Lecture 6 Notes: The Fourier Transform and its Properties
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We have discussed the Fourier series and its relative, the Fourier integral. There are many specific forms that the Fourier integral can take, but the one that we are most interested in is known as the Fourier Transform.
For many applications we find that it is much easier to represent our physical quantities in terms of complex numbers rather than just using real numbers alone. The concept of complex numbers comes from the continuation of functions such as square-root and logarithm that only apply to positive...