ECE-GY 9013 Special Topics in ECE: A Linear System Approach to Wave Propagation

Linear System

Date: January 28, 2021 - May 11, 2021

Lectures (remote - Zoom): Tuesday 9:30 – 10:45AM, Thursday 9:30 – 10:45AM

Tuition and Fees: $6,120

*This will be billed by the NYU Bursar's office only after you officially register for the course.

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Course Description

This course treats systems governed by the wave equation via the tools of linear system theory: convolutions and space/time Fourier transforms. In contrast, the traditional physicist's approach to teaching the subject entails scalar and vector potentials, the method of separation of variables, spherical coordinates, and the use of special functions – all of which we circumvent. The course will benefit both wireless communication researchers and signal processing researchers. It will equip them to pursue advanced research topics, such as super-directive antenna arrays, large intelligent surfaces, holographic MIMO, wireless power transfer, wavefield extrapolation, and video motion detection. The course also serves as a physical introduction to multidimensional signal processing. The concepts learned in this course are readily applicable to geophysics, acoustics, and ultrasonics.


Undergraduate linear systems, electromagnetics, and complex variables.


Homework, Exam, and grading Policy

Midterm Exam (take-home): 35%, Final Exam (take-home): 35%, Written Homework and MATLAB exercises: 30%. 


Week 01 (Jan 28, Feb 2): Classical network theory

  • N-port networks
  • impedance matrix and properties
  • real and reactive power
  • application: wireless power transmission

Week 02 (Feb 4, 9): Scalar (acoustic) wave equation

  • physical derivation with distributed source
  • Helmholtz equation
  • review of space/time Fourier transforms
  • solution in frequency/wavenumber domain
  • 1D system (wave-guide)

Week 03 (Feb 11, 16): Plane-wave expansion of the radiated field

  • review of Cauchy residue theorem
  • plane-wave expansion of the spherical wave
  • Green's function (impulse response) solution
  • plane-wave solution for arbitrary distributed source

FEBRUARY 18 - NO CLASSES: Legislative Day

Week 04 (Feb 23, 25): Methods of computing real power

  • integration over far-field
  • integration over a source distribution
  • integration over plane waves

Week 05 (March 2, 4): Reactive power; self/mutual impedance

  • computation in space-domain
  • computation in the wavenumber domain
  • physically meaningful sources

Week 06 (March 9,11): Degrees of freedom for 1D, 2D, 3D arrays

  • non-line-of-sight propagation: plane-wave scattering
  • application: MIMO communications

Week 07 (March 16, 18): Take-home Midterm Exam

Week 08 (March 23,25): Maxwell's equations; distributed sources

  • review of Maxwell's equations
  • direct solution in frequency/wavenumber domain

Week 09 (March 30, April 1): Plane-wave expansion of the radiated field

  • Polarization
  • vertical and horizontal plane-wave amplitudes

Week 10 (April 1, 6): MIMO communications

  • degrees-of-freedom for 1D, 2D, 3D polarimetric arrays
  • non-line-of-sight propagation: plane-wave scattering

Week 11 (April 6, 8): Power: real/reactive; self/mutual impedance

  • methods of computation
  • idealized antennas

Week 12 (April 20,22): Application: super-directive antenna arrays

  • wireless communication
  • wireless power transfer

Week 13 (April  27,29): Multi-dimensional digital signal processing

  • video motion detection using space/time fan filters
  • inference of far-field antenna pattern from near-field measurements

Week 14: (May 4, 6) Additional applications

  • random field models for small-scale fading
  • electromagnetic imaging

Week 15: (May 11) Take-home Final Exam