Calculating Phase Difference Between Two Sine Wave Signals Using Goertzel Algorithm

Using the Goertzel algorithm to calculate the phase difference between two sine wave signals is a widely adopted approach in digital signal processing. This algorithm efficiently measures the time shift between signals to determine their phase offset, which represents the temporal displacement between waveforms and helps analyze signal correlations. The Goertzel algorithm provides a computationally optimized method for phase difference calculation by implementing a simplified discrete Fourier transform (DFT) at specific frequency bins, requiring fewer arithmetic operations compared to full FFT implementations. In code implementation, the algorithm involves: - Precomputing cosine terms for the target frequency using: coeff = 2 * cos(2π * target_freq / sampling_rate) - Processing signal samples through recursive filtering: y[n] = x[n] + coeff * y[n-1] - y[n-2] - Extracting complex phasor components from the final two filter states - Calculating phase angles using arctangent functions: phase = atan2(imaginary_component, real_component) This efficient single-frequency DFT implementation makes it particularly suitable for real-time applications in signal processing, communication systems, and audio analysis where computational resources are constrained. The method maintains accuracy while reducing memory requirements and processing latency compared to conventional Fourier transforms.