Many countries have adopted a public health approach that aims to address the particular challenges faced during the pandemic Coronavirus disease 2019 (COVID-19). Researchers mobilized to manage and limit the spread of the virus, and multiple artificial intelligence-based systems are designed to automatically detect the disease. Among these systems, voice-based ones since the virus have a major impact on voice production due to the respiratory system's dysfunction. In this paper, we investigate and analyze the effectiveness of cough analysis to accurately detect COVID-19. To do so, we distinguished positive COVID patients from healthy controls. After the gammatone cepstral coefficients (GTCC) and the Mel-frequency cepstral coefficients (MFCC) extraction, we have done the feature selection (FS) and classification with multiple machine learning algorithms. By combining all features and the 3-nearest neighbor (3NN) classifier, we achieved the highest classification results. The model is able to detect COVID-19 patients with accuracy and an f1-score above 98 percent. When applying FS, the higher accuracy and F1-score were achieved by the same model and the ReliefF algorithm, we lose 1 percent of accuracy by mapping only 12 features instead of the original 53.