This thesis deals with the application of Principal Component Neural Network (PCNN) in signal processing problems that arise in the areas of sonar and speech. Specifically, we address the application in signal separation and frequency estimation. The aim of the research work is to explore the role of neural networks in extracting the relevant features from an observed signal. PCNNs are neural networks which perform Principal Component Analysis (PCA). Basically, PCA is a transformation which represents a data set in more compact form. Principal components are the directions along which the data points in the data, set have maximum variance. PCNN can extract the principal component.^ in its weights by learning from input data. PCA is widely applied in data compression and signal processing. This thesis focuses on signal processing applications. Introducing nonlinearity in PCNN brings the higher order statistics into computation and makes the network to perform independent component analysis. This helps in the separation of independent source signals present in a received signal. The role of nonlinearity in a nonlinear PCNN for signal separation application is explored. This thesis addresses the signal processing problems such as signal separation and frequency estimation for which the PCNN can be applied. The applications related to these signal p r ocessing problems in the areas of sonar and speech are identified. The issues that arise in the case of real da ta which makes the signal separation problem difficult are addressed. Most of the real signals like sonar and speech consist of multiple subsignals which are closely spaced in frequency. A single nonlinear PCNN cannot extract all the subsignals independently. A hierarchical approach is proposed in which the subsignals are extracted a t different levels using more than one network. In the studies conducted for signal separation, the nonlinearity is introduced in the learning algorithm. From the experiments, it is observed that the extraction of a particular subsignal depends on the choice of nonlinearity. A combination learning algorithm is proposed which brings the combined effect of different nonlinearities. Most of the passive sonar and speech signals are nonstationary. PCNN can be used effectively for tracking the changes in the frequencies of a input nonstationary signal. This is done by estimating the frequencies with a frequency estimation method that uses the principal components computed by the network at different instants of time. The studies in signal separation and frequency tracking are performed with both synthetic and real data. The synthetic data is generated as the sum of sinusoids of different frequencies. The sinusoids are pure frequencies in the case of sonar and damped in the case of speech. The efficacy of the proposed methods is demonstrated.