Design Criteria for Simple Sinusoidal Parameter Estimation based on Quadratic Interpolation of FFT Magnitude Peaks

Due to its simplicity and accuracy, quadratic peak interpolation in a zero-padded Fast Fourier Transform (FFT) has been widely used for sinusoidal parameter estimation in audio applications. While general criteria can guide the choice of window type, FFT length, and zero-padding factor, it is sometimes desirable in practice to know more precisely the requirements for achieving a prescribed error bound. In this paper, we theoretically predict and numerically measure the errors associated with various choices of analysis parameters, and provide precise criteria for designing the estimator. In particular, we determine 1) the minimum zero-padding factor needed for a given error bound in quadratic peak interpolation, and 2) the minimum allowable frequency separation for a given window length, for various window types.