GCC-PHAT Frequency Domain Algorithm for Time Delay Estimation

The term "GCC-PHAT frequency domain" refers to a commonly used algorithm in speech signal processing. The GCC-PHAT (Generalized Cross Correlation with Phase Transform) algorithm is a time delay estimation method used to determine the location of sound sources arriving simultaneously at two or more microphones. This algorithm operates based on phase difference by transforming input signals into the frequency domain to compute time delays. The implementation typically involves applying Fast Fourier Transform (FFT) to convert signals to frequency domain, calculating cross-power spectrum, applying phase transformation to weight the spectrum, and then performing inverse FFT to obtain the generalized cross-correlation function. The peak detection in this function reveals the time difference of arrival between microphone signals. This technique finds extensive applications in speech recognition, speech enhancement, and audio source localization systems, particularly in environments requiring robust time delay estimation under noisy conditions.