SYLLABUS of the course BASIC ELECTRONICS AND DIGITAL SIGNAL PROCESSING Master in Computer Science, University of Bolzano-Bozen, a.y. 2017-2018 Lecturer: LEONARDO RICCI (last updated on November 27, 2017) 1
(23/10/2017) 1. Introduction. Linear circuits. Basics: Statics: current and voltage; resistance and Ohm s law; series and parallel resistances; power supplies (power line, batteries); power and Joule s law; ground and load. direct current (DC; from batteries and power supplies); voltage divider, the issue of transforming voltages, transformers (that require AC...). Dynamics: alternating current (AC; from generators); capacitance as a reaction to voltage variations and the RC circuit; inductance as a reaction to current variations; transmission lines and the speed of light. the speed of light accounting for a signal propagation delay observed by means of a 10 m long coaxial cable. (24/10/2017) 2. Analog electronics. Non linear circuital devices: diodes, use as rectifiers, LEDs; transistors, use as switches, use as amplifiers. Operational amplifiers (op-amp): basic features; basic, negative-feedback, linear configuration; 2
negative-feedback application examples, inverting amplifier, non-inverting amplifier, follower, inverting adder, differential amplifier, differentiator, integrator; - (for the last four circuits, the theoretical proof of function is left as homework); positive-feedback application examples, oscillator. oscillator relying on two op-amps. (06/11/2017) 3. Introduction to digital electronics: logic ports and combinatorial circuits. Basic logic ports: NOT, AND, OR, NOR, NAND, XOR; De Morgan s theorem; transistor-transistor logic (TTL); mention of transistor implementation, switch time, fan-out, low-voltage TTL (LVTTL). Basic combinatorial circuits: combinatorial circuits are based on states; single-bit adders and multipliers; binary arithmetic operations; use of AND and OR ports as digital switches and digital mixers, respectively; multiplexers and demultiplexers; the issue of a memory unit; RS flip flops. 3
(07/11/2017) 4. Introduction to digital electronics: sequential circuits. NOR port by using two 2N2222 transitors and a LED-array display. Basic sequential circuits: sequential circuits are based on change of states; D-type flip flops, master-slave configuration (negative-edge-triggered), positive-edge-triggered; clock; Asynchronous and synchronous circuits: dividers by 2 and 2 n ; asynchronous counters; state diagrams; dividers by 3; synchronous counters. (13/11/2017) 5. Analog meets digital (part 1 of 2). A topic of analog electronics: Thevenin s theorem: statement; application to the voltage divider. A topic of analog electronics: Comparators: simple comparators; a mention of Schmitt triggers. A topic of digital electronics: Shift registers: from serial input to parallel output and viceversa; closed-loop shift-register; basic tool to implement state diagrams; a mention of pseudorandom generators. Digital-to-Analog Converters (DACs): a simple DAC by summing scaled currents (scheme and drawbacks); R 2R (ladder) voltage output DAC. 4
Programmable logic devices (PLDs) and hardware description languages (HDLs): introduction to FPGAs; introduction to Verilog; (prototypical example:) a simple counter in Verilog, structure of the code. (14/11/2017) 6. Analog meets digital (part 2 of 2). Analog-to-Digital Converters (ADCs): an ADC based on a comparator, a DAC, and a counter; succesive-approximation-register (SAR) ADCs; mention of other kinds of ADCs (flash, integration, tracking). Main features of AD-DA conversion: linearity; monotonicity; precision; speed. Sampling rate and sampling depth. Nyquist Shannon sampling theorem: statement; aliasing. Nyquist Shannon sampling theorem made real(by means of a FPGA board); (prototypical example; see lecture 5.:) a simple counter in Verilog, implementation. (20/11/2017) 7. A first DSP (Digital Signal Processing) topic: from analog to digital filters. Systems. Linear, time-invariant systems: trasfer function G(t) and convolution integral; response to an input cos(ωt) (via Fourier terms A(ω), B(ω)); 5
a mention of the general case(arbitrary input), via Fourier transform. A prototypical example: low pass filter: structure and differential equation; solution in the frequency domain, linearity and time-invariance of the system, evaluation of A(ω), B(ω), Bode-diagram of the amplitude of the transfer function. Simulating a differential equation by means of a difference equation: bilinear transformation (in the time-domain only); software and hardware (FPGA) implementation. Practical part: simulation of a harmonic oscillator via y[n] = 2cy[n 1] y[n 2], with c = 1 ǫ, 0 < ǫ 1 and the period given by 2π/arctan ǫ(2 ǫ)/(1 ǫ); exercise proposed: simulation of a low pass filter via y[n] = αy[n 1]+β(x[n]+x[n 1]), with α = (1 π/t 3dB )/(1+π/T 3dB ), β = (π/t 3dB )/(1+π/T 3dB ). (21/11/2017) 8. Data compression. Binary symbol codes and compression: definitions related to symbol codes, (binary) symbol code, extended code, length of codewords, uniquely decodable symbol code and prefix code (a prefix code is uniquely decodable; the contrary is not true, see for example {1, 101}), examples; expected length L(C,X) of a symbol code C encoding an ensamble X; compression issue: given an ensamble X, generate a symbol code C that is... uniquely decodable, easy to decode, 6
minimizing the expected lengt L(C, X); Kraft inequality in the case of unique decodeability, expression and proof, complete symbol code. Shannon s source coding theorem for symbol codes: proof via Gibbs inequality( Kullback Leibler divergence Jensen s inequality convex functions); meaning of Shannon s entropy (information as uncertainty). Huffman lossless coding algorithm: algorithm; example; properties, Huffman algorithm generates prefix symbol codes (provable by construction), Huffman is complete (provable by construction), Huffman coding is optimal (statement only, i.e. no proof). A mention of lossless Lempel Ziv coding algorithm. (27/11/2017) 9. Summary of the main topics addressed in the short course. A summary of the main topics addressed in the short course: linear circuits; analog electronics; digital electronics: logic ports and combinatorial circuits; digital electronics: sequential circuits; analog meets digital ; a first DSP (Digital Signal Processing) topic: from analog to digital filters; data compression. HH: Horowitz P., Hill W., The Art of Electronics (3th ed., 2015), Cambridge University Press. SH: Hayes M. H., Digital Signal Processing (2nd ed., 2011), Schaum s Outlines McGraw-Hill Education. 7