The Fal function is the core unit of the nonlinear extended state observer(Fal_NESO), and its constituent filter(FalFilter) also has an important influence on the performance of the control system. By analysing the performance of the FalFilter and the Fal function, a CFal function is proposed, which is continuously derivable in the definition domain and has only one parameter to be rectified, and the feasibility of constituting a filter(CFalFilter) and a nonlinearly extended state observer(CFal_NESO) from the CFal function is proved. Then, by combining the CFalFilter and the CFal_NESO, a new type of observer with a filter(CFalFilter-CFal_NESO) is obtained to deal with the case of noise interference in the measurement link. Finally, the CFal function is compared with the two improved Fal functions through typical examples, and the experimental results show that the CFalFilter has the best effect under the condition of convergence of tracking speed; by changing only the parameter of the Fal function, the CFal_NESO can better extract the state of the signal in the noisy environment, and at the same time, it also reduces the difficulty in parameter tuning due to the increase in the number of orders of the observer; without changing the parameter, the CFalFilter-CFal_NESO further improves the state tracking performance of the signal with measurement noise. The CFalFilter, CFal_NESO and CFalFilter-CFal_NESO proposed in this paper are applicable to the filtering and observation of most nonlinear and high-order systems, which are of great academic significance and practical application value.