General difference equations
  • How to compute the impulse response of a difference equation
Down sampling / Up sampling
  • Their expression as a function of the sample index n.
  • Their schematic expression.
Solutions to HW1
  • Review of even / odd functions and the real exponential input.
Continuous Fourier Transform
  • Definition of the Continous Fourier Transform and it's inverse.
  • Definition of the magnitude spectrum & the phase spectrum.
  • Definition of the sufficient conditions for the continuous Fourier Transform to exist.
Energy Density Spectrum
  • Definition of the energy density spectrum
  • Know Parseval's relation and that it prooves the Fourier Transform is a lossless transform.
  • Definition of Lowpass / Highpass / Bandpass signals.
Discrete Time Fourier Transform
  • Definition of the Discrete Time Fourier Transform (DTFT) and it's inverse. Note that the frequency domain is still continous in this analysis.
  • Know that the DTFT is discrete time, continuous frequency.
  • Know that the Inverse-DTFT is indeed exactly the originally transformed discrete signal.
  • Definition of the DTFT, i.e., the analysis equation, and the Inverse-DTFT , i.e., the synthesis equation.