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Signals and systems

Signals and systems. EE1205 Introduction to electrical engineering The University of Texas at Arlington Compiled by Md. Raziul Hasan Revised and amended by K. Alavi . What is signal?. Sign -> Signal Traffic signal Flashing indicator light of a car Mobile network signal

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Signals and systems

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  1. Signals and systems EE1205 Introduction to electrical engineering The University of Texas at Arlington Compiled by Md. Raziul Hasan Revised and amended by K. Alavi

  2. What is signal? Sign -> Signal • Traffic signal • Flashing indicator light of a car • Mobile network signal • In the fields of communications, signal processing, and in electrical engineering more generally, a signal is any time-varying or spatial-varying quantity. ref: http://en.wikibooks.org/wiki/Signals_and_Systems/Definition_of_Signals_and_Systems

  3. Signal V(t) t • "A signal is a function of independent variables that carry some information.“ • e.g. A Voltage V(t) or a Current C(t) that depends on time

  4. Complex number representation: • Three ways to represent a complex number • cartesianz=x+iy • polar • Exponential z=r eiφ

  5. Complex representation: • Euler's formula: eiφ = cosφ+i sin φ Then x= cosφ and y= sin φ And x=Re {eiφ } and y= Im {eiφ} Let φ= ωt+ Then x=Re{eiωt+}=cos(ωt+) And y=Im{eiωt+}=sin(ωt+) y= sin(ωt+) = Im{ei(ωt+)}

  6. How is a Signal Represented? • Mathematically, signals are represented as a function of one or more independent variables. • Below signal depends on independent variable t with parameters A, ω and  . • s= A Sin(ωt+)=A Im{ej(ωt+)} A=Amplitude real ω =angular frequency  =phase Sin( ~ )=function ref: http://radarproblems.com/chapters/ch05.dir/ch05pr.dir/c05p1.dir/c05p1.htm

  7. Types of Signal: Analog and digital signals Continuous and Discrete-Time Signals Periodic aperiodic Signal

  8. Types of Signal (contd.) • Unit Step Function u(t) • Ramp function r(t)

  9. System: • A Systemis any physical set of components that takes a signal and transforms it into another signal. • A system can be a simple one that turns a light ON/OFF. Or can be a complex one that does all the computation in a microprocessor. Input signal x(t) Output signal y(t) System ref: http://www.dreamstime.com/royalty-free-stock-image-microchip-circuit-image12540796

  10. Amplifier • An electronic amplifier is a device for increasing the power of a signal. • It does this by taking energy from a power supply and controlling the output to match the input signal shape but with a larger amplitude. • There are various types of amplifier. Amplifier

  11. Time shifter t t • A time shifter system shifts the function f(t) forward or backward by a specific time. • The above system is a forward time shifter. It adds a delay (t0) to the signal. Time shifter f(t) f(t – t0)

  12. Sampler • sampling is the reduction of a continuous-time signal to a discrete-time signal • The sampling frequency must be higher than the frequency of the signal to be sampled. (minimum twice as high) Sampler ref: http://en.wikipedia.org/wiki/Sampling_%28signal_processing%29

  13. Analog to Digital Converter • An analog-to-digital converter(ADC, A/D) is a device that converts a continuous quantity to a discrete time digital representation. • The system that does the opposite is called DAC Analog to Digital DAC ref: http://pictureofgoodelectroniccircuit.blogspot.com/2010/04/phase-and-function-of-analog-signal-or.html

  14. Analog to Digital Conversion • Conversion of Analog to digital is done in two step. • Continuous analog Sampled signal • Sampled signal  Quantized digital signal Sampler A/D ref: http://en.wikipedia.org/wiki/Quantization_%28signal_processing%29

  15. Low Pass filter • A low-pass filter is a filter that passes low-frequency signals but attenuates (reduces the amplitude of) signals with frequencies higher than the cutoff frequency. Low Pass Filter ref: http://en.wikipedia.org/wiki/Low-pass_filter

  16. High Pass filter • A high-pass filter (HPF) is a device that passes high frequencies and attenuates (i.e., reduces the amplitude of) frequencies lower than its cutoff frequency. Low Pass Filter ref: http://en.wikipedia.org/wiki/High-pass_filter

  17. Band Pass filter • A band-pass filter is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range. Band Pass Filter ref: http://en.wikipedia.org/wiki/Band-pass_filter

  18. Band Stop filter • band-stop filter or band-rejection filter is a filter that passes most frequencies unaltered, but attenuates those in a specific range to very low levels Band –stop Filter ref: http://en.wikipedia.org/wiki/Band-stop_filter

  19. Signal Processing: • In signal processing, sampling is the reduction of a continuous signal to a discrete signal. • Sampling frequency defines the sampling ‘RESOLUTION’ ref: http://en.wikipedia.org/wiki/Sampling_%28signal_processing%29, http://fourier.eng.hmc.edu/e101/lectures/Sampling_theorem/node1.html

  20. Signal processing: • Fourier Series expansion: The first four Fourier series approximations for a square wave. ref: http://mathworld.wolfram.com/FourierSeries.html

  21. The Fourier Series expansion: • A periodic square wave function ƒ(x) can be expressed with infinite Fourier series expansion. f(x)=sin(x)+ sin(3x)+ sin(5x)+sin(7x)+….. Figure: Construction of a square wave from sinusoids of different frequencies ref: http://www.intmath.com/fourier-series/2-full-range-fourier-series.php

  22. Application: • Communication Applications: Transmission of information (signal) over a channel “Modulation” • Control Applications: Control the speed of fan • Signal Processing Applications: • Speech and audio processing • Multimedia processing • Biological Signal Analysis: • Brain signals (EEG) • Cardiac signals (ECG) • Medical images (x-ray, PET, MRI) ref: http://images.yourdictionary.com/amplitude-modulation, http://en.wikipedia.org/wiki/Amplitude_modulation

  23. Amplitude Modulator • An Amplitude modulator takes a low frequency message signal and a high frequency carrier signal and combines it into a modulated signal of varying amplitude. Amplitude Modulator ref: http://encyclopedia2.thefreedictionary.com/Amplitude+Modulation

  24. Amplitude Demodulator • An Amplitude demodulator takes a modulated signal as input and gives output the original message signal. • The above system is an amplitude demodulator. Its also called ‘envelope detector’. It takes the envelope of the modulated signal to get the information signal. Amplitude Demodulator ref: http://encyclopedia2.thefreedictionary.com/Amplitude+Modulation

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