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Signals and systemsM. C. Fernando Pea CamposIntroductionSignal: A physical quantity which is function of one or more variables

Signal classificationMulti-dimensional: A signal dependent on two or more variablesB/W imageMulti-channel signal: A signal with two or more sources or sensorsPosition of a object on a 3D spaceMulti-channel multi-dimensionalColor image

Signal classificationContinuous signals: Defined within a continuous interval of the dependent variable.Discrete signals: Defined only on discrete values of the dependent values (with uniform or non-uniform distribution).Continuous valued signals: Can take any value (infinite possibilities) within a interval.Discrete valued signals: Can take values only from a countable set.

Signal classification

Signal classificationSystemsSystem: An entity that transforms a signal or a set of signals. The system can be in continuous time or discrete time depending on the nature of its I/O

Systems classification8Systems classification9SystemsSystemsContinuous time frequencyContinuous time frequencyDiscrete time frequencyExercise: demonstrate this statement14Periodic condition and Max frequencyPeriodic condition and Max frequency

16Periodic condition and Max frequencyUse previous picture to explain17SystemsDSP system

Analog to digital conversion

Sampling

Conversion of a continuous-time signal in to a discrete-time signal by taking its values on discrete instants. The output signal is not defined out of sampling instants.

Sampling

Alias

Quantization

QuantizationTypes of quantizationCeil: Quantized value is the minimum q-level greater or equal to the real value.Floor: Quantized value is the maximum q-level less or equal to the real valueRound: Quantized value is the closest q-level

Quantization error

Quantization errorQuantization errorQuantization errorQuantization error

Quantization errorQuantization error: exampleQuantization error: example