Various methods for acoustic impulse event detection and identification are available. They are usually based on time or frequency domain algorithms. Both these domains have their limitations and disadvantages. This article presents acoustic impulse events (such as gunshots) identification based on the Cepstral domain, combining the advantages of both frequency and time domains. It compares the efficiency of classification based on four different frequency Cepstral coefficients, namely Mel-frequency Cepstral Coefficients (MFCC), Inverse Mel-frequency Cepstral Coefficients (IMFCC), Linear-frequency Cepstral Coefficients (LFCC) and Gammatone-frequency Cepstral Coefficients (GFCC). These, originally speech features, showed to be promising in the other applications with good results. This work compares the classification accuracy of gunshots from several short and rifle guns and multiple impulse acoustic events (various types of slams, slaps, etc.) to represent false alarms. In total, more than four hundred acoustic event records have been acquired, where approx. 70% has been used for training, and the rest for validation. For a classification, a Support Vector Machine (SVM) classifier with 26 frequency Cepstral Coefficients from each MFCC, IMFCC, LFCC, and GFCC served as features are used. Accuracy and Matthew’s correlation coefficient measure the classification success rate. The results confirm the superiority of GFCC to other analyzed methods.