A segmentation algorithm, which detects a single cardiac cycle (S1-Systole-S2-Diastole) of Phonocardiogram (PCG) signals using Homomorphic filtering and K-means clustering and a three way classification of heart sounds into Normal (N), Systolic murmur (S) and Diastolic murmur (D) using Grow and Learn (GAL) neural network, are presented. Homomorphic filtering converts a non-linear combination of signals (multiplied in time domain) into a linear combination by applying logarithmic transformation. It involves the retrieval of the envelope, a(n) of the PCG signal by attenuating the contribution of fast varying component, f(n) using an appropriate low pass filter. K-means clustering is a nonhierarchical partitioning method, which helps to indicate single cardiac cycle in the PCG signal. Segmentation performance of 90.45% was achieved using the proposed algorithm. Feature vectors were formed after segmentation by using Daubechies-2 wavelet detail coefficients at the second decomposition level. Grow and Learn network was used for classification of the segmented PCG signals and a classification accuracy of 97.02% was achieved. It is concluded that Homomorphic filtering and GAL network could be used for segmentation and classification of PCG signals without using a reference signal.