1.Calculus.

2.First/second-order differential equations.

3.Superposition.

4.RLC circuits: time and frequency response characteristics

1) Determine whether a signal has the following properties: discrete time, continuous time, power, energy, periodic, aperiodic, even, odd

2) Perform the following operations on signals, alone or in combination: amplitude scaling, addition, multiplication, differentiation, integration time scaling, reflection, time shifting

3) Identify and use the following elementary signals: exponentials, sinusoids, complex exponentials, exponentially damped sinusoids step functions, impulses, sifting and time scaling properties of impulses

4) Identify and manipulate series and parallel interconnections of systems

5) Determine whether an input/output description for a system has the following properties: stability, memory, memoryless, causality, invertibility (simple cases), time invariance, linearity

6) Evaluate the convolution sum and integral given an input and the impulse response

7) Use the commutative, associative, and distributive properties of convolution

8) Determine whether a system described by an impulse response has properties: memoryless, causal, stable

9) Find the step and frequency responses of a system given the impulse response

10) Characterize the natural response, forced response, and complete response for systems described by second order difference or differential equations

11) Determine whether a system described by a difference or differential equation is stable

12) Determine whether the DTFS, FS, DTFT, or FT representation is appropriate for a give signal

12) Evaluate the DTFS, FS, DTFT, and FT representations of time signals using the defining equations

13) Evaluate the time domain signal corresponding to DTFS, FS, DTFT, and FT representations using the defining equations

14) Use partial fraction expansions to find the inverse DTFT and FT

15) Use the tables of representations and properties to find the appropriate representation or time signal

16) Use the frequency response to solve for the input, output, or impulse response of a system given the other two signals

17) Determine the frequency response of systems described by differential and difference equations

18) Use the FT or DTFT representation for periodic signals to analyze mixtures of periodic and aperiodic signals

19) Determine the FT representation for a sampled signal

20) Determine the conditions on the sampling rate or interval that guarantee a bandlimited signal can be uniquely reconstructed from its samples

21) Identify the specifications of an anti-imaging filter for reconstructing continuous-time signals from samples

22) Find the Laplace transform of a time signal using the defining equation

23) Find the Laplace transform and inverse Laplace transform using the tables of transforms and properties

24) Use the method of partial fractions to find inverse Laplace transforms

25) Use the unilateral Laplace transform to solve second order differential equations. Identify the natural and forced response components of the solution.

(Section headings are for Haykin and Van Veen)

1. Introduction (Sections 1.1-1.8) Continuous and discrete-time signals Operations on signals Properties of signals Elementary signals Continuous- and discrete-time systems Interconnections of systems System Properties

2. Time Domain Representations for Linear Time Invariant Systems (Sections 2.1-2.4) Convolution Properties of convolution Difference and differential equations - characterizing solutions

3. Fourier Representations of Signals (Sections 3.1-3.6) Discrete time periodic signals - the discrete time Fourier series Continuous time periodic signals - the Fourier series Discrete time nonperiodic signals - the discrete time Fourier transform Continuous time nonperiodic signals - the Fourier transform Properties of Fourier representations

4. Applications of Fourier Representations (Sections 4.1-4.7) Frequency response from time-domain system descriptions Fourier transform representations for periodic signals Convolution and modulation revisited - mixing periodic and nonperiodic signals The Fourier transform representation for discrete-time signals Sampling continuous-time signals Reconstruction of continuous-time signals from samples

5. The Laplace transform (Sections 6.1-6.5) Definition Convergence Properties Inversion Solving Differential Equations Transform Analysis of Systems

VARIES WITH SEMESTER OF OFFERING: Three 50 minute lectures per week OR Two 75 minute lectures per week

The following statement indicates which of the following considerations are included in this course: economic, environmental, ethical, political, societal, health and safety, manufacturability, sustainability.