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Image and Localization of Behindthe-Wall Targets Using Collocated and Distributed Apertures
Published in Moeness G. Amin, Through-the-Wall Radar Imaging, 2017
For a backscattered signal with a moderate SNR, the detection of the STFT peaks that reflect the true signal power concentration is straightforward. For weak signals, however, the detection of such STFT peaks may not be always reliable. One of the techniques that can be used to further enhance the SNR for improved peak detection is to average the magnitude of the STFT results obtained from all the available frequencies. The advantage of such averaging becomes more pronounced in a multifrequency radar. Due to the frequency resolution limitation, the STFT signature of s2(t) may approximately coincide with that of s1(t). In this case, direct averaging can be performed. In some situations, however, the STFT corresponding to the true signal signatures may not overlap. In this case, the STFT signatures corresponding to all the frequencies can be aligned through scaling and interpolating the time axis of the received signal at each frequency.
Radar Monitoring of Humans with Assistive Walking Devices
Published in Moeness G. Amin, Radar for Indoor Monitoring, 2017
Ann-Kathrin Seifert, Moeness G. Amin, Abdelhak M. Zoubir
When calculating the spectrogram, the choice of the window function is eminent as it trades off the time and frequency resolutions. A larger window length will typically degrade the time resolution as signal components with a shorter duration than the window length may get smeared out. However, a smaller window length amounts to convolution with a wideband signal limiting the frequency resolution. As the time window lengths in time and frequency are inversely proportional to each other by the uncertainty principle, using the STFT has the effect of trading off time resolution against frequency resolution (Chen and Ling 2001). The multiwindow spectrogram can be used to partially mitigate this effect and has been successfully used for fall detection (Jokanović et al. 2015).
Transform Domain Speech Processing
Published in Shaila Dinkar Apte, Random Signal Processing, 2017
We started with STFT. We discussed the meaning of sliding window transform and indicated how the frequency resolution is decided by the size of the window. STFT uses a short-time windowed sines and cosines as basis functions. STFT can be considered as a Fourier analysis of the short time windowed signal. Multiplying the signal with window localizes the signal in time domain, but results in a convolution of signal spectrum with the spectrum of the window. The narrower the window, the better we localize the signal in time domain and poorer we localize its spectrum. Heisenberg uncertainty principle applies here. Δt×Δf≥1/2, i.e., if we improve the resolution in time domain, we have to sacrifice for frequency domain resolution, and vice versa.
Magnetoresistance sensor-based rotor fault detection in induction motor using non-decimated wavelet and streaming data
Published in Automatika, 2022
S. Kavitha, N. S. Bhuvaneswari, R. Senthilkumar, N. R. Shanker
Fast Fourier transform (FFT) is mainly used for frequency-based signal analysis for IM rotor fault detection [46]. FFT-based power spectral analysis of the IM error signal computes the peak value of the asymmetric rotor harmonics [4]. However, rotor bar failure harmonics are undifferentiated in FFT analysis, according to the research findings and experimental results [47]. The Fourier analysis method leads to inaccurate rotor fault diagnosis due to drifts and abrupt changes. To overcome the above limitations of Fourier-based motor signal analysis, short-time Fourier transform (STFT) is used as an alternative method for motor signal analysis. STFT performs time and frequency analysis simultaneously in a signal. It has a fixed-size window during the analysis of a signal,whereas signal analysis for broken rotor needs reliable and varying window for accurate rotor fault diagnosis. Wavelet analysis is preferred for rotor fault detection in IM [48]. Wavelet transform has [49] variable window size and time–frequency domain analysis. Wavelet transform analysis provides time and frequency information of a signal by expressing the signal as a series of oscillatory functions. In wavelet transform, an input signal is decomposed and information is localized in time-scale plane, which is appropriate for the non-stationary signal analysis for IM rotor fault detection. In this paper, a unique hybrid wavelet analysis for outward anti-clockwise magnetic spectra is implemented by the hybridization of DWT, NDWT, and dyadic wavelet transform.
Real-time Automated Event Analysis and Supervisory Framework for Power Systems using Synchrophasor Measurements
Published in Electric Power Components and Systems, 2019
Ajeet Kumar Singh, Manoj Fozdar
Normally, power system functions in a quasi-static state. However, the unexpected occurrence of an event initiates power imbalance in the system, which is reflected as an abrupt variation in voltage and frequency measurements recorded by PMUs. This imbalance is corrected by governor action and excitation control, which take up to 2 sec to participate in stabilizing the system. The voltage and frequency waveforms during this period are deemed as the natural response of the power system to the event. The post-disturbance waveforms of voltage and frequency associated with the similar type of events exhibit very similar characteristics in both time and frequency domain [17]. It illustrates that sufficient information for detection and classification of events is available in the waveform. But, the absence of fundamental frequency in the event signals hinder their frequency representation by simple Fourier Transform [9]. The STFT which requires sectionalizing the signal and applying the conventional Fourier Transform on individual section is another procedure for analysis of non-stationary signals. But, choice of a suitable window and inverse relationship between time and frequency resolution limit its applicability. Hence, the simultaneous analysis in time-frequency domain is a suitable choice. The DWT renders a better trade-off between temporal and frequency resolution, i.e., it offers good time resolution at high frequencies and good frequency resolution at low frequencies. Therefore, in this article, DWT is used to analyze the voltage and frequency signals received in real-time through synchrophasor measurements.
Support vector machine (SVM) classification of cognitive tasks based on electroencephalography (EEG) engagement index
Published in Brain-Computer Interfaces, 2018
Several techniques exist for spectral estimation and representation of EEG signals. Among these is the fast Fourier transform (FFT), which allows for the efficient estimation of the component frequencies in data from a discrete set of values sampled at a fixed rate. However, for signals whose frequencies change in time (like EEG), the FFT has disadvantages. The FFT cannot provide simultaneous time and frequency localization, which means that the power spectrum does not provide information about when certain frequencies occur in the signal. It is therefore not very useful for analyzing time-variant, nonstationary signals like EEG. This problem is overcome by using the short-term Fourier transform (STFT). The STFT segments the signal into narrow time intervals, and takes the Fourier transform (FT) of each segment. Each FT provides the spectral information of a separate time-slice of the signal, providing simultaneous time and frequency information. We used the STFT in the present study. It was used to estimate the power spectrum of the EEG bands. This was implemented with the spectrogram function in MATLAB. The spectrogram computes an FFT-based spectral estimate over each sliding window and allows for the visualization of how the frequency content of the signal changes over time. The spectrogram function divides a signal into segments. Long segments or windows (also known as narrowband spectrogram) provide better frequency resolution whereas short segments (also known as wideband spectrogram) provide better time resolution. In the present study, we segmented the data into quarter-second windows with a 50% overlap of the previous segment and 50% of the next. The Hann window, which has good frequency resolution and reduced spectral leakage [37], was used. The log power, computed as 10 * log 10(power), of the data in each window was computed for the theta band (4–8 Hz), alpha band (8–12 Hz), and beta band (12–30 Hz).