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Discrete Fourier Transform and Spectral Analysis (MATLAB)
Rating: 4.0 out of 5(9 ratings)
134 students

Discrete Fourier Transform and Spectral Analysis (MATLAB)

Introduction to Fourier Transform and Spectral Analysis - Part 2
Created byAlexander Taratorin
Last updated 4/2021
English

What you'll learn

  • Understanding Discrete Fourier transform basics, implementing DFT, convolution and correlation in Matlab/Octave
  • Essential signal processing skills using Matlab/Octave

Course content

1 section • 17 lectures • 4h 48m total length

  • Introduction11:25

    Review of course content - DFT, introduction to Matlab and scripts

  • Discrete Fourier Transform15:43

    DFT transform, frequency resolution and frequency bins

  • Spectrum Leakage and Signal Windows33:22

    Explains DFT Spectral Leakage and Signal windows

  • Introduction to Matlab23:03

    Demonstration of Command Window and explanation of scalars, vectors and matrices in Matlab

  • Matlab Scripts and plot functions17:39

    Preparing and running scripts using Matlab Editor, summary of basic plot functions

  • Using Complex numbers in Matlab7:23

    Operations with complex numbers, complex vectors, absolute value and angle

  • Angle, Phase and phase unwrapping method7:04

    Phase unwrapping method - comparison of angle and phase

  • Sine Wave generation example8:55

    Example of generating Sine Wave signals at different frequencies

  • Sine Wave, Square Wave and FFT example11:43

    Generating sine wave, square wave, calculation and comparison of FFT of both signals

  • Using sum of sinusoidal waves for approximation9:10

    Approximate square wave by sum of sine waves

  • DFT and Spectrum Leakage Example22:08

    Illustration of spectral leakage problem using DFT. Using spectral windows and analyzing DFT spectrum

  • Delay and Phase shift using phase information10:42

    Delaying signal and calculating resulting DFT phase shift

  • Up and Down Conversion using DFT22:49

    Generating band-limited signals, calculating DFT of up-converted and down-converted signals

  • Product of signals and DFT spectrum7:20

    Calculation of DFT for product of two signals

  • Convolution of Signals in Matlab25:33

    Discrete convolution using Matlab. Generating pulse, impulse response and convolution results

  • Signal Detection in noise using Cross-Correlation12:06

    Using cross-correlation for signal detection in noise

  • Time Domain, Spectral and Phase methods for Frequency detection42:26

    Detection of unknown frequency with high resolution using time domain, DFT and phase methods

Requirements

  • Familiarity with Fourier transform and spectral analysis
  • My course "Introduction to Fourier Transform and Spectral Analysis Part 1" on UDEMY is desirable prerequisite

Description

This course is continuation of Fourier transform and spectral analysis series. In this course I will introduce discrete Fourier Transform, explain concepts of frequency bins and frequency resolution and illustrate spectral leakage effect.

The best way to understand what happens with signals and spectral components is to generate test signals and spectra. The shortest route is to learn Matlab (or use compatible open-source Octave program). I will describe very simple basic set of Matlab programming skills and after a couple of short lectures you will be able to edit and run simple scripts and plot your output results.

The rest of the course illustrates using Matlab for signal processing.  It is always useful to have source code of programs - it saves a lot of time and provides "prototyping" for program development. Each lecture will have attached downloadable script.

In the video lecture I will explain all program steps and  show real-time results of script execution. I will start from very simple generation of sinusoidal signals and calculation of FFT, going to more complicated examples such as up- and down-conversion, convolution and cross-correlation, frequency measurement using phase approximation.

After taking this course you will have a set of essential skills of signal processing and FFT analysis using Matlab. I will explain a number of useful tricks which will help you to develop and run your signal processing programs.


Who this course is for:

  • Electrical Engineering, Physics, Data Science, Biomedical Science

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