![Discrete-Time Signals : Sequences Continuous-time signal will be sampled into set of its values at definite time. If duration of each sampling time is fixed in equal period called sampling period, T. Thus n th value of sampled signal is equal to the value of the continuous-time signal x c (t) at time nT. Representation of sampled values will be shown in a sequence of numbers x = {x[n]}. 1/T is called the sampling frequency.](https://image.slidesharecdn.com/discretetime-signal-processing-4568/85/Discrete-Time-Signal-Processing-12-320.jpg)
Discrete-Time Signal Processing
- 1. 2102576 Digital Signal Processing Dr.Somchai Jitapunkul Digital Signal Processing Research Laboratory Department of Electrical Engineering Chulalongkorn University
- 2. Course Outlines Introduction Discrete-Time Signals and Systems Sampling of Continuous-Time Signals The z-Transform Transform Analysis of Linear Time-Invariant Systems Structures for Discrete-Time Systems Filter Design Techniques The Discrete Fourier Transform Computation of the Discrete Fourier Transform Discrete Hilbert Transform Fourier Analysis of Signals Using the Discrete Fourier Transform Introduction to Cepstrum Analysis and Homomorphic Deconvolution
- 3. Bibliography Text: A.V. Oppenheim, and R.W. Schafer, Discrete-Time Signal Processing , Prentice Hall, 1989. References: J.G. Proakis, and D.G. Manolakis, Digital Signal Processing , 3 rd ed., Prentice Hall, 1996. E.C. Ifeachor, and B.W. Jervis, Digital Signal Processing , Addison Wesley, 1993. S.K. Mitra, Digital Signal Processing , 2 nd ed., McGraw-HILL, 2001. Etc.
- 4. Examination and Grading Final Examination: Date: Monday 25 February 2001 Time: 08:00 am ~ 12:00 am Paper Examination Time: 12:00 am ~ 17:00 pm (tentatively) Design Project Room: DSP Laboratory and neighbor room Building: Engineering 4 (Charoen Vissawakam) Grading: Depend mainly on each individual achievement
- 5. 10 Outstanding Achievements Between 1964 and 1989 Selected by National Academy of Engineering, Washington D.C. Moon Landing Application Satellites Microprocessors Computer-Aided Design and Manufacturing Computerized Axial Tomography Scanner Advanced Composite Materials Jumbo Jets Lasers Fiber-Optics Communications Genetically Engineered Products
- 6. Grand Challenges in Science and Engineering need high-performance computing Office of Science and Technology Policy, Washington D.C. Prediction of Weather, Climate, and Global Change Speech Recognition and Understanding Machine Vision Vehicle Performance Superconductivity Enhanced Oil and Gas Recovery Nuclear Fusion
- 7. DSP Applications Image Processing Pattern recognition Robotic vision Image enhancement Facsimile Satellite weather map Animation Instrumentation/Control Spectrum analysis Position and rate control Noise reduction Data compression Speech/audio Speech recognition/synthesis Text to speech Digital audio equalization Military Secure communication Radar processing Sonar processing Missile guidance Telecommunications Echo cancellation Adaptive equalization ADPCM transcoders Spread spectrum Video conferencing Data communication Biomedical Patient monitoring Scanners EEG brain mappers ECG analysis X-ray storage/enhancement
- 8. Reasons of Using DSP Signals and data of many types are increasingly stored in digital computers, and transmitted in digital form from place to place. In many cases it makes sense to process them digitally as well. Digital processing is inherently stable and reliable. It also offers certain technical possibilities not available with analog methods. Rapid advances in IC design and manufacture are producing ever more powerful DSP devices at decreasing cost. Flexibility in reconfiguring Better control of accuracy requirement Easily transportable and possible offline processing Cheaper hardware in some case In many case DSP is used to process a number of signals simultaneously. This may be done by interlacing samples (technique known as TDM) obtained from the various signal channels. Limitation in speed & Requirement in larger bandwidth
- 9. DSP in ASIC (Application Specific Integrated Circuit) Advantages High throughput Lower silicon area Lower power consumption Improved reliability Reduction in system noise Low overall system cost Disadvantages High investment cost Less flexibility Long time from design to market
- 10. Discrete-Time Signals and Systems One-dimensional signal (time) Multidimensional signal (spatial coordinate) Real-valued function Complex-valued function Dependent variable Independent variable Analog signal/system Continuous-time signal/system Continuous-amplitude signal/system Discrete-amplitude signal/system Quantized boxcar signal/system Discrete-time signal/system Sampled-data signal/system Digital signal/system Stationary signal Cyclostationary Non-stationary signal Time-invariant system Time-varying system Causal Non-causal Deterministic signal Periodic Non-periodic Random signal Stochastic signal Noise or interference Analytical signal Distribution
- 11. Discrete-time Signals and Systems Continuous-time signals are defined along a continuum of times and thus are represented by a continuous independent variable. Discrete-time signals are defined at discrete times and thus the independent variable has discrete values. Analog signals are those for which both time and amplitude are continuous. Digital signals are those for which both time and amplitude are discrete.
- 12. Discrete-Time Signals : Sequences Continuous-time signal will be sampled into set of its values at definite time. If duration of each sampling time is fixed in equal period called sampling period, T. Thus n th value of sampled signal is equal to the value of the continuous-time signal x c (t) at time nT. Representation of sampled values will be shown in a sequence of numbers x = {x[n]}. 1/T is called the sampling frequency.
- 13. Signal Processing Operation Time-domain/spatial-domain operation Frequency-domain operation Real-time operation Off-line operation
- 14. Time-Domain Signal Operation Basic operations Scaling : gain Amplification Attenuation Delay / Advance Addition Elementary operations Integration / Summation Differentiation / Difference Production Convolution
- 15. Filtering Filter Parameters Passband Stopband Transition band Cutoff frequency Band Edge Frequency Filter Types Basic Types Lowpass Highpass Bandpass Bandstop/band eject Other Types Notch filter Comb filter Single band Multiband
- 16. Mathematical Tools Differential Equation Difference Equation Laplace Transform z-Transform Fourier Transform Hilbert Transform Discrete-Time Fourier Transform Discrete Fourier Transform
- 17. Definitions Modulation Coding Multiplexing Modulated signal Carrier signal Single Sideband (SSB) Double Sideband (DSB) Coding Source Coding Channel Coding Fading Rayleigh Fading Ricean Fading Nakagami Fading Interference Noise White Noise Gaussian Noise White Gaussian Noise (WGN) Equalization Quantization Scalar Quantization Vector Quantization Spread Spectrum Direct Sequence or Pseudo-noise Frequency Hopping Time Hopping Combination Hidden Markov Model Kalman (Recursive Least Square) Algorithm Pseudo-noise (PN) Sequence M sequences Gold Sequences Kasami Sequences
- 18. Modulation/Coding Methods Pulse Amplitude Modulation (PAM) Digital PAM or Amplitude-Shift Keying (ASK) Phase Modulation Digital Phase Modulation or Phase-Shift Keying (PSK) Binary PSK (BPSK) Quadrature PSK (QPSK) Differential PSK (DPSK) Staggered Quadrature PSK (SQPSK) Quadrature Amplitude Modulation (QAM) Frequency-Shift Keying (FSK) Continuous-Phase FSK (CPFSK) Amplitude Modulation (AM) Frequency Modulation (FM) Pulse Width Modulation (PWM) Pulse Position Modulation (PPM) Continuous-Phase Modulation (CPM) Minimum-Shift Keying (MSK) Fixed-Length Code Word Variable-Length Code Word Entropy Coding Huffman Coding Variable-to-Fixed Length Code Word Lempel-Ziv Algorithm Temporal Waveform Coding Pulse coded modulation (PCM) Adaptive PCM (APCM) Differential PCM (DPCM) Adaptive DPCM (ADPCM) Open-loop DPCM (D*PCM) Delta modulation (DM) or 1-bit or 2-level DPCM Linear DM (LDM) Adaptive DM (ADM) Continuously Variable Slope DM (CVSD) Model-Based Source Coding Linear Predictive Coding (LPC) Spectral Waveform Coding Subband Coding (SBC) Transform Coding (TC)
- 19. Multiplexing Time Division Multiplexing (TDM) Frequency Division Multiplexing (FDM) Code Division Multiplexing (CDM) Code Division Multiple Access (CDMA) or Spread Spectrum Multiple Access (SSMA) Orthogonal Frequency Division Multiplexing (OFDM)
- 20. Examples of Signals Electrocardiography (ECG) Signal Electroencephalogram (EEG) Signal Seismic Signals Engine Signal Speech, Musical Sound, and Audio Signals Vibration Signal Time Series Signal (daily stock prices, etc.) Images and Video Signals
- 21. Typical Sampling Rates and System Latencies for Selected Applications < 50 ms* 1~14 MHz Video < 50 ms* 44.1 kHz Audio < 50 ms 8 kHz Voice System dependent* > 0.1 kHz Control System dependent* 1 Hz Instrumentation Latency (Delay) I/O Sampling Rate Application * Many times, a signal may not need to be concerned with latency: for example, a TV signal is more dependent on synchronization with audio than the latency. In each of these cases, the latency is dependent on the application. Nasser Kehtarnavaz, and Mansour Keramat, DSP System Design: Using the TMS320C6000 , Prentice Hall, 2001.
- 22. Examples of Applications Sound Recording Applications Compressors and Limiters Expanders and Noise Gates Equalizers and Filters Noise Reduction Systems Delay and Reverberation Systems Special Effect Circuits Speech Processing Speech Recognition Speech Communication Telephone Dialing Applications FM Stereo Applications Electronic Music Synthesis Subtractive Synthesis Additive Synthesis Echo Cancellation in Telephone Networks Interference Cancellation in Wireless Telecommunication
- 23. Cellular Phone Wireless Communication DSP System Nasser Kehtarnavaz, and Mansour Keramat, DSP System Design: Using the TMS320C6000 , Prentice Hall, 2001.
- 24. ADSL Wired Communication DSP System Nasser Kehtarnavaz, and Mansour Keramat, DSP System Design: Using the TMS320C6000 , Prentice Hall, 2001.
- 25. PCM Voiceband DSP System Nasser Kehtarnavaz, and Mansour Keramat, DSP System Design: Using the TMS320C6000 , Prentice Hall, 2001.
- 26. Gigabit Ethernet DSP System Nasser Kehtarnavaz, and Mansour Keramat, DSP System Design: Using the TMS320C6000 , Prentice Hall, 2001.
- 27. Hard Disk Drive DSP System Nasser Kehtarnavaz, and Mansour Keramat, DSP System Design: Using the TMS320C6000 , Prentice Hall, 2001.
- 28. Motor Control DSP System Nasser Kehtarnavaz, and Mansour Keramat, DSP System Design: Using the TMS320C6000 , Prentice Hall, 2001.