Communications and Signal Processing Prof. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at Austin June 12, 2002

1-2 Audio CD Samples at 44.1 kHz Human hearing is from about 20 Hz to 20 kHz Sampling theorem: sample analog signal at a rate of more than twice the highest frequency in the analog signal –Apply a filter to pass frequencies up to 20 kHz (called a lowpass filter) and reject high frequencies, e.g. a coffee filter passes water through but not coffee grounds –Lowpass filter needs 10% of cutoff frequency to roll off to zero (filter can reject frequencies above 22 kHz) –Sampling at 44.1 kHz captures analog frequencies of up to but not including kHz.

1-3 Signal Processing Systems Speech synthesis and speech recognition Audio CDs Audio compression (MP3, AC3) Image compression (JPEG, JPEG 2000) Optical character recognition Video CDs (MPEG 1) DVD, digital cable, and HDTV (MPEG 2) Wireless video (MPEG 4/H.263) Examples of communication systems?

1-4 Communication Systems Voiceband modems (56k) Digital subscriber line (DSL) modems –ISDN: 144 kilobits per second (kbps) –Business/symmetric: HDSL and HDSL2 –Home/asymmetric: ADSL and VDSL Cable modems Cell phones –First generation (1G): AMPS –Second generation (2G): GSM, IS-95 (CDMA) –Third generation (3G): cdma2000, WCDMA

1-5 Wireline Communications HDSL High bitrate Mbps in both directions ADSL Asymmetric 1-10 Mbps down, Mbps up VDSL Very high bitrate, 22 Mbps down, 3 Mbps up Customer Premises downstream upstream Voice Switch Central Office DSLAM ADSL modem Lowpass Filter PSTNPSTN Interne t

1-6 Wireless Communications Time-frequency (Fourier) analysis Digital communication increases SNR/capacity Antenna array adds further increase in SNR & capacity by using spatial diversity 2.5 and 3rd generation systems transmit voice and data Picture by Prof. Murat Torlak, UT Dallas

1-7 EE345S can be used for advanced laboratory pre-requisite for senior design project Telecomm Technical Areas Comm. & Networking EE345S Real-Time DSP Lab EE360K Digital Comm. EE371M Comm. Systems EE372N Telecom. Networks EE379K-18 Network Security EE379K-19 Networking Engineering Laboratory EE379K-21 Information and Cryptography Signal/Image Processing EE345S Real-Time DSP Lab EE351M DSP EE371D Neural Networks EE371R Digital Image and Video Processing Related Technical Areas Electromagnetics Embedded Systems System Software VLSI Design

1-8 Signals Continuous-time signals are functions of a real argument x(t) where t can take any real value x(t) may be 0 for a given range of values of t Discrete-time signals are functions of an argument that takes values from a discrete set x[n] where n  {...-3,-2,-1,0,1,2,3...} We sometimes use “index” instead of “time” when discussing discrete-time signals Values for x may be real or complex

1-9 1 Analog vs. Digital The amplitude of an analog signal can take any real or complex value at each time/sample Amplitude of a digital signal takes values from a discrete set

1-10 Systems A system is a transformation from one signal (called the input) to another signal (called the output or the response). Continuous-time systems with input signal x and output signal y (a.k.a. the response): y(t) = x(t) + x(t-1) y(t) = x 2 (t) Discrete-time system examples y[n] = x[n] + x[n-1] y[n] = x 2 [n] x(t)x(t) y(t)y(t) x[n]x[n] y[n]y[n]

1-11 Causality Output depends only on the current and past inputs and past outputs y(t) = y(t -1) + x(t) + 2 x(t -1) is causal y(t) = y(t +1) + x(t +1) - 2 x(t -100) is NOT causal For systems that involve functions of time (e.g audio signals), we must use causal systems if we must process signals in real-time For systems that involve functions of spatial coordinates (images), this is not of concern when entire image is available for processing

1-12 Philosophy Pillars of electrical engineering (related) –Fourier analysis –Random processes Pillars of computer engineering (related) –System state –Complexity Finite-state machines for digital input/output –Finite number of states –Models all possible input- output combinations –Can two outputs be true at the same time? Given output observation, work backwards to inputs to see if output is possible This is called observability