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, proposed a CFal function which is continuously derivable in the definition domain and has only one parameter to be rectified, and proved the feasibility of constituting a filter (CFalFilter) and a nonlinearly extended state observer (CFal\_NESO) from the CFal function. Then, by combining CFalFilter and CFal\_NESO, a new type of observer with filter (CFalFilter-CFal\_NESO) was 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, 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, CFalFilter-CFal\_NESO further improves the state tracking performance of the signal with measurement noise. Without changing the parameters, CFalFilter-CFal\_NESO further improves the state tracking performance for signals 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.