Aiming at the amplitude modulated signal with frequency

a fast sinusoidal fitting algorithm for finding envelope is proposed. The algorithm is based on the least squares linear sinusoidal fitting method which does not need iterative operation. The forward recursive idea is used to fully utilize the intermediate parameters of the previous operation

and the amplitude and phase of each point on the amplitude modulation signal are fitted in order

which greatly reduces the amount of operation and is suitable for the rapid solution of the envelope curve of the AC amplitude modulation（AM） sensing signal. By using the algorithm and combining the entire period smoothing method of the absolute value mean of fitting parameters

a practical algorithm for solving envelope curve satisfying the embedded system is presented. The experimental application of ultrasonic signal processing shows that the method can effectively suppress the influence of local noise points

which is more flexible and effective than the general method.