Croup, a respiratory tract infection common in children, causes an inflammation of the upper airway restricting normal breathing and producing cough sounds typically described as seallike "barking cough." Physicians use the existence of barking cough as the defining characteristic of croup. This paper aims to develop automated cough sound analysis methods to objectively diagnose croup.In automating croup diagnosis, we propose the use of mathematical features inspired by the human auditory system. In particular, we utilize the cochleagram for feature extraction, a time-frequency representation where the frequency components are based on the frequency selectivity property of the human cochlea. Speech and cough share some similarities in the generation process and physiological wetware used. As such, we also propose the use of mel-frequency cepstral coefficients which has been shown to capture the relevant aspects of the short-term power spectrum of speech signals. Feature combination and backward sequential feature selection are also experimented with. Experimentation is performed on cough sound recordings from patients presenting various clinically diagnosed respiratory tract infections divided into croup and non-croup. The dataset is divided into training and test sets of 364 and 115 patients, respectively, with automatically segmented cough sound segments.Croup and non-croup patient classification on the test dataset with the proposed methods achieve a sensitivity and specificity of 92.31% and 85.29%, respectively.Experimental results show the significant improvement in automatic croup diagnosis against earlier methods.This paper has the potential to automate croup diagnosis based solely on cough sound analysis.