Lecture 1 - Notes

January 5, 2016

ELEC 310

Why DSP?

  • Variety of techniques
  • Software implementations don't require physical modification
  • Analog tuning is not required

Signals

Signals are a description of how one parameter changes with another parameter.

  • Voltage changes over time in an electric circuit
  • Brightness changes with distance in an image

The pattern of the change conveys information. Signals may not convey information directly and may not be free from disturbances, i.e., the signal to noise ratio.

We need to process signals for:

  • Enhancing the signal-to-noise ratio
  • Signal storage and compression
  • Sig transmission and modulation
  • Signal analysis

Independent Variables

To carry information the signal must have some variation. We represent this with functions,

e.g. An image signal ${ R(x,y), G(x,y), B(x,y)}$

We'll be looking at time,

  • Continuous Time Signal: $x(t)$
  • Discreet Time Signal: $x[n]$

Notation

Continuous Discreet
$x_c(t)$ $x_d[n]$

We can write,

were $T$ is the sampling period.

Systems

A system is any process that generates an output an output signal when receiving an input signal.

We'll draw signals with block diagrams and model them using transforms.