Introduction to signals and systems

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  • A signal is a function of time, e.g.,

    • f is the force on some mass

    • vout is the output voltage of some circuit

    • p is the acoustic pressure at some point

  • notation:

    • f, vout, p or f(.), vout(.), p(.) refer to the whole signal or function

    • f(t), vout(1.2), p(t + 2) refer to the value of the signals at times t, 1.2, and t + 2, respectively

for times we usually use symbols like t, t , t1, . .

  • AM radio signal

  • FM radio signal

  • cable TV signal

  • audio signal

  • NTSC video signal

  • 10BT Ethernet signal

  • telephone signal

  • Signal: something conveys information, represented mathematically as functions of one or more independent variables. Classified as:

  • Continuous-time (analog) signals, discrete-time signals, digital signals

  • Signal-processing systems are classified along the same lines as signals: Continuous-time (analog) systems, discrete-time systems, digital systems

  • In sampling of an analog signal xa(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


  • a system transforms input signals into output signals

  • a system is a function mapping input signals into output signals

  • we concentrate on systems with one input and one output signal, i.e., single-input, single-output (SISO) systems

  • notation:

Block System

  • systems often denoted by block diagram

  • boxes denote systems; arrows show inputs & outputs


  • Modeling the physical world

    • Physical system (e.g., LRC circuit) – using mathematical equation

    • Input/output signal – using mathematical function

Example :LRC

Different systems can be MODELED using the same mathematical function

Human speech production system — anatomy and block diagram

Signals and System Categorizations

  • Continuous time (analog)

Discrete time (digital)

Continuous System Example

  • A digital player/recorder

Analog Input Sampling Signal Reconstructed Digital Output

Digital Signal

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