Research Institute for Future Media Computing 未来媒体技术与计算研究所 Research Institute for Future Media Computing http://futuremedia.szu.edu.cn Signal Processing 1. Introduction to Signals & Systems 江健民，国家千人计划特聘教授 深圳大学未来媒体技术与计算研究所所长 Office Room: 409 Email: jianmin.jiang@szu.edu.cn http://futuremedia.szu.edu.cn

Research Institute for Future Media Computing 未来媒体技术与计算研究所 Research Institute for Future Media Computing http://futuremedia.szu.edu.cn Overview All lectures will be delivered in English, and each week we have one lecture and one tutorial； Major source of references: (i) Matlab Signal Processing Toolbox; (ii) http://en.wikibooks.org/wiki/Signals_and_Systems Lecturer: Professor Jianmin Jiang, office located in 409; Assessment: no exam, but to submit a research report on designated topics to be decided.

Why signal processing in computer science? To enable you to have more capability and skills in pursuing your further studies in computer science, such as PhD programme; To enable you to be more knowledgeable in technology innovations, especially in terms of computer programming; To extend your views and visions for computing related research and development; To prepare you for thinking, reading and writing in English for your overseas studies.

Coverage of this module Introduction of signal & systems； Signal processing in time domain (key operations: correlation, convolution and filtering etc.)； Signal processing in frequency domain (Fourier transform, DCT transform and z-transform etc.); Case studies and applications

Basic concept of signals and systems Input Signals Output Signals Computing system (Signal processing) Signals are electrical representation of information, mathematical description of a signal is: f=f(t) (time domain); When f(t) is projected to any space other than time, it is referred to as frequency domain or specially named domain (Fourier transform, DCT, wavelet transform etc.) Systems are any functional module, which has the power of processing signals, delivering any functionalities, and producing new signals (outputs);

A system can be described by the relationship between input and output as shown below; Input x Output F(x) F(x) = x Input x Output F(x) F(x) = 2x A typical example of systems is a filter, which blocks part of the input signal and let go of the rest. f0 f0 Input x Output F(x) F(x) = x N f1 f2 f0 There exist four types of filters described in frequency domain, low-pass, high-pass, band-pass, and band-stop.

Signal classification and properties Continuous-Time vs. Discrete-Time; Analog vs. Digital; Periodic vs. Aperiodic; Finite vs. Infinite Length; Causal vs. Anticausal vs. Noncausal; Even vs. Odd; Deterministic vs. Random

Continuous-Time vs discrete time: time axis t has continuous values or not f(t) t … (ii) Analog vs. Digital: Both f(t) axis and t-axis have continuous values or not; f(t) t … 24 32 42 47

Mathematically, periodic signals can be represented by: f(t) = f(t+nT) (iii) Periodic vs. aperiodic: Periodic signals repeat with some period T, while aperiodic, or nonperiodic, signals do not. Mathematically, periodic signals can be represented by: f(t) = f(t+nT) (iv) Finite vs. Infinite Length: f1 < f(t) < f2 f(t) t

(v) Causal vs. Anticausal: Causal signals are signals that are zero for all negative time; anticausal are signals that are zero for all positive time. Noncausal signals are signals that have nonzero values in both positive and negative time

(vi) Even vs. Odd: An even signal is any signal f such that f(t)=f(−t) Even signals can be easily spotted as they are symmetric around the vertical axis. An odd signal is a signal f such that f(t)=−f(−t) Advanced level: any signal can be written as a combination of an even and odd signal.

(vii) Deterministic vs. Random: A deterministic signal is a signal in which each value of the signal is fixed and can be determined by a mathematical expression, rule, or table. A random signal has a lot of uncertainty about its behavior. The future values of a random signal cannot be accurately predicted and can usually only be guessed based on the averages of sets of signals.

Key techniques of manipulating signals Given a signal: f = f(t), we can have a number of simple manipulations, which are important for understanding the signal properties. These include: shifting F1 = f(t-a); F2 = f(t+a); F3 = f(t)+a; F4 = f(t)-a; f(t) t f(t-a) t a f(t+a) t -a f(t)-a t a f(t)+a t -a

(ii) Given a signal: f = f(t), we can also have a number of scaling manipulations, including: F5 = f(at); F6 = af(t). f(at) t af(t) t