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Time-Stretched Short-Time Fourier Transform
Abstract
The authors propose and demonstrate the time-stretched short-time Fourier transform (TS-STFT) technique to overcome the limitation of an analog-digital converter (ADC) in the time-frequency analysis of ultrafast signals. Experimentally, the time-frequency analysis of highly chirped RF signals, with a chirp rate as high as 350 GHz/ns, is demonstrated. An effective real-time sampling rate of 320 GSa/s is achieved. Time stretching enhances the analog bandwidth and the effective sampling rate of the ADC and enables measurement of the instantaneous behavior of highly nonstationary ultrawideband signals.
... Since the sampling frequencies vary from one to the other, the time-stretching technique should be considered to augment the percussive audio. It should be noticed that the time stretching algorithm can be performed both in the time domain and frequency domain [48]. When the signal scaling is at a large scale, the audios are more subtle and less distorted using frequency domain operations. ...
... With the gradual development and improvement of signal analysis techniques, various methods have been developed and applied. Empirical Modal Decomposition (EMD), Wavelet Analysis, Short Time Fourier Transform, or STFT, empirical wavelet transform, and tunable Q-factor wavelet transform (TQWT) contribute to the reduction of redundant components [11][12][13][14][15][16]. However, their capability is weak in terms of complex bearing fault feature extraction. ...
Bearings are a critical component of rotating machines; when they fail, critical equipment becomes unavailable, damage may occur beyond the bearing itself, and safety concerns arise. Determining that a bearing structure is compromised before catastrophic failure permits the protection of plant, people, and productivity. When bearings malfunction, the features of single and multiple faults are masked and accompanied by noise and other signal degrading artifacts affecting the signals from the vibrational sensors. In these circumstances, detection and diagnosis of multistate bearing faults is difficult. To overcome these challenges, an improved convolutional sparse coding (ICSC) model, based on a priori periodic filter groups (PPFG), is proposed to respond to the multistate fault problems of bearings. A Laplace wavelet is constructed with one-sided decay related to the vibration pattern of the signal. The best-matched wavelet is optimally determined by correlation analysis of the signal frequency domain parameters and the time domain damping parameters. The best-matched wavelet and the kurtosis criterion are used to construct a PPFG based on the theoretical period of the fault. The ICSC based on the PPFG obtains mapping coefficients characterizing different vibrational features of the signal. The envelope spectrum analysis of the various mapping coefficients identifies and confirms the fault-revealing components in the multistate signal. The ICSC results have a relatively good sparse time domain, and the fault-identifying features in the envelope spectrum are enhanced. Multiple faults can be easily identified. The effectiveness and robustness of the PPFG/ICSC are demonstrated through a complete experimental analysis of simulated, single-fault, and multifault signals, as well as a comparative analysis of the previous methods – Fast SK, CBPDN, and VMD-ICA – which verifies that the PPFG/ICSC is more robust, accurate, and efficient than the previous methods.
... Because the signal is segmented in the STFT by applying a window w(t − τ) to it, the limiting element is the size of the corresponding window function [27]. The window size thus determines the resolution to distinguish two targets and the precision for the extraction of the implemented fingerprint features. ...
In this paper, we present a novel two dimensional (2D) frequency-modulated continuous-wave (FMCW) localization method for handheld systems based on the extraction of distinguishable subchannel fingerprints. Compared with other concepts, only one subdivided radar source channel is needed in order to instantly map a one-dimensional measurement to higher-dimensional space coordinates. The additional information of the detected target is implemented with low-cost hardware component features, which exhibit distinguishable space-dependent fingerprint codes. Using the given a priori information of the hardware thus leads to a universally applicable extension for low-cost synthetic aperture radar (SAR)-demining purposes. In addition to the description of the system concept and its requirements, the signal processing steps and the hardware components are presented. Furthermore, the 2D localization accuracy of the system and the classification accuracy of the frequency-coded fingerprints are described in a defined test environment to proof the operational reliability of the realized setup, reaching a classification accuracy of 94.7% and an averaged localization error of 4.9 mm.
... If it is directly transformed to the frequency domain by Fourier transform, the frequency distribution of the signal can be seen without time-domain information, and the change of frequency distribution over time cannot be obtained. Therefore, the second kind of characteristic is collected by converting time-series features to spectrograms with the help of short-time Fourier transform[34]. ...
As the voice disorder is a typical early symptom of Parkinson, some researchers attempt to diagnose this disease based on voice data collected from suspected patients. Although existing methods can provide acceptable results, they just work in partial scenarios. In other words, they are not generable and robust enough. To this end, we present a Parkinson’s auxiliary diagnosis system based on human speech, which can adaptively build a suitable deep neural network based on sound features. The system includes two modules: hybrid features extraction and adaptive network construction. We extract kinds of information from the voice data to form a new compound feature. Furthermore, particle swarm optimization (PSO) algorithm is employed to build the corresponding 1D convolution network for features classification. Extensive experiments on two datasets consisting of English and Italian are conducted for evaluation purposes. Experimental results show that our method improves the accuracy of voice-based Parkinson’s disease detection to some extent.
... It does provide a good solution for many applications that require a more detailed analysis of the signal in the time and the frequency domain. DWT, in contrast, provides a viable solution for signal compression, denoising or transmission [30]. ...
Seizure detection is a particularly difficult task for neurologists to correctly identify the Electroencephalography (EEG)-based neonatal seizures in a visual manner. There is a strong demand to recognize the seizures in more automatic manner. Developing an expert seizure detection system with an acceptable performance level can partly fill this research gap. This paper proposes a new framework for the automated detection of neonatal seizures based on the Morse Wavelet approach that is coupled with a local binary pattern algorithm, and a graph-based community detection algorithm. An ensemble classifier method is designed to detect neonatal seizures prevalent in EEG signals. Our findings show that only 59 of the texture features can exhibit the abnormal increase in an EEG amplitude and the spikes notable during a seizure. The present results demonstrate that the proposed seizure detection model is more accurate for the detection of seizures compared with some of the traditional approaches.
... The observation bandwidth can be further extended by photonics-assisted spectrum analysis approaches [6], while high acquisition frame rate and large observation bandwidth are difficult to achieve at the same time in these schemes. For example, an effective high-speed sampling rate of the ADC can be achieved leveraging ultrafast optical sampling or time stretch, but massive data may lead to intolerant digital processing delay [7]- [9]. The compressed sensing technology can effectively increase the observation bandwidth, but complex reconstruction algorithm for the spectrally-sparse signals limits the acquisition frame rate [10], [11]. ...
Short-time Fourier transform (STFT) is a fundamental concept that enables the observation of dynamic spectral evolution for non-stationary signals. Broadband STFT based on digital signal processing (DSP) usually has limited acquisition frame rate, which is inherently constrained by the performance limitations of present DSP engine. The further extended acquisition frame rate can be achieved by all-optical spectrum analysis approaches, while the frequency resolution is usually worse than 1 GHz. In this paper, STFT based on bandwidth-scaled microwave photonics is proposed, where the requirement for dispersion is relaxed and the attendant transmission delay in dispersive media is greatly reduced. Moreover, the frequency resolution towards MHz level could be expected in the proposed STFT. We prove that “bandwidth scaling” combined with periodic wavelength-to-time mapping (WTM) mathematically agrees with the definition of STFT. The method of customizing system parameters according to the requirements of ultrafast spectrum measurement is carefully clarified. Experimentally, joint time-frequency analysis for a variety of ultrafast non-stationary RF signals is demonstrated, where dynamic frequency resolution of 60 MHz, dynamic observation bandwidth of 1.98 GHz and acquisition frame rate of 160 MHz are simultaneously realized. The scheme we proposed is promising for the dynamic spectrum monitoring of broadband non-stationary RF signals.
Deep learning (DL) based percussion-acoustic methods have gained attention, but their 12 multi-layer architectures and iterative processes increase computational time and power. This paper 13 proposes a lightweight concrete-filled steel tubular (CFST) void detection method using Mel-14 frequency cepstral coefficient (MFCC) algorithm and ensemble machine learning. A global 15 averaging pooling (GAP) layer was applied to downscale the two-dimensional MFCC matrix to 16 one-dimensional (1D) time-frequency parameters. Combined with ensemble machine learning, 17 lightweight models that require fewer model parameters, less computation, and smaller memory 18 usage are constructed. Validation experiments were carried out on a CFST specimen with different 19 depths of voids (0, 30, 50, and 80mm). Robustness tests, considering tap intervals, sampling 20 frequencies, and background noise, were performed by using data augmentation strategies. Two 21 studies investigate feature extraction methods: the selection of the time-frequency analysis 22 algorithm (MFCC or short-time Fourier transform) and the comparison of dimensionality reduction 23 operation (average, maximum, and minimum pooling layers). Comparative analyses with a 1D 24 dilated convolutional neural network (1D dilated CNN) reveal that the MFCC-based ensemble 25 machine learning achieves excellent test accuracy on the raw signal dataset and better generalization 26 capability on the reconstructed signal dataset. Moreover, the ensemble machine learning model 27 exhibits significantly higher computational efficiency compared to DL models. Specifically, the 28 training time of random forest is 17,510 times faster than the 1D dilated CNN. Therefore, the 29 proposed lightweight CFST void detection method, incorporating 1D MFCC parameters and 30 ensemble machine learning, achieves high model accuracy with low computational cost and holds 31 promising potential for practical CFST applications. 32 Revised manuscript with changes marked Click here to view linked References
A photonics-based multidomain features extraction approach for radio frequency (RF) signals is proposed and demonstrated. Through the time-mapped Fourier transform (TM-FT) and optical interference on the RF signals captured by multiple antennas, the spectrum and the 2-D angle of arrival (AOA) of the RF signals are mapped to the time domain simultaneously. Thus, the simultaneous multidomain features extraction of the RF signals will be guaranteed. In addition, due to the use of the chirped optical pulse with MHz repetition rate as the time window for the features extraction, the proposed scheme can analyze wideband and transient RF signals. In the experiment, the multidomain features of 4-GHz wideband RF signals and 5-ns RF transient signals are extracted, and the signal types are classified successfully. The frequency measurement range of 6–16 GHz with an error of
$\pm$
25 MHz and the 2-D AOA measurement range of
$\pm$
40
$^{\circ}$
with an error of
$\pm$
2.5
$^{\circ}$
are verified. The proposed approach provides an innovative option for real-time multidomain features extraction and classification of RF signals in complex electromagnetic environments.
A method to provide bandwidth compressed time-mapped spectrogram analysis based on temporal Talbot effect and temporal magnification is proposed and numerically demonstrated in this paper. The signal under test (SUT) is firstly sampled by a periodic pulse train, then passes through a dispersive medium under the Talbot condition and the spectrogram of the SUT is mapped to the time domain, so-called time-mapped spectrogram (TM-SP). Subsequently, a temporal magnification technique is implemented to stretch the time axis and compress the spectrum bandwidth, so that the effect of detection bandwidth on the frequency resolution is alleviated. Though the TM-SP cannot be acquired in a continuous way, the SUT is analyzed with ultrahigh frame rate in the temporal aperture. Additionally, a method to improve acquisition frame rate is proposed. The proposed bandwidth compressed TM-SP analysis is compared with the dispersion-based Fourier transform, and the related tradeoffs are provided in detail. The bandwidth compressed TM-SP analysis with a frequency resolution of 0.1 GHz, a measurable frequency range of 4.85 GHz, an analysis period of 0.1 ns, and an observation period of 4 ns is achieved by simulation.
This work is devoted to introducing an extended form of the instantaneous spectral analysis (ISA) technique recently reported. ISA is based on the extension of Euler’s formula
$e^{jx}=\cos (x)+j\sin (x)$
to fractional powers of
$j$
of the special form
$e^{j^{a}x}$
with
$a=2^{(2-m)}$
and integer values of
$m$
. Here, we generalize the technique to the case where the exponent
$a$
in the extended Euler’s formula is an arbitrary fraction
${m}/{n}$
, where
$m$
and
$n$
are integers with no common factors. Hence, we propose an extended form of ISA (E-ISA), which is not restricted to the values of
$a= 0.5, 0.25, 0.125\ldots$
Compared to the standard Fourier transform (FT), E-ISA is shown to be more suitable in dealing with nonergodic signal sources having nonstationary spectra. In addition, the bandwidth utilized by E-ISA is much smaller than the corresponding one in standard FT. Application of E-ISA to synthetic data, an electrocardiogram signal, and nonstationary current time series data from a submerged electrochemical microplasma system are demonstrated.
We propose and demonstrate a new wavelength-division-sampling technique with high temporal resolution. A discrete-time true-time delay generates multiwavelength near-transform-limited pulses from a supercontinuum source. Pulses sample the analog signal in an electro-optic modulator and are subsequently demultiplexed in a wavelength-division-multiplexing filter. A 100-Gsample/s experimental demonstration of this concept is presented.
Ultra-wide-band analog-to-digital (A/D) conversion is one of the most critical problems faced in communication, instrumentation, and radar systems. This paper presents a comprehensive analysis of the recently proposed time-stretched A/D converter. By reducing the signal bandwidth prior to digitization, this technique offers revolutionary enhancements in the performance of electronic converters. The paper starts with a fundamental-physics analysis of the time-wavelength transformation and the implication of time dilation on the signal-to-noise ratio. A detailed mathematical description of the time-stretch process is then constructed. It elucidates the influence of linear and nonlinear optical dispersion on the fidelity of the electrical signal. Design issues of a single-sideband time-stretch system, as they relate to broad-band operation, are examined. Problems arising from the nonuniform optical power spectral density are explained, and two methods for overcoming them are described. As proof of the concept, 120 GSa/s real-time digitization of a 20-GHz signal is demonstrated. Finally, design issues and performance features of a continuous-time time-stretch system are discussed.
We propose and demonstrate the time stretch optical header recognition technique where a high speed header is extracted and slowed down by more than an order of magnitude, in optical domain, to facilitate the capture and processing in electronic domain. The technique can be implemented in continuous time or discrete time. Both implementations are experimentally demonstrated for stretching a 10 Gb/s header by a factor of 20. Eye diagrams and Q values are generated to evaluate the quality of stretched headers. While both implementations are capable of slowing down the header bit rate, each method has its own advantages and disadvantages in terms of bandwidth, maximum header length, latency, and sensitivity to the sampling clock jitter.
The bandwidth limitation of a high-frequency analogue-to-digital
(A/D) conversion technique based on photonic time-stretch is
investigated. Single-sideband modulation of the electrical input signal
is proposed to avoid this limitation. This technique is promising for
A/D conversion of ultrafast signals (>100 Gflops)
The authors report a method for stretching electrical signals in
time. A high chirp rate is imposed on the electrical signal by mixing it
with a dispersed ultra-short optical pulse in an electrooptic intensity
modulator. This is followed by a passive optical dispersion element to
produce a time-magnified copy of the input electrical signal
Method and apparatus for a wavelength selective true-time delay for an optically controlled device
- B Jalali
- S Yegnanarayanan