The impulse invariant method is a technique used in signal processing to convert a continuous-time system into a discrete-time system. It involves sampling the continuous-time system at regular intervals and using the impulse response of the continuous-time system to determine the impulse response of the discrete-time system.
The impulse transfer function is the ratio of the output to the input of a system in response to an impulse input. To find the impulse transfer function using the impulse invariant method, the impulse response of the continuous-time system is sampled and then converted into the impulse response of the discrete-time system. The impulse transfer function can then be determined by taking the Fourier transform of the discrete-time impulse response.
The impulse invariant method is a popular technique because it allows for an accurate representation of the continuous-time system in the discrete-time domain. It also preserves the stability and causality of the system and is relatively easy to implement.
One limitation of the impulse invariant method is that it assumes a perfect impulse response, which may not always be the case in real-world systems. This can lead to errors in the conversion from continuous-time to discrete-time. Additionally, the sampling rate used in the method may need to be high to accurately represent the continuous-time system, which can be computationally expensive.
The impulse invariant method is a model-based approach that relies on the impulse response of the continuous-time system. Other methods, such as the bilinear transform, use different techniques to convert the continuous-time system into the discrete-time domain. The choice of method depends on the specific system being analyzed and the desired level of accuracy.