Automatic infant cry classification is one of the significant studies under medical engineering, adopting the medical and engineering techniques for the classification of diverse physical and physiological states of the infants. This paper proposes a new investigation of time-frequency (t-f)-based signal processing technique using wavelet packet spectrum (wpspectrum) for classification of newborn cry signals. The study was initialised with the extraction of a cluster of t-f features from the generated t-f matrix of recorded cry signals using wpspectrum by extending time-domain and frequency-domain features to the joint t-f domain. In accordance, conventional features such as mel-frequency cepstral coefficients (MFCCs) and linear prediction coefficients (LPCs) were also extracted in order to compare the performance of the suggested t-f approach. Probabilistic neural network (PNN) and general regression neural network (GRNN) were used in classification. The proposed methodology was implemented to classify different sets of infant cry signals and the best empirical result of above 99% was reported.