谐波信号恢复的有限脉冲设计法

A Finite Pulse Method for Harmonic Retrieve

对带衰减因子的谐波信号恢复提出一种有限脉冲设计法。通过设计一种特殊的脉冲信号，使原信号与该脉冲信号的卷积最快地衰减到零，实现信号的恢复。文中推导了算法，并进行了不同信噪比下的计算机仿真，表明该方法对信号恢复效果很好，特别是对信号频率估计尤佳。

Harmonic retrieve is very important in signal processing. Several method are available for harmonic retrieve [5] . We present a new method——finite pulse method——for harmonic retrieve. Such a method, to our best knowledge, has not been reported in the open literatures. Suppose the signal x(t) to be retrieved is described by eqs.(1) and (2). What we need to do is to determine n,A i,θ i,β i,f i . We first construct a pulse function e(t) as described by eqs.(4) and (5), so as to make the evolution of x(t) and e(t) be zero, i.e. x(t)e(t)=0 (t>T) , where T is a self determined time constant. From x(t)e(t)=0, we can get eq.(10), which is our main result. Then we set up a criterion as described by eq.(11). Minimize eq.(20) and we can get n . By eq.(25) we can get β i and f i . As for A i and θ i , we can easily estimate them by least square method from samples. Section 3 gives two simulation results. Figs.1 and 4 give the original signals with noise. Figs.2 and 5 are the signals retrieved by our method. They show that our method is quite effective.