PSD, Signal and System 1/15 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

PSD, Signal and System 2/15 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

PSD, Signal and System 3/15

PSD, Signal and System 4/15 Person is resting Radar Signal

PSD, Signal and System 5/15

PSD, Signal and System 6/15

PSD, Signal and System 7/15 Classification of Signals  Multichannel and Multidimensional Signals  Continuous-Time vs Discrete-Time Signals  Continuous-Valued vs Discrete-Valued Signals  Deterministic vs Random Signals

PSD, Signal and System 8/15 Multi-channel Signal Signals are generated by multiple sources or multiple sensors Multidimensional Signal Signal is a function of multiple independent variables Earthquake Signals

PSD, Signal and System 9/15 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)

PSD, Signal and System 10/15 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

PSD, Signal and System 11/15 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.

PSD, Signal and System 12/15 The Frequency Concept in Signals Continuous-Time Sinusoidal Signals Discrete-Time Sinusoidal Signals Continuous-Time Exponential Signals Discrete-Time Exponential Signals

PSD, Signal and System 13/15 Continuous-Time Sinusoidal Signals X a (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, x a (t) is periodic x a (t + T p ) = xa(t); T p = 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

PSD, Signal and System 14/15 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)

PSD, Signal and System 15/15 Continuous-Time Exponentials s k (t) = e jkΩ 0 t = e j2πkF 0 t ; k = 0, ±1, ±2 Discrete-Time Exponentials S k+N (n) = e j2πn(k+N)/N = e j2πn s k (n) = s k (n)