Signals and Systems EE235 Leo Lam Leo Lam © 2010-2011

Today’s menu Lab – detailed arrangements Homework – vacation week From yesterday (Intro: Signals) Intro: Systems More: Describing Common Signals Leo Lam © 2010-2011

Office hours Mine: Monday 10-11am Chris: Wednesday 10-11am Leo Lam © 2010-2011

Taking a signal apart A+a0 a0 A sound signal t (seconds) T Offset (atmospheric pressure) A sound signal Frequency Amplitude A+a0 a0 t (seconds) T Leo Lam © 2010-2011

Frequency = 196 t (seconds) f (Hz) time-domain frequency-domain Leo Lam © 2010-2011

t to f 196 293.66 440 659.26 t (seconds) F (Hz) Leo Lam © 2010-2011

Combining signals Leo Lam © 2010-2011

Summary: Signals Signals carry information Signals represented by functions over time or space Signals can be represented in both time and frequency domains Signals can be summed in both time and frequency domains Leo Lam © 2010-2011

Systems A system describes a relationship between input and output Examples? v(t) g(t) y(t) Leo Lam © 2010-2011

Definition: System A system modifies signals or extracts information. It can be considered a transformation that operates on a signal. Leo Lam © 2010-2011

Motivation: Complex systems Leo Lam © 2010-2011

Filters All kinds, and everywhere Leo Lam © 2010-2011

Surprising high pass Leo Lam © 2010-2011

Summary: System System transforms an input to an output System can extract information System can “shape” signals (filters) Leo Lam © 2010-2011

Signals: Digging in Types of signals Some “standard” signals (alphabets!) Leo Lam © 2010-2011

Signals: A signal is a mathematical function x(t) x is the value (real, complex)  y-axis t is the independent variable (1D, 2D etc.)  x-axis Both can be Continuous or Discrete Examples of x… Leo Lam © 2010-2011

Signal types Continuous time / Discrete time An x-axis relationship Discrete time = “indexed” time Leo Lam © 2010-2011

Signals: Notations A continuous time signal is specified all values of time, when time is a real number. Leo Lam © 2010-2011

Signals: Notations A discrete time signal is specified at only discrete values of time (e.g. only on integers) Leo Lam © 2010-2011

What types are these? 90.3 FM radio transmitted signal Daily count of orcas in Puget Sound Muscle contraction of your heart over time A capacitor’s charge over time A picture taken by a digital camera Local news broadcast to your old TV Video on YouTube Your voice (continuous) (discrete) (c) ((c)) (d) (c) (d) (c) Leo Lam © 2010-2011

Analog / Digital values (y-axis) An analog signal has amplitude that can take any value in a continuous interval (all Real numbers) Where Z is a finite set of values Leo Lam © 2010-2011

Analog / Digital values (y-axis) An digital signal has amplitude that can only take on only a discrete set of values (any arbitrary set). Where Z and G are finite sets of values Leo Lam © 2010-2011

Nature vs. Artificial Natural signals mostly analog Computers/gadgets usually digital (today) Signal can be continuous in time but discrete in value (a continuous time, digital signal) Leo Lam © 2010-2011