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## Ali Tajer

## Associate Professor

## Electrical, Computer, and Systems Engineering

## Rensselaer Polytechnic Institute

##

(518) 276-8237

6040 Jonsson Engineering Center, 110 8th Street, Troy, NY 12180

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## Introduction to Stochastic Signals & Systems

Fall 2023

Lecture | Topic |
---|---|

Lecture 01 | Axioms, discrete probability models |

Lecture 02 | Cconditional probability, total probability, Baye's rule |

Lecture 03 | Continuous probability models, moments, PMF |

Lecture 04 | CDF, PDF |

Lecture 05 | Functions of random variables, pairs of random variables, correlation |

Lecture 06 | Definition of stochastic process, auto-correlation, auto-covariance |

Lecture 07 | Cross-correlation, arrival process, renewal process, sum process, Poisson processes |

Lecture 08 | Properties of Poisson processes, stationary processes |

Lecture 09 | Poisson Process Derivation, Poisson Randomness, |

Lecture 10 | Systems with Stoch. Inputs: Memoryless Systems, LTI systems |

Lecture 11 | LTI systems mean and autocorrelation |

Lecture 12 | Fourier Transform review, power spectral density |

Lecture 13 | Power spectral density in LTI systems |

Lecture 14 | Random Walks and Wiener Process |

Lecture 15 | Wiener Process |

Lecture 16 | Notes on PSD and Autocorr., Mean Ergodicity |

Lecture 17 | Ideal filtering of Stoch. Processes, maximum Likelihood estimation |

Lecture 18 | Minimum mean square estimation |

Lecture 19 | Optimum Filters |

Lecture 20 | Optimum filtering applications: Filtering, prediction, smoothing |

Lecture 21 | Kalman filters |

Lecture 23 | Kalman filters |

Lecture 24 | Introduction to measure theory |

Lecture 25 | Introduction to measure theory |

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