI children have not established distinct categories for the Mandarin fricatives in terms of the place of articulation.

Spectral contrast effects in vowel categorization by listeners with sensorineural hearing loss

The auditory system is highly sensitive to changes in acoustic input. This is especially true for sounds with relatively stable (reliable) spectral properties across time. Over a limited range, changes to the spectrum (e.g., spectral peak location upon introduction of a new sound) are perceptually enhanced in proportion to the property's long-term reliability, producing spectral contrast effects (SCEs). For example, a neutral vowel between /i/-/e/ is more likely to be labelled /e/ (high-F1) when preceded by sounds with a reliable low-frequency peak in the F1 range for /i/, and vice versa. Yet, it is unknown how SCEs affect speech perception by hearing-impaired (HI) listeners because research has only examined normal-hearing (NH) listeners. Here, listeners with mild-to-moderate HI identified target vowels varying from /i/-/e/ that followed a precursor sentence. Reliability of precursor spectral peaks was manipulated using low-F1 or high-F1 bandpass filters with +5 to +20 dB gain. SCE magnitude was proportional to precursor filter gain (like NH listeners), and surprisingly, to the amount of low-frequency hearing loss. Thus, mechanisms responsible for SCEs are not dependent on healthy hearing, and are magnified by auditory filter broadening associated with sensorineural hearing loss. Implications of these findings for speech perception will be discussed.

Relaxation Time Coupling Method for Ultrasonic Sensor Design

In our previous work [Sens. Actuator B: Chem. 203 1-8 (2014)], a ultrasonic sensor has been proposed to detect gas compositions by the acoustic spectral peak location. However, the effective relaxation area constructed by existing theoretical model cannot match the detection method when there are more than one strong relaxational components in gas mixture. A method that calculates the relaxation time of a multi-component relaxation process is presented. Based on acquirement of decoupled relaxation times and their corresponding effective specific heat values, it calculates the whole relaxation time of a multi-component relaxation process. The method is based on the fact that for a multi-component gas mixture, such as occurs in many polyatomic gas mixtures, the relaxation process should be considered as a whole rather than being decoupled as some single relaxation processes. Acquiring relaxation time provides the approach to obtain the acoustic absorption spectral peak value directly.

Using Hyperspectral Fluorescence Spectra of Deli Commodities to Select Wavelengths for Surveying Deli Food Contact Surfaces

Purpose: The inability to adequately judge the efficacy of cleaning and sanitation procedures in deli departments is a recognized food safety concern. In a prior study, our research group demonstrated that visual inspection of cleaned produce processing surfaces could be enhanced through the use of a portable fluorescence imaging device that detected residual produce residues. Methods: To explore the feasibility of using fluorescence imaging to similarly detect residual deli residues, spectra of American, Cheddar, Provolone, and Swiss cheeses and of processed chicken, ham, roast beef, and turkey were acquired using a laboratory hyperspectral imaging system. Circular punches of these commodities were placed onto stainless steel and high density polyethylene coupons for imaging. The coupon materials were selected to represent common surfaces found in deli departments. Results: Analysis of hyperspectral fluorescence images showed that cheeses exhibited peaks in the blue-green region and at around 675 nm. Meats exhibited peaks in the blue-green region with one of four ham and one of four chicken brands exhibiting peaks at around 675 nm, presumably due to use of plant-derived additives. When commodities were intermittently imaged over two weeks, locations of spectral peaks were preserved while intensity of peaks at shorter wavelengths increased with time. Conclusion: These results demonstrate that fluorescence imaging techniques have the potential to enhance surface hygiene inspection in deli departments and, given the immediate availability of imaging results, to help optimize routine cleaning procedures.

Metamaterial-based theoretical description of light scattering by metallic nano-hole array structures

We have experimentally and theoretically investigated the light-matter interaction in metallic nano-hole array structures. The scattering cross section spectrum was measured for three samples each having a unique nano-hole array radius and periodicity. Each measured spectrum had several peaks due to surface plasmon polaritons. The dispersion relation and the effective dielectric constant of the structure were calculated using transmission line theory and Bloch's theorem. Using the effective dielectric constant and the transfer matrix method, the surface plasmon polariton energies were calculated and found to be quantized. Using these quantized energies, a Hamiltonian for the surface plasmon polaritons was written in the second quantized form. Working with the Hamiltonian, a theory of scattering cross section was developed based on the quantum scattering theory and Green's function method. For both theory and experiment, the location of the surface plasmon polariton spectral peaks was dependant on the array periodicity and radii of the nano-holes. Good agreement was observed between the experimental and theoretical results. It is proposed that the newly developed theory can be used to facilitate optimization of nanosensors for medical and engineering applications.

Configurational entropy theory for streamflow forecasting

This study develops configurational entropy theory (CET) for monthly streamflow forecasting. The theory is comprised of three main parts: (1) determination of spectral density (2) determination of parameters by cepstrum analysis, and (3) extension of autocorrelation function. Comparison with the Burg entropy theory (BET) shows that CET yields higher resolution spectral density with more accurate location of spectral peaks. Cepstrum analysis yields more accurate parameters than the Levinson algorithm in the autoregressive (AR) method and the Levinson–Burg algorithm in BET. CET is tested using monthly streamflow data from 19 river basins covering a broad range of physiographic characteristics. Testing shows that CET captures streamflow seasonality and satisfactorily forecasts both high and low flows. High flows are satisfactorily forecasted with the coefficient of determination (r2) higher than 0.92 for one year ahead of time, with r2 higher than 0.85 for two years ahead of time, and up to 60 months ahead with r2 higher than 0.80. However, low flows are forecasted with r2 higher than 0.50 for one year ahead time. When relative drainage area is considered for analyzing streamflow characteristics and spectral patterns, it is found that upstream streamflow is forecasted more accurately (r2 = 0.84) than downstream streamflow (r2 = 0.75). Residuals of forecasted values relative to observed values are found to follow normal distribution.

Acoustic absorption spectral peak location for gas detection

Based on the full acoustic absorption spectrum detection, an approach has been developed for real-time monitoring of gas compositions by Petculescu and Lueptow (2012) [15]. However, the full acoustic absorption spectrum based approach is difficult to be implemented in practical gas sensing due to its theoretical complexity. Since the primary relaxational spectrum can be reconstructed from its spectral peak, this paper proposes a method to detect the gas compositions based on the location of the spectral peak, which is synthesized only by the measurements of acoustic absorption and sound speed at two fixed frequencies. The deviations in the location of the spectral peak resulted from measuring errors can be eliminated effectively by an iteration algorithm. This method, based on measuring the acoustic absorption spectral peak, provides guidelines for sensor fabrication in practical gas detection.

Terahertz Frequency Continuous-Wave Spectroscopy and Imaging of Explosive Substances

Continuous-wave terahertz (THz) radiation spectroscopy was performed on high explosive materials using a tuneable optical parametric oscillator (OPO). Military grade, solid-phase, explosive substances, such as cyclotetramethylenetetranitramine (HMX), cyclotrimethylenetrinitramine (RDX), pentaerythritol tetranitrate (PETN), and composition-4, were spectrally scanned over the 0.7–1.9 THz frequency range under experimental conditions modeling that of “real-world” security screenings. Spectral peak locations and spectral line broadening effects were quantified using a Lorentz lineshape fit algorithm. The full-width half-maximum (FWHM) parameter computed by the Lorentz fit algorithm was shown to help in the identification of samples with broad and sparse spectral characteristics. A concealed explosives identification scheme was demonstrated through raster scan THz frequency radiation imaging at specific OPO tuning frequencies.