Introduction to signals and systems

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  A signal is a function of time, e.g.,
  
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    f is the force on some mass
    
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    vout is the output voltage of some circuit
    
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    p is the acoustic pressure at some point
    
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  notation:
  
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    f, vout, p or f(.), vout(.), p(.) refer to the whole signal or function
    
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    f(t), vout(1.2), p(t + 2) refer to the value of the signals at times t, 1.2, and t + 2, respectively
    

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  AM radio signal
  
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  FM radio signal
  
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  cable TV signal
  
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  audio signal
  
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  NTSC video signal
  
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  10BT Ethernet signal
  
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  telephone signal
  

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  Signal: something conveys information, represented mathematically as functions of one or more independent variables. Classified as:
  
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  Continuous-time (analog) signals, discrete-time signals, digital signals
  
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  Signal-processing systems are classified along the same lines as signals: Continuous-time (analog) systems, discrete-time systems, digital systems
  

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  Discrete-Time signals are represented as
  

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  In sampling of an analog signal x_a(t):
  

1/T (reciprocal of T) : sampling frequency

Fig:1 Graphical representation of a discrete time signal; the abscissa is continuous while the x[n] is defined only at discrete instances

System

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  a system transforms input signals into output signals
  
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  a system is a function mapping input signals into output signals
  
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  we concentrate on systems with one input and one output signal, i.e., single-input, single-output (SISO) systems
  
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  notation:
  
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    y = S(u) means the system S acts on input signal u to produce output signal y
    

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  systems often denoted by block diagram
  
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  boxes denote systems; arrows show inputs & outputs
  
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    lines with arrows denote signals (not wires)
    
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    special symbols for some systems
    

SIGNALS AND SYSTEMS

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  Modeling the physical world
  
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    Physical system (e.g., LRC circuit) – using mathematical equation
    
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    Input/output signal – using mathematical function
    

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  LRC represented by a mathematical Equation
  
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    ordinary diff. eqn.
    
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    No sampling (continuous time system)
    
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  V(i) is a mathematical function
  

Human speech production system — anatomy and block diagram

Signals and System Categorizations

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  Continuous time (analog)
  

Continuous System Example

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  A digital player/recorder
  

Analog Input Sampling Signal Reconstructed Digital Output