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<math>y[n] = \sum_{k= -\infty}^n x[k] </math> | <math>y[n] = \sum_{k= -\infty}^n x[k] </math> | ||
| − | In analogue electronics a capacitor is represented mathematically by the integral <math> y(t) = 1/C\int_{-\infty}^t x(\tau) d\tau </math> 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. | + | In analogue linear electronics a capacitor is represented mathematically by the integral <math> y(t) = 1/C\int_{-\infty}^t x(\tau) d\tau </math> 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== | ==Causality== | ||
Latest revision as of 18:20, 18 September 2008
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 linear 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.
