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:


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

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
 * adders
 * multipliers

Physically Realizeable Systems
There is a distinction to be made between systems which are possible mathematically, and systems that can be physically implemented in digital hardware. Some systems might look good on paper, but they are difficult, if not impossible, to actually build. One criterion we have already seen is that a physically realizable digital system must not rely on future values, only on past values. We will discuss other criteria in future chapters, as the concepts involved become more familiar.