Introduction to Fourier Analysis (Webinar)

In Introduction to Fourier Analysis, you'll learn ...

• Equations describing transformation from time to frequency domains
• Difference between Fourier Series and Fourier Transforms
• Principles behind use of Discrete Fourier Series, Discrete Fourier transform and Fast Fourier Transform algorithms

Overview

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In this webinar, models will be presented to transform time signals into the frequency domain. These models will include Fourier Series as well as Fourier Transforms to show the spectral components content of these time dependent signals. Signal characteristics which lead to the use of the appropriate model will be discussed in order to understand the applicability and limitations of the transformations discussed.

Complex Exponential Series and Trigonometric Series for real valued functions will be used with various examples to illustrate the mathematical calculations and approach to arrive at the transformation to the frequency domain. These calculations will use “well-behaved signals” for which analytical expressions are readily available.

The Fourier Transform, a more general and convenient transformation for all types of signals will be discussed and examples provided for “well behaved functions” for which the mathematical calculations involved are rather straight forward.

For “non-well behaved” signals, for which analytical expressions are not readily available, direct measurement of the spectrum using a Scanning Spectrum Analyzer will be described by means of a block diagram of that spectrum measurement instrument and its associated block functions.

Discrete Fourier Series and Discrete Fourier Transforms, used in conjunction with a digital computer, will be discussed to illustrate the manner in which transformation of time dependent signals to the frequency domain is achieved for signals of all types for which time analytical expressions are not available. Theorems such as “Sampling Theorem” and “Nyquist Sampling Rate” will be discussed as they the fundamental basis for these discrete measurements. The Fast Fourier Transform algorithms will be described to illustrate the manner in which computation time and storage for the digital computers can be minimized when using the discrete approach to transformation to the frequency domains.

Specific Knowledge or Skill Obtained

This course teaches the following specific knowledge and skills:

• Recognizing the difference between energy and power signals
• Using Exponential and Trigonometric Fourier Series for periodic signals
• Using Fourier Transform equation applicable to aperiodic signals
• Understand use of Scanning Spectrum Analyzer to obtain signal spectrum measurements
• Use of Sampling Theorem and Nyquist Sampling Rate to use with DFT and FFT applications