Semesters Offered

Learning Objectives

  • Interpolate discrete-time sinusoids using knowledge of sampling rate and bandwidth
  • Use complex phasors to represent and manipulate real-valued sinusoids
  • Represent finite-dimensional linear transformations by matrices; interpret the latter in terms of the former
  • Calculate orthogonal projections and least-squares approximations for both real and complex vectors
  • Compute simple low-dimensional DFTs and their inverses from first principles
  • Correctly interpret the information in a DFT spectrum and use it to reconstruct a time-domain signal as a sum of its Fourier components
  • Understand and apply DFT properties pertaining to index reversal, index shift, modulation, periodic extension and zero-padding
  • Compute Fourier series coefficients of simple periodic signals in continuous time
  • Determine the frequency response of a FIR filter; interpret the frequency response in the context of frequency selection
  • Compute the time-domain response of a FIR filter to exponential, periodic and finite-duration inputs
  • Use MATLAB to visualize, analyze and process signals and images, thereby applying the theory and tools taught in the lectures

Topics Covered

  • Real and complex sinusoids in continuous time
  • Sampling of sinusoids, discrete-time sinusoids, aliasing
  • Matrices and linear transformations, linear systems
  • Matrix inversion, Gaussian elimination
  • Inner products, norms, projections; orthogonal bases
  • DFT as an orthogonal projection, interpretation of the DFT
  • Signal transformations and the DFT, symmetry, duality
  • Zero-padded and periodic extensions and the DFT
  • Periodicity in continuous time, sums of harmonically related sinusoids
  • Fourier series of a periodic signal; evaluation of coefficients, properties
  • LTI filters and impulse response, FIR filters
  • FIR filters and finite duration inputs: linear convolution
  • FIR filters with sinusoidal and exponential inputs: frequency response, system function

Learning Outcomes

  • Ability to apply knowledge of math, science, & engineering (Significant)
  • Ability to design/conduct expt. & analyze/interpret data (Moderate)
  • Ability to identify, formulate, and solve engineering problems (Moderate)
  • Techniques, skills, and modern engineering tools necessary for engineering practice (Significant)