Using step signal to represent complex signal can simplify the study of some characteristics of complex signal. The linear combination of step signal and its delayed step signal is expressed or approximated, and then the superposition principle of the system is used.
The spectrum of more complex signals can be discussed by simple signals, such as the spectrum and frequency domain characteristics of unit step signals, thus reducing the difficulty of calculating the spectrum of complex signals.
Extended data:
Research based on step function
Natural ecology
A mathematical model for solving natural ecological problems is proposed by using step function. For example, "Study on the Change Model of Mangrove Litter Based on Step Function": Because the change of litter with time has a peak value, using step function, two problems that the segmented model has been unable to solve: one is the mathematical determination method of change point, and the other is the continuity of change point.
High precision approximation
In order to improve the efficiency of ICM method in solving structural topology optimization problems, the approximate approximation function of step function and its inverse function-polishing function and filtering function is improved.
Engineering field
For example, the research on the method of solving repetitive engineering control route with delayed step function, the step function fitting method of bridge aerodynamic admittance identification, the construction of grid multi-scroll chaotic attractor with polynomial and step function and its circuit realization have been discovered to varying degrees.
Baidu Encyclopedia-Step Function