A Novel Method for Microphone Channel Frequency Response Calibration Based on Newton Algorithm

Microphone arrays are widely applied in practical applications. In an array, each channel conventionally contains an acoustic sensor and a following signal conditioning circuit (SCC). Frequency response mismatches among channels will adversely affect array's overall performance. Existing calibration methods provide promising results; however, their accuracy varies considerably across full frequency band and the passband bandwidth shrinkage problem also arises. To address these problems, we propose a novel calibration method based on Newton algorithm. The proposed method cascades calibration filters after channel output signals allowing the frequency response calibration to be equivalent to the optimization of calibration filter coefficients. First, all uncalibrated channels' bandwidths are analyzed using a chirp calibration signal, resulting in appropriate construction of the desired output. Next, a spectrum mean square error criterion between each channel output and the desired signal is utilized to formulate the frequency response mismatch. Finally, we employ Newton algorithm to design the calibration filter coefficients corresponding to each channel. Explicit mathematical derivation is provided. Since the cost function is quadratic, expressions of the constant Hessian matrix and its inverse are derived. Furthermore, the inverse Hessian can be efficiently computed using spectral coefficients of channel outputs. Simulation results reveal that the proposed method significantly outperforms the state-of-the-art calibration approaches in terms of calibration accuracy, calibrated passband bandwidth performance, and convergence rate. Real-world experiments also verify its effectiveness.