1. What is Inverse System Function?

Inverse System Function means that we have a continuous time LTI system with impulse response h(t) and its inverse system with impulse response h1(t) which results in an output equal to x(t).

2. How Does the Calculator Work?

The calculator uses the inverse system function formula:

Where:

• \( H_{inv} \) — Inverse System Function
• \( H_s \) — System Function

Explanation: The inverse system function is calculated by taking the reciprocal of the original system function.

3. Importance of Inverse System Function

Details: System Function refers to the function used to study the conditions under which a system is causal, stable, and can be inverted. The inverse system function is crucial for system analysis and signal processing applications.

4. Using the Calculator

Tips: Enter the System Function value (Hs). The value must be valid and greater than 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of inverse system function?
A: The inverse system function allows us to recover the original input signal from the output, which is essential in many signal processing and control system applications.

Q2: When can a system be inverted?
A: A system can be inverted when it is both causal and stable, and when the system function has no zeros at the origin or on the imaginary axis.

Q3: What are the limitations of this calculation?
A: This simple reciprocal calculation assumes that the system function is a real number. For complex system functions, more complex inversion methods are required.

Q4: How is this used in practical applications?
A: Inverse system functions are used in equalization, system identification, and in designing systems that can undo the effects of another system.

Q5: What happens if the system function is zero?
A: If the system function is zero, the inverse does not exist as division by zero is undefined. This indicates a non-invertible system.