Howtosignalprocessing
- Is the impulse response the zero-input response?
- How do you solve a zero-input response?
- How do you calculate impulse response?
- How do you find impulse response from step response?
Is the impulse response the zero-input response?
The impulse response of a system, possibly described by an ODE, is the zero-state response to an input signal x(t)=δ(t).
How do you solve a zero-input response?
To find the zero input solution, take the Laplace Transform of the input with f(t)=0 and solve for Xzi(s). Note: since the initial condition was doubled, the zero input response was doubled.
How do you calculate impulse response?
Given the system equation, you can find the impulse response just by feeding x[n] = δ[n] into the system. If the system is linear and time-invariant (terms we'll define later), then you can use the impulse response to find the output for any input, using a method called convolution that we'll learn in two weeks.
How do you find impulse response from step response?
To develop this relationship, consider first the unit step response of a system. so the output is the impulse response (the derivative of the unit step response). It is important to keep in mind that the impulse response of a system is a zero state response (i.e., all initial conditions equal to zero at t=0-).
