Frequency Estimation for Zero-Padded Signal Based on the Amplitude Ratio of Two DFT Samples

In practical hardware platforms such as FPGA orDSP, the FFT operation is based on a length of
$2^{L}$
. However, due to the system limitation, the length of sampled signal would be not equal to
$2^{L}$
. Thus, zero-padding is performed on the signal before FFT operation. Most traditional sinusoidal frequency estimation methods are for signals without zero-padding. When applying these methods to the zero-padded signal, the performances would degrade. To solve this problem, a novel frequency estimation method for zero-padded signal is proposed in this paper. In the proposed method, by using the analytical expression of the DFT signal after zero-padding, an amplitude ratio function is defined between the two DFT samples nearest to the true frequency. Based on the monotonic property of the ratio function, Newton-Raphson method or bisection search is used to estimate the residual frequency. Two implementation flows are proposed, with similar performance and computational complexity. Experimental results show that the proposed method achieves better RMSE performance than the traditional methods. More importantly, the proposed estimation method can be applied to both the zero-padded signal and the non-padding signal.