System Physical Realization
- Signal and System Spring 2023 Homework Requirements and Reference Answer Summary
- Signals and Systems 2023 (Spring) Homework Requirements - Fourteenth Homework
- Signals and Systems 2023 (Spring) Homework Reference Answers - 14th Homework
01 The fourteenth homework
1. Introduction to Exercises
This exercise asks whether a given system function can be physically realized? Both system functions are rational fractions of omega. The physical realizability of the system needs to be applied to the Perry-Wiener criterion. The Perivina criterion corresponds to the fact that the integral value is less than infinity. For half rational fractions, after taking the logarithm of its amplitude, the value diverges only at some discrete points such as zero points and poles, and the corresponding integral is still limited. Therefore, to judge whether the system is physically realizable, it needs to be applied to whether the system function is absolutely square integrable. Next, apply this condition to judge whether the previous two systems are physically realizable.
2. Problem solving
Consider the first sub-problem first, in order to find its integral, it is necessary to solve the original function corresponding to the integral function. Here is a direct result of a search on the Internet. This is its corresponding original function. Next, solve the value of the variable at the upper and lower limits of the integral, that is, at plus or minus infinity. The integral value can be obtained by subtracting the values at the upper and lower limits. The second item can know whether x is positive or negative infinity, the internal value of the logarithm is 1. So the final calculated value is 0 at the end. For the above item, when x takes positive or negative infinity, the corresponding value is positive or negative Pi, so the difference inside is 2 Pi, considering the coefficient of the first sixth and the lower 3, the final integral value is one third Next three, Pi. This value is less than infinity, and the square integral of the system function is finite. The system is physically realizable.
The second sub-problem, the degree of omega corresponding to the numerator and denominator is fourth order, so when omega tends to plus or minus infinity, the modulus of the system function tends to 1, therefore, its integral tends to plus or minus infinity. From this, it can be known that the physical system cannot be realized physically.
※ Summary ※
This paper discusses the physical realizability of system functions corresponding to two rational fractions. It is judged by whether the square of the modulus of the system function is integrable.
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