Cough is a common symptom that manifests in numerous respiratory diseases. In chronic respiratory diseases, such as asthma and COPD, monitoring of cough is an integral part in managing the disease. This paper presents an algorithm for automatic detection of cough events from acoustic signals. The algorithm uses only three spectral features with a logistic regression model to separate sound segments into cough and non-cough events. The spectral features were derived using simple calculation from two frequency bands of the sound spectrum. The frequency bands of interest were chosen based on its characteristics in the spectrum. The algorithm achieved high sensitivity of 90.31%, specificity of 98.14%, and F1-score of 88.70%. Its low-complexity and high detection performance demonstrate its potential for use in remote patient monitoring systems for real-time, automatic cough detection.