Healthcare professionals routinely use audio signals, generated by the human body, to help diagnose disease or assess its progression. With new technologies, it is now possible to collect human-generated sounds, such as coughing. Audio-based machine learning technologies can be adopted for automatic analysis of collected data. Valuable and rich information can be obtained from the cough signal and extracting effective characteristics from a finite duration time interval that changes as a function of time. This article presents a proposed approach to the detection and diagnosis of COVID-19 through the processing of cough collected from patients suffering from the most common symptoms of this pandemic. The proposed method is based on adopting a combination of Singular Value Decomposition (SVD), and Discrete Wavelet Transform (DWT). The combination of these two signal processing techniques is gaining lots of interest in the field of speaker and speech recognition. As a cough recognition approach, we found it well-performing, as it generates and utilizes an efficient minimum number of features. Mean and median frequencies, which are known to be the most useful features in the frequency domain, are applied to generate an effective statistical measure to compare the results. The hybrid structure of DWT and SVD, adopted in this approach adds to its efficiency, where a 200 times reduction, in terms of the number of operations, is achieved. Despite the fact that symptoms of the infected and non-infected people used in the study are having lots of similarities, diagnosis results obtained from the application of the proposed approach show high diagnosis rate, which is proved through the matching with relevant PCR tests.  The proposed approach is open for more improvements with its performance further assured by enlarging the dataset, while including healthy people.