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Signal Basics ELEC 309 Prof. Siripong Potisuk

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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 xs Range of f = set of all ys

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The Usual Notation y = f(x) A single x cannot be mapped or assigned to more than one y Multiple xs can be assigned to a single y Elements of Domain = independent variable(s) Elements of Range = dependent variable

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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

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Mode Classification of Signal Continuous-time Signal defined at every instant of time, i.e., the independent variable is continuous Discrete-time Signal defined at discrete instants of time, i.e., the independent variable is discrete undefined between sampling instances

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Continuous-time Signals Continuous-time, continuous-valued amplitude (Analog signal) mathematically represented by a continuum of points in both the independent and dependent variables a finite number of amplitude discontinuities allowed Continuous-time, discrete-valued amplitude (quantized boxcar signal)

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Discrete-time Signals Discrete-time, continuous-valued amplitude (sampled-data signal) Discrete-time, discrete-valued amplitude (digital signal) In practice, we work with digital signals

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Quantization & Encoding

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Mathematical Representation x(t) represents a CT signal whose amplitude varies continuously with time (analog signal). x[n] represents a DT signal, i.e., a sequence of numbers defined only on integer values of n (undefined for noninteger values of n) Each number x[n] is called a sample x[n] may be a sample from an analog signal x d [n] = x a (nT s ), where T s = sampling period

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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

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Typical Signal Processing Operations Addition/multiplication Amplification/attenuation Integration/differentiation Delay/advance Modulation/demodulation Multiplexing/demultiplexing filtering

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Typical Signal Processing Applications Audio Processing (noise reduction, equalization, special effects) Echo cancellation in telephone networks Speech Processing (recognition, synthesis, compression, enhancement) Image Processing (compression, recognition) Biomedical Signal Processing (tomography) Feedback control Systems (a stabilizer, fuel injection)

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Block Diagram of a Communication System

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