Continuous Time Signal Analysis - A first course in Signal Processing, Communications, and Controls.

• A signal is a set of information or data that can be modeled as a function of one or more independent variables (e.g. t ∈ R). Examples - Speech, image, weather information, sales information, voltage in a circuit, car locations on the freeway, video, music, etc.

• A system modifies signals or extracts information. It can be considered a transformation that operates on a signal. Examples: electronics, radio or TV, MR system, guidance system, communication system, filter, equalizer, synthesizer, etc.

A signal can be an input, an output or an internal function that is processed or produced by a system.

Examples of Signals and Systems

1. Human vocal tract (system) has air as an input signal and produces speech as an output signal

2. Voltage (signal) in an RLC circuit (system)

3. Music (signal) produced by a musical instrument (system)

4. Radio (system) has radio frequency as input and the output is the sound you listen to

Continuous Time - data are available or measured every time (or space) instant - the data are defined over a continuous input.

Discrete Time - defined only for discrete points in time such as every minute, hour, 3 months, year, etc. You sample or collect data at these times only.

This course covers continuous-time signals and rules of operations.

Examples of Signal Processing

1. Spectrum Analysis - Determine cyclic patterns or other information in a signal and display it - spectrogram

2. Filter - change signal in some way - smooth, reduce noise, remove the signal in a certain frequency band such as a low pass filter

3. Prediction - predict the future based on past trends - sales, stock market, inventory

4. Synthesizer - generate output signal - speech, music, signal generator.

5. Communication channel- convey a signal from one location to another.

Speech coding (an example of a communications or signal processing application) - process speech and transmit a likeness to the original speech signal. The steps are:

1. Determine filter parameters

2. Determine pitch and energy

3. Quantize and send

4. Synthesizer generates speech at receiver.

Common consumer products that use signal processing: CD players, DVD players, audio and video codecs used by the web, magnetic resonance imaging systems, modems, MP3 players, wireless PDAs, etc.