Revision as of 18:18, 18 September 2008 by Aehumphr (Talk)

Homework 3_ECE301Fall2008mboutin - A - B - C

Memory

A system is said to be memoryless if its output for each value of the independent variable at a given time is dependent only on the input at that same time.

$ y[n] = (2x[n]-x^2[n])^2 $ : is a good example of a system without memory


The notion of a system with memory is a system that has current outputs corresponding to outputs in the past. A simple summation is an example of a system with memory.

$ y[n] = \sum_{k= -\infty}^n x[k] $

In analogue electronics a capacitor is represented mathematically by the integral $ y(t) = 1/C\int_{-\infty}^t x(\tau) d\tau $ which is also a system that has memory as each voltage value at the present is dependent on the voltage across the capacitor at all times in the past.

Causality

Linear System

Time Invariance

Stability

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