This paper analyses the source of excitation and vocal tract influenced filter components to identify the biomarkers of COVID-19 in the human speech signal. The source-filter separated components of cough and breathing sounds collected from healthy and COVID-19 positive subjects are also analyzed. The source-filter separation techniques using cepstral, and phase domain approaches are compared and validated by using them in a neural network for the detection of COVID-19 positive subjects. A comparative analysis of the performance exhibited by vowels, cough, and breathing sounds is also presented. We use the public Coswara database for the reproducibility of our findings.