This work proposes a novel investigation of time-frequency (t-f) based signal processing approach using Quadratic time-frequency distributions (QTFDs) namely Spectrogram (SPEC), Wigner-Ville distribution (WVD), Smoothed-Wigner Ville distribution (SWVD), Choi-William distribution (CWD) and Modified B-distribution (MBD) for classification of infant cry signals. T-f approaches have proved as an efficient approach for applications involving the non stationary signals. In feature extraction, a cluster of t-f based attributes were extracted from the suggested t-f approaches by extending time-domain and frequency-domain features to the joint (t-f) domain. Conventional features such as Mel-frequency cepstral coefficients (MFCCs) and Linear prediction coefficients (LPCs) were also extracted and their effectiveness was compared with the suggested methodology. The efficacy of the extracted feature vectors was validated using probabilistic neural network (PNN) and general regression neural network (GRNN). The proposed methodology was implemented to classify different sets of infant cry signals cry including binary and multiclass problems. Findings of this study significantly demonstrate the use of t-f method as an efficient practical clinical decision tool for infant cry classification.