KEET3114

KEET3114Instructor: Noraisyah Mohamed Shahnoraisyah@um.edu.myMain referencesTextbookAlan V. Oppenheim & Ronald W. Schafer, Discrete Time Signal & Systems Prentice Hall, 1995.Sanjit K. Mitra, Digital Signal Processing: A Computer based approach, McGraw-Hill, 2006, International Edition.Richard Lyons, Understanding Digital Signal Processing, Prentice Hall 2004Boaz Porat, A course in digital signal processingReferencesWebsite:MIT OpenCourseWaresignal.ece.utexas.edu/~arslan/courses/dsp/Course outcomes:1. Define the fundamental concepts such as 'linearity', 'time-invariance', 'impulse response', 'convolution', 'frequency response', z-transforms and the 'discrete time Fourier transform'.

2. Analyze the LTI systems using difference equations, DTFT and Z-transforms.

3. Design FIR type digital filters.

4. Design techniques for IIR type digital filters.Assessment weightage:Continuous assessment: 40%Test 1: 15%Test 2: 15%Tutorial: 10% (due at the beginning of Fridays class)

Final exams: 60%What is DSPWhat is [a] DSP?In brief, DSPs are processors or microcomputers whose hardware, software, and instruction sets are optimized for high-speed numeric processing applications an essential for processing digital data representing analog signals in real time. When acting as a digital filter, for example, the DSP receives digital values based on samples of a signal, calculates the results of a filter function operating on these values, and provides digital values that represent the filter output; it can also provide system control signals based on properties of these values. The DSPs high-speed arithmetic and logical hardware is programmed to rapidly execute algorithms modelling the filter transformation.DSP is everywhereSound applicationsCompression, enhancement, special effects, synthesis, recognition, echo cancellation,Cell Phones, MP3 Players, Movies, Dictation, Text-to-speech,CommunicationModulation, coding, detection, equalization, echo cancellation,Cell Phones, dial-up modem, DSL modem, Satellite Receiver,AutomotiveABS, GPS, Active Noise Cancellation, Cruise Control, Parking,MedicalMagnetic Resonance, Tomography, Electrocardiogram,MilitaryRadar, Sonar, Space photographs, remote sensing,Image and Video ApplicationsDVD, JPEG, Movie special effects, video conferencing,MechanicalMotor control, process control, oil and mineral prospecting,Source: signal.ece.utexas.edu/~arslan/courses/dsp/Signal processingHumans are the most advanced signal processorsspeech and pattern recognition, speech synthesis,We encounter many types of signals in various applicationsElectrical signals: voltage, current, magnetic and electric fields,Mechanical signals: velocity, force, displacement,Acoustic signals: sound, vibration,Other signals: pressure, temperature,Most real-world signals are analogThey are continuous in time and amplitudeConvert to voltage or currents using sensors and transducers Source: signal.ece.utexas.edu/~arslan/courses/dsp/Analog signal processingAnalog circuits process these signals usingResistors, Capacitors, Inductors, Amplifiers,Analog signal processing examplesAudio processing in FM radiosVideo processing in traditional TV setsLimitation to analog signal processingAccuracy limitations due to Component tolerancesUndesired nonlinearitiesLimited repeatability due toTolerancesChanges in environmental conditionsTemperatureVibrationSensitivity to electrical noiseLimited dynamic range for voltage and currentsInflexibility to changes Difficulty of implementing certain operationsNonlinear operationsTime-varying operationsDifficulty of storing information

Digital signal processingRepresent signals by a sequence of numbersSampling or analog-to-digital conversionsPerform processing on these numbers with a digital processorDigital signal processingReconstruct analog signal from processed numbersReconstruction or digital-to-analog conversionA/DDSPD/Aanalogsignalanalogsignaldigital signaldigital signalAnalog input analog output Digital recording of musicAnalog input digital outputTouch tone phone dialingDigital input analog outputText to speechDigital input digital outputCompression of a file on computerPros and Cons of digital signal processingProsAccuracy can be controlled by choosing word lengthRepeatableSensitivity to electrical noise is minimalDynamic range can be controlled using floating point numbersFlexibility can be achieved with software implementationsNon-linear and time-varying operations are easier to implement Digital storage is cheapDigital information can be encrypted for securityPrice/performance and reduced time-to-marketConsSampling causes loss of informationA/D and D/A requires mixed-signal hardwareLimited speed of processorsQuantization and round-off errors

Continuous and discrete signal and systemsContinuous and discrete signal and systems.. (cont.)Signal TypesAnalog signals: continuous in time and amplitudeExample: voltage, current, temperature,Digital signals: discrete both in time and amplitudeExample: attendance of this class, digitizes analog signals,Discrete-time signal: discrete in time, continuous in amplitudeExamples: hourly change of temperatureTheory is based on discrete-time continuous-amplitude signalsMost convenient to develop theoryGood enough approximation to practice with some care

Discrete sequences and their notationDiscrete-time signal: a signal whose independent time variable is quantized so that we know only the value of the signal at discrete instants in time.Discrete-time signal also quantizes the signal amplitudeRepresented as sequence of values not by a continuous waveform.

Sinewave as a sequence of discrete valuesThere is nothing between the dots of x[n]!Discrete sequences and their notationAnother example of discrete time system

Discrete-time signals are represented mathematically as sequences of numbers, where n is an integerT is the sampling period in secondfs = 1/T is the sampling frequency in HzSampling frequency in radian-per-second s=2fs rad/secUse [.] for discrete-time and (.) for continuous time signals

Sequence operatorsBasic sequences & Sequence Operators

Or

An arbitrary sequence can be represented as a sum of scaled, delayed impulsesDiscrete-Time SystemsDiscrete-Time Sequence is a mathematical operation that maps a given input sequence x[n] into an output sequence y[n]

Example Discrete-Time SystemsMoving (Running) Average

Maximum

Ideal Delay System

T{.}x[n]y[n]

MemorylessMemoryless SystemA system is memoryless if the output y[n] at every value of n depends only on the input x[n] at the same value of n

Example Memoryless SystemsSquare

Sign

Counter ExampleIdeal Delay System

Linear SystemsLinear System: A system is linear if and only if

ExamplesIdeal Delay System

Time-invariant systemsTime-Invariant (shift-invariant) SystemsA time shift at the input causes corresponding time-shift at output

ExampleSquare

Counter ExampleCompressor System

Causal systemCausalityA system is causal its output is a function of only the current and previous samples

ExamplesBackward Difference

Counter ExampleForward Difference

Stable systemStability (in the sense of bounded-input bounded-output BIBO)A system is stable if and only if every bounded input produces a bounded output

ExampleSquare

Counter ExampleLog