Frequency estimation of multiple complex and real sinusoids in noise has attracted wide attention in many fields. In this paper, two frequency domain parametric methods are proposed to estimate the frequencies of multiple complex and real sinusoids accurately. The first method for complex sinusoids adopts Discrete Fourier Transform (DFT) and interpolation algorithm to obtain the coarsely estimated frequencies, and then the interpolation is used iteratively to refine the estimated frequencies. In each step, the estimated frequency components are subtracted to reduce spectrum leakage. The second method for multiple real sinusoids, which is modified based on the first one, focuses on reducing the spectrum leakage caused by negative frequencies and then employs iterative interpolation to refine the estimated frequencies. Simulation results show that two proposed methods have lower mean square error (MSE) and signal-to-noise ratio (SNR) breakdown threshold than other frequency domain parametric methods, and are capable of achieving the Cramér-Rao lower bound (CRLB) for both multiple complex and real signals under a wide range of SNR.

噪声中多个复数和实数正弦波的频率估计在许多领域引起了广泛关注。在本文中，提出了两种频域参数化方法来准确估计多个复数和实数正弦波的频率。复数正弦波的第一种方法采用离散傅立叶变换（DFT）和插值算法来获得粗估计频率，然后迭代地使用插值来细化估计频率。在每个步骤中，减去估计的频率分量以减少频谱泄漏。第二种多实正弦波方法是在第一种方法的基础上改进的，重点是减少负频率引起的频谱泄漏，然后使用迭代插值来细化估计的频率。