In this work, the problem of detecting neuronal spikes or action potentials (AP) in noisy recordings from a Microelectrode Array (MEA) is investigated. In particular, the spike detection algorithms should be less complex and with low computational complexity so as to be amenable for real time applications. The use of the MEA is that it allows collection of extracellular signals from either a single unit or multiple (45) units within a small area. The noisy MEA recordings then undergo basic filtering, digitization and are presented to a computer for further processing. The challenge lies in using this data for detection of spikes from neuronal firings and extracting spatiotemporal patterns from the spike train which may allow control of a robotic limb or other neuroprosthetic device directly from the brain. The aim is to understand the spiking action of the neurons, and use this knowledge to devise efficient algorithms for Brain Machine Interfaces (BMIs). An effective BMI will require a realtime, computationally efficient implementation which can be carried out on a DSP board or FPGA system. The aim is to devise algorithms which can detect spikes and underlying spatio-temporal correlations having computational and time complexities to make a real time implementation feasible on a specialized DSP chip or an FPGA device. The time-frequency localization, multiresolution representation and analysis properties of wavelets make them suitable for analysing sharp transients and spikes in signals and distinguish them from noise resembling a transient or the spike. Three algorithms for the detection of spikes in low SNR MEA neuronal recordings are proposed: 1. A wavelet denoising method based on the Discrete Wavelet Transform (DWT) to suppress the noise power in the MEA signal or improve the SNR followed by standard thresholding techniques to detect the spikes from the denoised signal. 2. Directly thresholding the coefficients of the Stationary (Undecimated) Wavelet Transform (SWT) to detect the spikes. 3. Thresholding the output of a Teager Energy Operator (TEO) applied to the signal on the discrete wavelet decomposed signal resulting in a multiresolution TEO framework. The performance of the proposed three wavelet based algorithms in terms of the accuracy of spike detection, percentage of false positives and the computational complexity for different types of wavelet families in the presence of colored AR(5) (autoregressive model with order 5) and additive white Gaussian noise (AWGN) is evaluated. The performance is further evaluated for the wavelet family chosen under different levels of SNR in the presence of the colored AR(5) and AWGN noise. Chapter 1 gives an introduction to the concept behind Brain Machine Interfaces (BMIs), an overview of their history, the current state-of-the-art and the trends for the future. It also describes the working of the Microelectrode Arrays (MEAs). The generation of a spike in a neuron, the proposed mechanism behind it and its modeling as an electrical circuit based on the Hodgkin-Huxley model is described. An overview of some of the algorithms that have been suggested for spike detection purposes whether in MEA recordings or Electroencephalographic (EEG) signals is given. Chapter 2 describes in brief the underlying ideas that lead us to the Wavelet Transform paradigm. An introduction to the Fourier Transform, the Short Time Fourier Transform (STFT) and the Time-Frequency Uncertainty Principle is provided. This is followed by a brief description of the Continuous Wavelet Transform and the Multiresolution Analysis (MRA) property of wavelets. The Discrete Wavelet Transform (DWT) and its filter bank implementation are described next. It is proposed to apply the wavelet denoising algorithm pioneered by Donoho, to first denoise the MEA recordings followed by standard thresholding technique for spike detection. Chapter 3 deals with the use of the Stationary or Undecimated Wavelet Transform (SWT) for spike detection. It brings out the differences between the DWT and the SWT. A brief discussion of the analysis of non-stationary time series using the SWT is presented. An algorithm for spike detection based on directly thresholding the SWT coefficients without any need for reconstructing the denoised signal followed by thresholding technique as in the first method is presented. In chapter 4 a spike detection method based on multiresolution Teager Energy Operator is discussed. The Teager Energy Operator (TEO) picks up localized spikes in signal energy and thus is directly used for spike detection in many applications including R wave detection in ECG and various (alpha, beta) rhythms in EEG. Some basic properties of the TEO are discussed followed by the need for a multiresolution approach to TEO and the methods existing in literature. The wavelet decomposition and the subsampled signal involved at each level naturally lends it to a multiresolution TEO framework at the same time significantly reducing the computational complexity due the subsampled signal at each level. A wavelet-TEO algorithm for spike detection with similar accuracies as the previous two algorithms is proposed. The method proposed here differs significantly from that in literature since wavelets are used instead of time domain processing. Chapter 5 describes the method of evaluation of the three algorithms proposed in the previous chapters. The spike templates are obtained from MEA recordings, resampled and normalized for use in spike trains simulated as Poisson processes. The noise is modeled as colored autoregressive (AR) of order 5, i.e AR(5), as well as Additive White Gaussian Noise (AWGN). The noise in most human and animal MEA recordings conforms to the autoregressive model with orders of around 5. The AWGN Noise model is used in most spike detection methods in the literature. The performance of the proposed three wavelet based algorithms is measured in terms of the accuracy of spike detection, percentage of false positives and the computational complexity for different types of wavelet families. The optimal wavelet for this purpose is then chosen from the wavelet family which gives the best results. Also, optimal levels of decomposition and threshold factors are chosen while maintaining a balance between accuracy and false positives. The algorithms are then tested for performance under different levels of SNR with the noise modeled as AR(5) or AWGN. The proposed wavelet based algorithms exhibit a detection accuracy of approximately 90% at a low SNR of 2.35 dB with the false positives below 5%. This constitutes a significant improvement over the results in existing literature which claim an accuracy of 80% with false positives of nearly 10%. As the SNR increases, the detection accuracy increases to close to 100% and the false alarm rate falls to 0. Chapter 6 summarizes the work. A comparison is made between the three proposed algorithms in terms of detection accuracy and false positives. Directions in which future work may be carried out are suggested.