Overview of Signals and Systems  Overview of Overview Administrative details Administrative details Syllabus, attendance, report, notebookSyllabus, attendance, report, notebook Signals Signals Systems Systems Examples of signals and systems Examples of signals and systems What we do with signals and systems in electrical engineering What we do with signals and systems in electrical engineering

Signals  Information or data that varies with time. Time is the independent variable that we’ll deal with in electrical engineering. Time is the independent variable that we’ll deal with in electrical engineering.  Examples: TV signal, radio signal, mp3 TV signal, radio signal, mp3 Electrical signals (voltages and currents) Electrical signals (voltages and currents) Acoustic signals (both analog and digital) Acoustic signals (both analog and digital) Video signals Video signals Variation in the intensity of a colorVariation in the intensity of a color Biological signals Biological signals DNA sequenceDNA sequence Economic signals – stock prices, DJIA Economic signals – stock prices, DJIA

The Independent Variables  Can be continuous Trajectory of a space shuttle Trajectory of a space shuttle Mass density in a cross-section of a brain Mass density in a cross-section of a brain  Can be discrete DNA base sequence DNA base sequence Digital Image pixels Digital Image pixels  However, we will focus on a single independent variable called time. Continuous (CT) signals: x(t), t Continuous (CT) signals: x(t), t Discrete (DT) signals: x[n], n Discrete (DT) signals: x[n], n

CT signals  Voltage, current, pressure, temperature, velocity… Most of the signals in the physical world. Most of the signals in the physical world.

DT Signals  x[n], n – integer, time varies discretely  Examples of discrete signals in nature: DNA base sequence. DNA base sequence. Population of the n th generation of a certain species Population of the n th generation of a certain species

Human-made DT signals  Why do we like digital signals?

Systems  Process inputs and produce outputs.  For the most part, we will take an input- output perspective.

Examples of Systems  An RLC circuit  An edge detection algorithm for medical images.  A DSP system in a cell phone How many systems are in a cell phone? How many systems are in a cell phone?

System Interconnections  Doing stuff to inputs to produce outputs. Transformations, shifting, scaling, inverting Transformations, shifting, scaling, inverting

What We’ll Be Doing  Math Linear algebra, complex numbers, some differential equations, time shifting, unit step function, linear systems, causal and noncausal systems. Linear algebra, complex numbers, some differential equations, time shifting, unit step function, linear systems, causal and noncausal systems.  Time domain analysis Power, size, singularity functions, convolution, easy continuous functions. Power, size, singularity functions, convolution, easy continuous functions. Discrete versions of the above; difference equations. Discrete versions of the above; difference equations.

What We’ll Be Doing  Laplace Transform for Continuous Systems Bode plots, filters, pole analysis Bode plots, filters, pole analysis  Z Transform for Discrete Systems Only briefly; at the end of the semester Only briefly; at the end of the semester  Fourier Series  Fourier Transform

Why We Are Doing This  Will you ever have to do these by hand at your job? Probably not. Probably not.  You will, however, need to know how to provide a computer proper inputs and be able to interpret the outputs. Garbage in, garbage out. Garbage in, garbage out.  To develop an appreciation and an understanding of how signal analysis works.

Examples of Signals that Need Processing  Motion What’s the domain and range? What’s the domain and range? How do you see motion on a TV? How do you see motion on a TV?  Sound Associates a pressure value to every value of time and 3 space coordinates. A microphone converts sound pressure at just one place to just a function of time, using a voltage signal as an analog of the sound signal. Associates a pressure value to every value of time and 3 space coordinates. A microphone converts sound pressure at just one place to just a function of time, using a voltage signal as an analog of the sound signal.  Pictures Are these analog or digital? Are these analog or digital? What’s the domain and range?What’s the domain and range?