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How do you find impulse response given input and output?
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.
What is the relationship between input and output of an LTI system?
Input is a sequence of impulses (photons). Output is superposition of impulse responses (light). The response of an LTI system is completely characterized by its impulse response h(t).
What makes a system time invariant?
A system is time-invariant if its output signal does not depend on the absolute time. In other words, if for some input signal x(t) the output signal is y1(t)=Tr{x(t)}, then a time-shift of the input signal creates a time-shift on the output signal, i.e. y2(t)=Tr{x(t−t0)}=y1(t−t0).
Which system has unique relationship between input and output?
Explanation: In this example, the input is finite and output is not finite. Hence the given system is unstable. Explanation: The system is said to have memory if its output signal depends on the past values of the input signal and also it is called dynamic system.
How to determine in the system is LTI or not when?
How can we determine in the system is LTI or not when: Using the definitions is somewhat vague in this case, so I am lost how to explicitly explain that they are not linear and time invariant for 1 and 2 at least.
Which is an example of extended linearity in a system?
Linearity and Extended Linearity Linearity: A system S is linear if it satis\\fes both Homogeneity: If y = Sx, and a is a constant then ay = S(ax): Superposition: If y 1= Sx 1and y 2= Sx
Which is the function of the variable t?
˝(t) = H(\ ˝(t)) the variable t serves di\erent roles on each side of the equation. t on the left is a speci\\fc value for time, the time at which the output is being sampled. t on the right is varying over all real numbers, it is not the same t as on the left.