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Analysis of Human Walking Trajectories for Surveillance
Published in Yangsheng Xu, Ka Keung C. Lee, Human Behavior Learning and Transfer, 2005
We convert the real-valued human trajectory data into sequences of discrete symbols by data preprocessing. The human trajectory data is firstly normalized to be between [—1, 1]. It is then segmented into possibly overlapping window frames. Hamming window is applied to each frame to minimize spectral leakage caused by data windowing. Discrete Fourier Transform is used to convert the real vectors to complex vectors. Using power spectral density estimation (Fourier), a feature matrix V is created. By applying LGB vector quantization algorithm, the feature vector V is converted to L discrete symbols such that the total distortion between the symbols and the quantized vectors can be minimized. The quantized sequence of human trajectory data will be used to train a five-state Bakis HMM for similarity measure.
Introduction to Signal Processing
Published in Ralph D. Hippenstiel, Detection Theory, 2017
This chapter introduces discrete time signals and typical processing tools. In particular, linear data processing is examined. FIR filtering is addressed in Section 3.5. The Fourier transform (DFT/FFT) are discussed in detail in Section 3.6, providing different useful interpretations of this processing operation. Sections 3.7 and 3.8 address fast correlation and the fast power spectral density estimation techniques. The final section provides a layman’s introduction to wavelet processing and contrast the Fourier and WT processing methods.
Stochastic analysis of dynamic stress amplification factors for slab track foundations
Published in International Journal of Rail Transportation, 2023
Hongwei Xie, Qiang Luo, Tengfei Wang, Liangwei Jiang, David P. Connolly
Power spectral density (PSD) characterizes the frequency content of a signal and is commonly used to interpret track geometry data. The purpose of spectral-density estimation (SDE) in statistical signal processing is to estimate the spectrum of a random signal based on a sequence of time samples. For a discrete digital signal , of non-zero duration , the discrete-time Fourier transform (DTFT) can be used to estimate PSD’s , for signals such as measured track irregularities: