# Digital Signal Processing/Digital Systems

## Systems Introduction

Digital systems can be conceptually very difficult to understand at first. Let's start out with a block diagram:

We have a digital system, h[n], that is going to alter the input (x[n]) in some way, and produce an output (y[n]). At each integer value for discrete time, n, we will feed 1 value of x[n] into the machine, turn the crank, and create 1 output value for y[n].

## Basic Example

Let's say that h[n] is a multiplier circuit with a value of 5. Every input value is multiplied by 5, and that is the output. In other words, we can show our difference calculus equation as such:

$y\left[n\right]=5x\left[n\right]$

now, for each successive value for n, we can calculate our output value, y[n]. As an example, using the above difference equation, we can feed in an experimental input:

x[n] = [1 0 1 2]


And by multiplying each data item by 5, we get the following result:

y[n] = [5 0 5 10]


## Properties of Digital systems

A loose definition of a causal system is a system in which the output does not change before the input. All real systems are causal, and it is impossible to create a system that is not causal.

## Circuit Symbols

• wires
• pickoff nodes