assignment 4(2).pdf - ECE 301 Homework 4 Systems in the time domain Q1 For the circuit depicted below find the differential equation relating outputs

assignment 4(2).pdf - ECE 301 Homework 4 Systems in the...

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ECE 301 Homework 4 Systems in the time domain Q1. For the circuit depicted below, find the differential equation relating outputs y 1 (t) and y 2 (t) to the input f(t). Q2. 1) Please state the definition for causality . 2) The following are the impulse responses of some discrete-time LTI systems. Please determine whether each system is causal or not and justify your answers. (a) ℎ[𝑛] = ( 1 5 ) 𝑛 ?[𝑛] (b) ℎ[𝑛] = (0.8) 𝑛 ?[𝑛 + 2] (c) ℎ[𝑛] = ( 1 2 ) 𝑛 ?[−𝑛] (d) ℎ[𝑛] = (− 1 2 ) 𝑛 ?[𝑛] + (1.01) 𝑛 ?[𝑛 − 1] Q3 . 1) Please state the definition of time-invariant . 2) Determine whether each of the following systems is time-invariant or not. Justify your answers. (In each question, y[n] denotes the system
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