At the point of the 3^rd exam in EE422, you should be able to do the following objectives:

EXAM III Objectives: Discrete Systems, Z-Transforms, and Filter Design

• All exam I and exam II objectives
• Understand the process of Analog-to-Digital conversion (HW #17)
• Model the (ideal) sampling process and derive the frequency domain representation, X_s(f) (Lecture Notes)
• Understand and apply the Nyquist Sampling Theorem (HW #17)
• Recover continuous signals from sampled signals (HW #17)
• Model the quantization process and derive an expression for MSE due to quantization (HW #18)
• Understand the effects of quantization and evaluate dynamic range and SNR (HW #18)
• Derive the Z-transform from the Laplace transform of the ideal sampling model (Lecture Notes)
• Define and understand the relationship between z and s and the z-plane and the s-plane (Lecture Notes)
• Understand and evaluate the region of convergence of Z transforms (HW #18)
• Derive and apply the Final Value Theorem for Z transforms (HW #18)
• Derive and apply properties of the Z transform (Lab #2)
• Use two methods to discretize a continuous-time state variable models (Lab #2)
• Find Z-transforms of discrete signals which are periodic after k=0 (HW #19)
• Use the Z-transform to solve the discrete state variable model and identify the zero-input and zero-state portions of the solution. (HW #20, HW #21, HW#23)
• Obtain discrete-time transfer functions and determine system stability (HW#23)
• Understand concepts of eigenvalues and eigenvectors as they relate to discrete systems
• Use the similarity transformation, x[k]=Pz[k], to decouple a discrete state variable model (HW #23)
• From a decoupled discrete state variable model, determine controllable/observable eigenvalues: (HW #23)
• Understand the how to design for control specifications such as settling time and no-overshoot in the discrete domain (HW #23)
• Design a feedback control law, w[n] = -Kx[n], to set the eigenvalues of a single input discrete system (HW #23)
• Derive the discrete time domain solution to the discrete state equation using the Z-transform (HW #23)
• Use three methods to find the discrete transition matrix, A^k
• Derive and apply the discrete convolution sum (HW #23)
• Perform discrete convolution both graphically and by evaluation of the discrete convolution sum (HW #23)
• Apply the properties of linear time-invariant (shift-invariant) discrete systems (HW #23)