# Course Websites

## ECE 210 - Analog Signal Processing

### Summer 2021

#### Official Description

#### Related Faculty

#### Subject Area

#### Course Director

#### Description

Introduction to analog signal processing, with an emphasis on underlying concepts from circuit and system analysis: linear systems, review of elementary circuit analysis, differential equation models of linear circuits and systems, Laplace transform, convolution, stability, phasors, frequency response, Fourier series, Fourier transform, active filters and AM radio.

#### Notes

Students may not receive credit for both ECE 211 and 210.

#### Goals

To introduce fundamentals of analog signal processing, with major emphasis on circuit analysis, differential equations, convolutions, Fourier methods, and applications in filtering and AM radio.

#### Topics

- Examples of signals and signal processing systems
- Analog linear time-invariant systems
- Circuits and linear systems
- Review of DC circuit analysis: KCL, KVL, dependent sources
- Capacitors and inductors as circuit elements
- Op-amp circuits
- Characterization and solution of LSI systems via linear, constant-coefficient differential equations
- Complex numbers and functions of a complex variable
- Impedance, phasors, and sinusoidal steady-state
- Frequency response and multi-frequency circuits
- Fourier Series
- Fourier transform
- AM radio
- Convolution
- Impulse and impulse response
- Sampling theorem and overview of digital signal processing
- Stability
- Laplace transform and transfer function
- Laplace transform solution of differential equations
- General form of solution to a differential equation
- Design of active filters

#### Detailed Description and Outline

- Signals and signal processing in analog linear time-invariant (LTI) circuits and systems
- Review of DC circuit analysis: KCL, KVL, dependent sources
- Capacitors and inductors as circuit elements, op amps
- Characterization and solution of LTI systems via linear, constant-coefficient differential equations
- Complex numbers and functions of a complex variable, impedance, phasors, and sinusoidal steady-state
- Frequency response and multi-frequency circuits, Fourier series and transforms, AM radio
- Convolution, impulse and impulse response, sampling theorem and system stability
- Laplace transform and transfer function, Laplace transform solution of differential equations
- General form of solution to a differential equation, design of active filters

#### Computer Usage

Optional MATLAB and Python Honors Sections are offered to introduce the students to elements of scientific computing and graphics.

#### Lab Projects

Five bi-weekly labs introduce the students to op-amp amplifiers, mixers, and filters. Students build a superhetrodyne AM receiver in Lab 4. In Lab 5 the receiver is modified to replace its IF section with a sound-card based sampler and software radio implementation.

#### Topical Prerequisites

- Calculus
- Concurrent registration in differential equations
- Physics-bases treatment of electricity and magnetism
- Introductory exposure to circuit analysis

#### Texts

E. Kudeki and D. C. Munson, *Analog Signals and Systems*, Prentice Hall, 2008.

#### ABET Category

Engineering Science: 90%

Engineering Design: 10%

#### Course Goals

ECE 210 is a required 4-hour course for both electrical engineering and computer engineering majors. The goals are to provide a solid foundation in analog signal processing that will serve as a strong base for further study in digital signal processing, communications, remote sensing, control, and electronics. Topics include circuit analysis, continuous- time linear system theory, Laplace and Fourier transforms, AM radio, and basic analog filter design. The course includes five laboratories to give students hands-on experience in exercising the theoretical concepts learned in class. The labs contain significant components of categories (1), (2), and (6) under Criterion 3, ABET Program Outcomes and Assessment. ECE 211 is the first half of ECE 210 and is taught as a service course for students outside electrical and computer engineering.

#### Instructional Objectives

**A. At the time of Exam 1 (after 14 lectures), students should be able to: **

- Calculate node voltages and branch currents in linear circuits containing resistors, independent and dependent sources, and operational amplifiers. (1)
- Design simple op amp circuits. (2)
- Sketch voltage and current waveforms (given one, sketch the other) for capacitors and inductors. (1)
- Design simple op amp integrators and differentiators. (2)
- Solve first- and second-order differential equations with constant inputs. (1)
- Manipulate complex numbers and demonstrate an understanding of their meaning. (1)

**B. At the time of Exam 2 (after 28 lectures), students should be able to do all of the items under A., plus: **

- Understand phasor representation of co-sinusoidal signals and use the method for solving linear differential equations with co-sinusoid inputs. (1)
- Apply the phasor concept to solve circuits for the sinusoidal steady-state response. (1)
- Understand the distinction between instantaneous and average power and use the concept of maximum power transfer. (1, 2)
- Derive and sketch the frequency response of a linear circuit or system. (1)
- Calculate the response of dissipative linear systems to multi-frequency inputs (1)
- Calculate the Fourier series of a periodic signal. (1)
- Apply the Fourier series concept to calculate the output of a system due to a periodic input. (1)

**C. At the time of Exam 3 (after 42 lectures), students should be able to do all of the items under A and B., plus: **

- Calculate the Fourier transform of finite-energy aperiodic signals and understand the concepts of signal energy and bandwidth. (1)
- Explain and analyze the concepts of AM coherent demodulation, noncoherent demodulation, envelope detection, and a complete AM superheterodyne receiver (built in the lab). (1, 2)
- Calculate and visualize convolution and apply the concept of impulse. (1)
- Explain the sampling theorem and select a sampling rate according to the Nyquist criterion. (1, 2)
- Determine whether a system is linear or nonlinear, causal or noncausal, time-invariant or time-varying, and decompose system outputs into zero-input and zero-state components. (1)
- Determine whether a circuit or system is stable or unstable and demonstrate an understanding of the definition of stability. (1)

**D. At the time of the Final Exam (after 58 lectures), students should be able to do all of the items under A, B, and C., plus: **

- Calculate the one-sided Laplace transform and its inverse. (1)
- Apply the concept of impedance to find the transfer function of a circuit. (1)
- Compute transfer functions from block diagrams. (1)
- Explain the relationship between pole and zero locations of a circuit and its corresponding frequency response. (1)
- Design a Butterworth filter having a desired cutoff frequency. (1, 2)
- Map a designed transfer function to a circuit composed of second-order op-amp building blocks. (1, 2)