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Signal Processing

  1. Discrete-time unit impulse function and its sifting property.
  2. Discrete-time unit step function and its relation to unit impulse.
  3. The definition of systems and signals. Also, we review the linear time-invariant (LTI) systems.
  4. Expressing the output of an LTI system using discrete convolution and impulse response.
  5. Continuous-time unit impulse and continuous-time unit step along with the sifting property are reviewed.
  6. Fourier series: Exponential and sine-cosine forms with some examples are included.
  7. Using z-transform for implementing convolution.
  8. Discrete-time Fourier transform (DTFT) is expressed along with some Python code.
  9. Continuous-time Fourier transform (CTFT) is mentioned here. Also, an example in Python code is included.
  10. The eigenfunctions and eigenvalues for discrete-time LTI systems are demonstrated with z-transform and discrete-time Fourier transform(DTFT).
  11. This time, the eigenfunctions and eigenvalues for continuous-time LTI systems are demonstrated with bilateral Lpalace transform and continuous-time Fourier transform(CTFT).