Applications of Signals and Systems

Application Areas

• Control

• Communications

• Signal Processing (our concern)

Control Applications

• Industrial control and automation (Control the velocity or position of an object)

• Examples: Controlling the position of a valve or shaft of a motor

• Important Tools: – Time-domain solution of differential equations– Transfer function (Laplace Transform)– Stability

Communication Applications

• Transmission of information (signal) over a channel

• The channel may be free space, coaxial cable, fiber optic cable

• A key component of transmission: Modulation (Analog and Digital Communication)

Modulation

• Analog Modulation: Transmitting audio signals.

• Advantage: Higher frequency range good propagation

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Lo c a l O sc illa to r

Ax(t)c o s(wt)

Modulation

• Frequency Modulation (FM), modulate the angle of the carrier.

• Advantage: More robust to interference

Digital Modulation

• Used in CDs, digital cellular service, digital phone lines and computer modems.

• Advantages: – Can be encrypted– Electronic routing of data is easier– Digital storage faster– Multimedia capability

Signal Processing Applications

• Signal processing=Application of algorithms to modify signals in a way to make them more useful.

• Goals:– Efficient and reliable transmission, storage and display of

information– Information extraction and enhancement

• Examples: – Speech and audio processing– Multimedia processing (image and video)– Underwater acoustic– Biological signal analysis

Multimedia Applications

• Compression: Fast, efficient, reliable transmission and storage of data

• Applied on audio, image and video data for transmission over the Internet, storage

• Examples: CDs, DVDs, MP3, MPEG4, JPEG

• Mathematical Tools: Fourier Transform, Quantization, Modulation

JPEG Example

43K 13K 3.5K

• JPEG uses Discrete-Cosine Transform (similar to Fourier Transform)

Biological Signal Analysis

• Examples:– Brain signals (EEG)– Cardiac signals (ECG)– Medical images (x-ray, PET, MRI)

• Goals: – Detect abnormal activity (heart attack, seizure)– Help physicians with diagnosis

• Tools: Filtering, Fourier Transform

Example

• Brain waves are usually contaminated by noise and hard to interpret

Biometrics

• Identifying a person using physiological characteristics

• Examples:– Fingerprint Identification– Face Recognition– Voice Recognition

Audio Signal Processing

• Active noise cancellation:Adaptive filtering– Headphones used in cockpits

• Digital Audio Effects– Add special music effects such as delay, echo,

reverb

• Audio signal separation– Separate speech from interference– Wind sound from music in cars

Filtering Example

Course Requirements

1. Calculus

2. Calculus

3. Calculus

4. Calculus (functions, Differentiation, integration, power series, sequences, Taylor expansions, complex analysis, vectors, and trigonometry )

Is the course complicated?

• Yes if no Calculus

• Very simple if calculus ok.

Text book

• Signals and systems demystified, 2007

• SCHAUM'S OUTLINES OF Theory and Problems of Signals and Systems, 1995

Assessment

• Mid term 15

• Final exam 60

• Project 10

• Participation 5

• Section and assignments 10