Acoustic event detection (AED) systems, combined with video surveillance systems, can enhance urban security and safety by automatically detecting incidents, supporting the smart city concept. AED systems mostly use mel spectrograms as a well-known effective acoustic feature. The spectrogram is a combination of frequency bands. A big challenge is that some of the spectrogram bands may be similar in different events and be useless in AED. Removing useless bands reduces the input feature dimension and is highly desirable. This article proposes a mathematical feature analysis method to identify and eliminate ineffective spectrogram bands and improve AED systems’ efficiency. The proposed approach uses a Student’s t-test to compare frequency bands of the spectrogram from different acoustic events. The similarity between each frequency band among events is calculated using a two-sample t-test, allowing the identification of distinct and similar frequency bands. Removing these bands accelerates the training speed of the used classifier by reducing the number of features, and also enhances the system’s accuracy and efficiency. Based on the obtained results, the proposed method reduces the spectrogram bands by 26.3%. The results showed an average difference of 7.77% in the Jaccard, 4.07% in the Dice, and 5.7% in the Hamming distance between selected bands using train and test datasets. These small values underscore the validity of the obtained results for the test dataset.