Test 2 - Review

It is assumed that you have basic knowledge of the pre-requisite continuous signals and systems material and also of the discrete-time systems material examined in the previous test, i.e., difference equations, convolution sum, unit impulse, stability, causality, frequency response function, impulse response, application of DTFT and z transform to system and signal analysis, simulation diagrams for FIR and IIR filters.

Sections to Study:

Z-transform: Definition, ROC, fundamental z-transform pairs,  poles/zeros of the transfer function and frequency response, stability, inverse z transform for causal/anticausal sequences, partial fraction for causal and non-causal sequences, residue theorem for causal sequences, transient and steady-state response using the inverse z-transform,

FIR filters, simulation diagrams, stability considerations, transient steady-state response, linear phase design, group delay, design using the Fourier series and windows, Kaiser window design and its application to FIR filter design, design by zero placement

IIR Filters,  simulation diagrams, stability considerations, transient steady-state response, analog filter approximations,  Impulse Invariance, Bilinear Transformation, Properties, Design of Butterworh filters, properties of Chebychev and Elliptic filters

Test Structure:   There will be two parts.

Part a: short questions examining knowledge of concepts.  No partial credit on those. This part will account for about 40% of the test grade.
Part b: will have problems.  There will be partial credit here.  This part will account for about 60% of the test grade.

Two basic guidelines:   You should basically study both from your notes AND from the relevant sections in Oppenheim and Schafer (sections
3.1, 3.2, 3.3, 3.4, .5.1, 5.2, 5.2.1, 5.3, 5.3.1 5.3.2, 5.7, 5.7.1-3,  6.1, 6.2,  7.1, 7.1.1, 7.1.2, 7.1.3, 7.2, 7.2.1, 7.2.2, 7.2.3, 7.3)
You should review, study, and understand thoroughly all of the assigned homework as well as the examples worked out in class

Test Examination Objectives:

You should be able to:
-       write difference equations from simulation diagrams and vice versa.
-      write transfer functions from simulation diagrams and from difference equations and vice versa
-       find impulse responses for FIR and IIR systems
- Evaluate inverse z transforms using partial fractions for causal and non-causal sequences
- Evaluate inverse z transforms using the residue theorem for causal sequences
- apply the inverse z-transform to transient and steady-state system analysis
- demonstrate that you understand relationships between ROC in the z-domain and causal/anticausal sequences
- demonstrate that you understand issues associated with poles/seros, ROC, stability, causality when analyzing transfer functions
- sketch the magnitude frequency response from pole-zero descriptions
- design simple FIR filters using zero placement
-      design FIR filters using the Fouries series and windows
-      describe and demonstrate that you understand the effects of windows on FIR filter design using the Fouries series
-      describe and demonstrate that you understand the Kaiser window design method for FIR filter design
-      describe and demonstrate that you understand IIR filter design using the impulse invariance method
- describe and demonstrate that you understand IIR filter design using the bilinear transformation
- describe and demonstrate that you understand Butterworth filter design