lecture1-f08

lecture1-f08 - EE264 Digital Signal Processing Lecture 1...

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EE264 Digital Signal Processing Lecture 1 Introduction & Overview September 22, 2008 Ronald W. Schafer Department of Electrical Engingeering Stanford University Stanford University, EE 264, Fall 2008 Course Overview • Instructor: Ronald W. Schafer, HP Fellow and Professor Emeritus, Georgia Tech • TAs: Raunaq Shah and ?? • Course content: theory, implementation and application of digital signal processing. • Grading: – Homework: 30% – Mid-term exam: 30% (10-29-2008) – Final exam: 40% • Today’s class: review of DSP fundamentals Stanford University, EE 264, Fall 2008 DSP in 1967 The TX-2 Computer, Circa 1967 Stanford University, EE 264, Fall 2008 What is DSP?? “That discipline which has allowed us to replace a circuit previously composed of a capacitor and a resistor with two anti-aliasing filters, an A-to-D and a D-to-A converter, and a general purpose computer (or array processor) so long as the signal we are interested in does not vary too quickly.” Thomas P. Barnwell, III Circa 1976 Digital Computer D-to-A A-to-D Input Output
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Stanford University, EE 264, Fall 2008 Digital Processing of Analog Signals A-to-D conversion: sampling and quantization Numerical algorithm: convolution, difference equations, DFT, LPC – Implemented on PCs with 64-bit floating-point or special instructions – Implemented on DSP chips or ASICs with finite- precision arithmetic D-to-A conversion: quantization and filtering Digital Computer D-to-A A-to-D x c ( t ) x [ n ] y [ n ] y c ( t ) Stanford University, EE 264, Fall 2008 hearing aids disk drives Today, DSP Applications are Everywhere Internet audio cell phones digital cameras media players Stanford University, EE 264, Fall 2008 Advantages of Digital Representations • Permanence and robustness of signal representations • Advanced IC technology works well for digital systems • Virtually infinite flexibility with digital systems * Multi-functionality * Multi-input/multi-output A-to-D Converter D-to-A Converter DSP Chip Input Output Stanford University, EE 264, Fall 2008 Basic Concepts and Issues in DSP Digital Filters: Filter design, noise analysis, structures Fourier Analysis : Spectrum estimation, FFT, cosine transform, cepstrum, short-time FT Signal Modeling and Analysis : Linear prediction, wavelets, chaos, fractals, compressed sensing Hardware and Software : Minicomputers, DSP chips, workstations, PCs, MATLAB, real-time operating systems Applications: Speech, radar, image, video, data, ...
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Stanford University, EE 264, Fall 2008 The Sampling Theorem T rate sampling / 1 T f s = ) ( ] [ nT x n x c = Which signal can we reconstruct knowing only T ? Stanford University, EE 264, Fall 2008 Discrete-Time Systems • A system transforms an input into an output. – Delay: – Modulator: – Squarer: – Compressor: (aka downsampler ) – Expander: (aka upsampler ) D-T System x [ n ] y [ n ] = T x [ n ] {} x [ n ] 6 y [ n ] = x [ n n d ] x [ n ] 6 y [ n ] = x [ n ]cos( ω 0 n ) x [ n ] 6 y [ n ] = ( x [ n ]) 2 y [ n ] = x [ Mn ] x [ n ] 6 y [ n ] = x [ n / L ], n = 0, ± L , 0, otherwise Stanford University, EE 264, Fall 2008 Discrete-Time Systems • Linearity (superposition): • Time-Invariance (shift-invariance): Τ ax 1 [ n ] + bx 2 [ n ] = a Τ x 1 [ n ] + b Τ x 2 [ n ] x 1
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lecture1-f08 - EE264 Digital Signal Processing Lecture 1...

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