VTechWorks staff will be away for the Thanksgiving holiday beginning at noon on Wednesday, November 27, through Friday, November 29. We will resume normal operations on Monday, December 2. Thank you for your patience.

Browsing by Author "Wirsing, Karlton"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Application of Wavelets to Filtering and Analysis of Self-Similar Signals
    Wirsing, Karlton (Virginia Tech, 2014-03-21)
    Digital Signal Processing has been dominated by the Fourier transform since the Fast Fourier Transform (FFT) was developed in 1965 by Cooley and Tukey. In the 1980's a new transform was developed called the wavelet transform, even though the first wavelet goes back to 1910. With the Fourier transform, all information about localized changes in signal features are spread out across the entire signal space, making local features global in scope. Wavelets are able to retain localized information about the signal by applying a function of a limited duration, also called a wavelet, to the signal. As with the Fourier transform, the discrete wavelet transform has an inverse transform, which allows us to make changes in a signal in the wavelet domain and then transform it back in the time domain. In this thesis, we have investigated the filtering properties of this technique and analyzed its performance under various settings. Another popular application of wavelet transform is data compression, such as described in the JPEG 2000 standard and compressed digital storage of fingerprints developed by the FBI. Previous work on filtering has focused on the discrete wavelet transform. Here, we extended that method to the stationary wavelet transform and found that it gives a performance boost of as much as 9 dB over that of the discrete wavelet transform. We also found that the SNR of noise filtering decreases as a frequency of the base signal increases up to the Nyquist limit for both the discrete and stationary wavelet transforms. Besides filtering the signal, the discrete wavelet transform can also be used to estimate the standard deviation of the white noise present in the signal. We extended the developed estimator for the discrete wavelet transform to the stationary wavelet transform. As with filtering, it is found that the quality of the estimate decreases as the frequency of the base signal increases. Many interesting signals are self-similar, which means that one of their properties is invariant on many different scales. One popular example is strict self-similarity, where an exact copy of a signal is replicated on many scales, but the most common property is statistical self-similarity, where a random segment of a signal is replicated on many different scales. In this work, we investigated wavelet-based methods to detect statistical self-similarities in a signal and their performance on various types of self-similar signals. Specifically, we found that the quality of the estimate depends on the type of the units of the signal being investigated for low Hurst exponent and on the type of edge padding being used for high Hurst exponent.
  • Thumbnail Image
    Identifying and Removing Interference and Artifacts in Multifractal Signals With Application to EEG Signals
    Hbibi, Bechir; Khiari, Cyrine; Wirsing, Karlton; Mili, Lamine M.; Baccar, Kamel; Mami, Abdelkader (IEEE, 2023-10-18)
    Recorded Electroencephalogram (EEG) signals are typically affected by interference and artifacts, which can both impact eye reading and computer analysis of the data. Artifacts are induced by physiological (noncerebral) activities of the patient, such as muscular activities of the eyes, or the heart, or the body, while interference may be of external or internal origin. External interference can be induced by electrical machines if the latter are in the same room as the patients, while internal interference can be caused by abnormal breathing, or body movement, or electrode malfunction, or headset movements. Interference may cause severe distortion of EEG signals, resulting in loss of some segments of brain signals, while artifacts are additive signals to brain signals. Therefore, in order to analyze the brain activity signals of a patient, we need to identify and eliminate interference and isolate artifacts. In this paper, we analyze the EEG signals that were recorded using a headset with fourteen channels placed on the heads of comatose patients at the National Institute of Neurology in Tunis, Tunisia. We identify the interference using a robust statistical method known as projection statistics and we separate the brain signals from the artifacts cited above by applying an independent component analysis method. Finally, we show the multifractal behavior of the EEG signals without interference by applying the wavelet leader method and analyze their properties using the singularity spectrum.