## Topic outline

- General
### General

Lecturer : - MUSA BIN MOHD MOKJI

Semester : Semester 1 2012/2013 Synopsis : Review on continuous-time signals and systems, introduction to digital signal processing, basic idea and benefits, examples and applications. Discrete-time signals and systems ; signal definition : periodic and periodic, stability, causality, convolution. Spectrum of representation of discrete-time signals ; sampling theorem, the discrete-time Fourier transform (DTFT) and its properties. Difference equations and discrete-time systems ; difference equations : infinite impulse response (IIR) and finite impulse response (FIR) and signal flow graphs. z-transform : derivations, region of convergence, transformation properties, stability-poles and zeros, inverse z-transform-long division and partial fraction expansion, conversion to analog to digital system : impulse invariant and bilinear transform. Analysis and design and of digital filters : Filter basics, analog filter prototypes, design of IIR filter – bilinear transformation method, design of FIR filter – window method, window functions. Discrete Fourier transform : Discrete Fourier Series (DFS), Discrete Fourier transform (DFT), spectrum analysis of signals, Fast Fourier transform (FFT), frequency domain implementations of linear systems. Application of digital signal processing : speech processing, image processing, signal analysis, and telecommunications.

This work, SKEL4223 DIGITAL SIGNAL PROCESSING by MUSA BIN MOHD MOKJI is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License - Topic 1
### Topic 1

**Discrete-time Signal**

The topic gives an introduction on the digital signal processing with related application. Then discrete-time signal is discussed starting with sampling theorem followed by topics on representing the discrete-time signal, types of signal and arithmetic operations on the discrete-time signal. - Topic 2
### Topic 2

**Discrete-time System**The topic covers the definition of the discrete-time system and characteristic of the system. The first two characteristic discussed are linearity and time invariant which will describe the consistency of the output of the system. The next two are causality and stability that describe implementation possibility of the discrete system . Additionally characeristic named memory is also discussed. - Topic 3
### Topic 3

**LTI System**The topic discussed on a spesific discrete-time system which is linear and time-invariant. The discussion starts with representation of the LTI system using difference equation and impulse response. Then the topic discussed the first type of the LTI system called Finite Impulse Response (FIR) system which also introduced fundamental operation of LTI system called convolution. The topic continues with Infinite Impulse Response (IIR) system, the second type of the LTI system. - Topic 4
### Topic 4

**Z-Transform**The topic discussed the foundation of z-transform which covers topics on the usage of z-transform, its formulation, Region of Convergence (ROC), LTI system test on causality and stability, and poles and zeros. - Topic 5
### Topic 5

**Inverse Z-Transform**The topic discussed methods on computing the inverse z-transform which are based on the number of poles and zeros. Additionally the discussion continue on z-transform properties which can be used to simplify the z transformation computation. - Topic 6
### Topic 6

**LTI System Function**The topic introduced the term System Function which is impulse response describe in z-domain. Based on the system function the discussion expand to finding difference equation and realization of LTI system on memory allocation. - Topic 7
### Topic 7

**Spectrum representation of discrete-time signals**The topic discussed the foundation representing signals based on frequency (spectrum). It starts with Fourier series that cater spectrum for periodic signal and followed by Fourier transform for aperiodic signal. The topic then continue with the spectrum representation of discrete-time signal. - Topic 8
### Topic 8

**Discrete-time Fourier Transform**The topic discussed the DTFT in terms of its definition, formulation, notation and spectrum representation. - Topic 9
### Topic 9

**Discrete-time Fourier Transform Properties**The topic discussed briefly on the basic properties of the DTFT and extensively on symmetry properties of the DTFT. Based on the knowledge of the symmetry property, relationship of the spectrum with the poles and zeros is discussed. - Topic 10
### Topic 10

**Phase System**The topic covers three types of LTI system categories based on the phase of the system. Additionally, topic on sampling is revisited to complete the DTFT discussion which starts at topic 7 (Spectrum representation of discrete-time signals). - Topic 11
### Topic 11

**Discrete Fourier Transform**The topic first gives review on Discrete Fourier Series (DFS) and followed by the Discrete Fourier transform (DFT) foundation. Then, spectrum analysis of signals based on the DFT is discussed. - Topic 12
### Topic 12

**IIR Filter Design**The topic starts with the discussion on filter basics and analog filter prototypes. From there the process of designing IIR filter based on bilinear transformation method is discussed. - Topic 13
### Topic 13

**FIR Filter Design**The topic discuss the design process of FIR filter based on windowing method.