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SIGNAL AND SYSTEM

SIGNAL AND SYSTEM. Sub-topics: Signal and System Signal Classification The Frequency Concept in Continuous-Time and Discrete-Time Signals Introduction to ADC and DAC. Signals and System.

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SIGNAL AND SYSTEM

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  1. SIGNAL AND SYSTEM Sub-topics: Signal and System Signal Classification The Frequency Concept in Continuous-Time and Discrete-Time Signals Introduction to ADC and DAC

  2. Signals and System • Signal: any physical quantity that varies with time, space, or any other independent variable or variables • e.g. ECG, EEG • System: a physical device that performs an operation on a signal • Signal Processing: the processing of the signal involves filtering the noise and interference from the desired signal

  3. Person is resting Radar Signal

  4. Classification of Signals • Multichannel and Multidimensional Signals • Continuous-Time vs Discrete-Time Signals • Continuous-Valued vs Discrete-Valued Signals • Deterministic vs Random Signals

  5. Multi-channel Signal • Signals are generated by multiple sources or multiple sensors • Multidimensional Signal • Signal is a function of multiple independent variables Earthquake Signals

  6. Continuous-Time Signal or Analog Signal • A signal as a function of a continuous variable (time) • Discrete-Time Signal • A signal as a function of a discrete variable (time)

  7. Continuous-Valued Signal • If a signal takes on all possible values on a finite or an infinite range • Discrete-Valued Signals • If the signal takes on values from a finite set of possible values • Digital Signal • A discrete-time signal having a set of discrete-value

  8. Deterministic Signal • Any signal can be described by an explicit mathematical expression, a table of data, or a well-defined rule • To emphasize the fact that all past, present, and future values of the signal are known precisely • E.g. Sinusoidal signal • Random Signal • Signals that either cannot be described to any reasonable degree of accuracy by explicit mathematical formulas • Signals evolve in time in an unpredictable manner • E.g. seismic signals, speech signals, etc.

  9. The Frequency Concept in Signals • Continuous-Time Sinusoidal Signals • Discrete-Time Sinusoidal Signals • Continuous-Time Exponential Signals • Discrete-Time Exponential Signals

  10. Continuous-Time Sinusoidal Signals • Xa(t)=A cos(Ωt + θ); -∞<t<∞ • A=amplitude • Ω=frequency (rad/s), θ = phasa (rad) • Relationship between F (frequency Hz) and Ω (frequency rad/s) is Ω = 2 πF • The analog sinusoidal signal is characterized by the following properties: • For every fixed value of the frequency F, xa(t) is periodic xa(t + Tp) = xa(t); Tp = 1/F is the fundamental period of the sinusoidal signal • Continuous-time sinusoidal signals which distinct freq. are themselves distinct • Increasing the freq. F results in an increase in the rate of oscillation of the signal, in the sense that more periods are included in a given time interval

  11. Discrete-Time Sinusoidal Signals • x(n)=A cos(n + θ); -∞<n<∞ •  = 2f • n=integer variable • A=amplitude of the sinusoid • =frequency (rad/sample) • θ=phasa (radian) • f=frequency (Cycle/sample or Hz) • x(n)=A cos(2fn + θ); -∞<n<∞ • The properties: • A discrete-time sinusoid is periodic only if its freq. f is a rational number • Discrete-time sinusoids whose freq. are separated by an integer multiple of 2 are identical • The Highest rate of oscillation in a discrete-time sinusoid is attained when  =  (or  = -) or equivalently, f = ½ (or f = -½)

  12. Continuous-Time Exponentials • sk(t) = ejkΩ0t = ej2πkF0t; k = 0, ±1, ±2 • Discrete-Time Exponentials • Sk+N(n) = ej2πn(k+N)/N = ej2πnsk(n) = sk(n)

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