EE 228 – Continuous-Time Signals & Systems – Learning Objectives Learning Objectives describe specific skills that students should acquire in a course. Following completion of each section, “Students should be able to…”

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TIME DOMAIN ANALYSIS: Introduction, Signals Ch 1, 2.0-2.6 Ch 2,3

Identify common signals (rect, sinc, impulse, step, ramp, tri, exp, sinusoids). Describe more complicated signals in terms of simpler ones. Sketch signal

results of simple operations (time shift, time reversal, etc.). 2.5 2.8

Determine periodicity (and period) of a signal or signal combinations. 2.4 2.6 Understand & utilize the properties of the impulse (delta) function. 2.6 2.10, 2.11

Systems and Classification Ch 4.0-4.2 Ch 4,5

Describe a system in terms of operators. Apply basic operations of time scaling, time reversal, time shift, amplitude scale and shift, d/dt, integral 2.2, 4.1 2.1, 2.8,

2.10

Determine if a system is: linear or nonlinear, time-invariant or time-variant, causal or non-causal, instantaneous or dynamic, stable or unstable. 4.0-4.2, 4.6 4.2, 4.15 4.19, 4.20,

4.21

Analysis of Systems via Differential Equations Ch 7 Find response to system modeled by differential equation via method of

undetermined coefficients. Find ZIR and ZSR. Sketch response. Identify forced and natural responses.

4.3-4.4 4.11, 4.12, 4.22 4.10

Determine impulse response from differential equation (directly or via step response). 4.5 4.14

Apply the properties of linearity (superposition) and time-invariance to predict system responses to multiple, delayed, or derivatives of input signals.

4.2, 4.4 4.22

Analysis of Systems via Convolution Ch 6

Evaluate convolution integral analytically and graphically (by ranges). Draw sketches of flip & slide process. 6.1-6.4 6.3, 6.4, 6.5

Apply properties of convolution (convolve with impulse, commutative, associative, linearity). 6.1-6.3 6.4, 6.9, 6.10 6.6

Use convolution with h(t) to find relaxed system response, including step response.

4.5, 4.7, 6.1, 6.4.2 6.3, 6.9

Determine stability via h(t). 6.5 6.11

Course Topic & Learning Objectives Text Text Problems

Lecture Notes (Nahvi)

Extra Problems

FREQUENCY DOMAIN ANALYSIS:

Analysis of Periodic Signals via Fourier Series Ch 13 Find Fourier coefficients (analysis process). Sketch in time & freq. domains. 8.1 8.4

Convert Fourier Series coefficients between trigonometric, polar, and exponential forms. 8.1

Identify symmetry to simplify Fourier analysis. 8.2 8.7 Use Parseval’s relationship to find signal power in harmonics 8.3 8.7

Knowledge of Fourier Series properties & Gibbs Phenomena 8.5, 8.6 8.7 Find steady state response of relaxed circuit or system to harmonic signals 8.7 8.18, 8.31

Analysis of Systems & Aperiodic Signals via Fourier Transforms Ch 14

Evaluate Fourier transform (analysis) and inverse transform (synthesis). 9.1 9.1 Derive and apply properties of Fourier transform 9.2 9.3, 9.4, 9.44

Determine zero state response of system using FT and freq. response. 9.3-9.4 9.16, 9.17, 9.19 Determine steady-state sinusoidal response of system using freq. response. 9.3.5 9.18, 9.44, 11.15

Derive frequency response from impulse response or differential equation (and reverse) 9.3

LAPLACE TRANSFORM SYSTEM ANALYSIS

Laplace Transforms Ch 11, 12.3 Ch 8 Evaluate forward transform using defining integral 11.1 11.1, 11.2

Apply tables and properties of Laplace Trans. for forward /inverse transforms 11.2 11.2, 11.3 11.4 11.8

Evaluate inverse transform via partial fraction expansion 11.4 11.7 11.13 11.14 11.21 11.25

Apply Initial Value and Final Value Theorems 11.5 11.6 Find & plot poles & zeros of H(s), predict form of natural response & stability 11.3, 11.5 11.5 Find h(t) via inverse transform. Find H(s) directly from h(t) or differential equ.

& differential equation from H(s), poles/zeros, or circuit. 11.2.3, 11.4 11.9, 11.10, 11.11, 11.14 11.8

Find response y(t) via forward [X(s) and H(s)] and inverse transforms. Sketch. 11.4, 11.6 11.12 11.27