This paper presents a novel time-frequency-based feature recognition system for gear fault diagnosis using autocorrelation of continuous wavelet coefficients (CWC). Furthermore, it introduces an original mathematical approximation of gearbox vibration signals which approximates sinusoidal components of noisy vibration signals generated from gearboxes, including incipient and serious gear failures using autocorrelation of CWC. First, the drawbacks of the continuous wavelet transform (CWT) have been eliminated using autocorrelation function. Secondly, the autocorrelation of CWC is introduced as an original pattern for fault identification in machine condition monitoring. Thirdly, a sinusoidal summation function consisting of eight terms was used to approximate the periodic waveforms generated by autocorrelation of CWC for normal gearboxes (NGs) as well as occurrences of incipient and severe gear fault (e.g. slight-worn, medium-worn, and broken-tooth gears). In other words, the size of vibration signals can be reduced with minimal loss of significant frequency content by means of the sinusoidal approximation of generated autocorrelation waveforms of CWC as reported in this paper.