Time perception is an intrinsic ability of human beings and animals which is used to percept and estimate time duration between events. How time perception system functions and its characteristics in human beings of different ages and sexes are still among biggest mysteries of neuroscience. In order to analyze this mechanism, various imaging and brain signal recording techniques such as fMRI, PET and EEG have been utilized so far. One of the inexpensive and easy methods with a high temporal resolution is to use Event Related Potentials (ERP). These signals are generated during EEG recording, when subjects are stimulated with visual, auditory or somatosensory stimuli. The main drawback of utilizing these signals is their very low signal to noise ratio (SNR) which makes difficult their observation and extraction from ongoing brain activity signals. The most conventional method to extract these signals is synchronized averaging. In this method, the subject is stimulated with frequent stimuli and their responses are recorded. Recorded signals are aligned according to the stimulus time and their average is calculated to remove random noise and extract ERPs. The high number of trials required to reach desired SNR, nonstationarity of ERPs in consecutive trials, and loss of useful physiologic information exist in variability of ERPs in various trials are the most important disadvantages of this method. As a result, various algorithms are proposed to extract ERPs in a single trial manner. In this thesis, different single trial ERP extraction methods are studied and their advantages and disadvantages are examined. To improve the efficiency of these algorithms in very low SNR conditions, a two stage algorithm is proposed. At the first stage, average of some trials is calculated and wavelet coefficients related to the averaged ERP are extracted using a new approach in wavelet transform and extended taut string algorithm. These coefficients are utilized as priori information in second stage to extract single trial ERPs by means of adaptive noise cancelers and wavelet reconstruction. Simulation results with additive white Gaussian noise and real EEG noise show the superiority of proposed algorithm over conventional and recently proposed algorithms for single trial ERP extraction and trial to trial amplitude variability tracking. In addition, single trial analysis of time perception signals shows that CNV component of trials in signals recorded from Fz electrode can be considered as a representative of accumulator behavior in central clock model of time perception system. Furthermore, the feeling of nowness time point was estimated usually between 2 and 3 seconds in healthy group of children. These results can be utilized in future researches such as comparison of healthy controls and children with ADHD. Keywords: Event Related Potential, Time Perception, Single Trial ERP, Wavelet Transform