Signals recorded from the brain often show rhythmic patterns at different frequencies, which are tightly coupled to the external stimuli as well as the internal state of the subject. These signals also have transient structures related to spiking or sudden onset of a stimulus, which have a duration not exceeding tens of milliseconds. Further, brain signals are highly non-stationary because both behavioral state and external stimuli can change over a short time scale. It is therefore essential to study brain signals using techniques that can represent both rhythmic and transient components of the signal. In Chapter 2, we describe a multi-scale decomposition technique based on an over-complete dictionary called matching pursuit (MP), and show that it is able to capture both sharp stimulus-onset transient and sustained gamma rhythm in local field potential recorded from the primary visual cortex. Gamma rhythm (30 to 80 Hz), often associated with high-level cortical functions, has been proposed to provide a temporal reference frame (“clock”) for spiking activity, for which it should have least center frequency variation and consistent phase for extended durations. However, recent studies have proposed that gamma occurs in short bursts and it cannot act as a reference. In Chapter 3, we propose another gamma duration estimator based on matching pursuit (MP) algorithm, which is tested with synthetic brain signals and found to be estimating the gamma duration efficiently. Applying this algorithm to real data from awake monkeys, we show that the median gamma duration is more than 330 ms, which could be long enough to support some cortical computations.