Synthesis of Gabor filtered signal by convolving low-Q filtered signal with Gaussian function for efficient computation

Gabor filters, first introduced in (Gabor, 1946), are joint entropy minimizing frequency sensitive filters. Since this Gabor filter is FIR Band-pass filter, the higher Q-factor needs the higher computational cost. Hence, the efficient calculation method is needed in high-Q Gabor filter. So, in this study, we aim to reduce the computational cost of the high-Q Gabor filtering by synthesizing the filtered signal from the low-Q Gabor filtered signal. By using our method, the filtered signal of any Q-factor can be synthesized from the low-Q filtered signal. Thus, we proposed a new method to convolve the filtered signal with a Gaussian function. The experimental results show that the total computational cost of our method is lower than that of direct filtering. For example, this method can reduce the computational cost to 0.12 with the 1/12 octave filter bank of 97 channels. Our method enables the complexity reduction of so general Gabor filtering with such a simple operation.