ELEC 423Digital Signal Processing

Prof. Siripong Potisuk

What is a function?

A rule of correspondence that maps or assigns to each element (x) of a given set A a uniquely determined element (y) of another set B

f: A B (f maps A into B) Domain of f = set of all x Range of f = set of all y

The Usual Notation y = f(x)

A single x cannot be mapped or assigned to more than one y

Multiple x’s can be assigned to a single y Element of Domain = independent variable(s) Element of Range = dependent variable

Signal

A function of independent variables such as time, distance, position, etc.

One-dimensional signal : speech, audio, music, ECG, seismic, time series

Two-dimensional signal : image Three-dimensional signal : video

Signal Processing

Extract useful information carried by the signal

Concerned with the mathematical representation of the signal and the algorithmic operation carried out on it to extract the information present

Typical Signal Processing Operations

Addition/multiplication Amplification/attenuation Integration/differentiation Delay/advance Modulation/demodulation Multiplexing/demultiplexing filtering

Typical Signal Processing Applications

Audio Processing (noise reduction, equalization, special effects)

Communications system Echo cancellation in telephone networks Speech Processing (recognition, synthesis,

compression, enhancement) Image Processing ( compression, recognition) Biomedical signal processing

Why Digital Signal Processing?

Operation of digital circuits not dependent on precise values of the digital signals

Require only bistable circuits and storage medium to process, store, and transmit signals

Possibility of perfect signal regeneration Low cost of digital processor hardware

Benefits (continued)

Any desirable accuracy achievable by increasing the binary wordlength subject to cost limitation

The same digital computer technology used for general information processing can be used for DSP

Applicability to very low frequency signals (seismic applications)

Disadvantages

Increased system complexity (A/D and D/A) Limited range of frequencies available for

processing because of the sampling requirement

Digital systems mostly constructed using active devices that consume electrical power

Advantages far outweigh disadvantages

Block Diagram of a Communication System