The estimated Power Spectral Density (PSD) gives the information regarding the architectural structure of random process; it can be utilized for mathematical modeling, removal of noise, prediction of the signal of the deserved processes. The objective of spectral density estimation is to approximation the spectral density of a random signal from a series of time sample of the signal. Spectral estimation and coefficient estimation is concerned with determining the distribution in frequency of the power of a random process. In this paper, a well-known adaptive filter is used to the estimation of the spectral density of the signal. It includes the LMS, RLS and improves RLS (proposed method) to analyze the coefficient of the sinusoidal signal.