Transcription of Example: the Fourier Transform of a rectangle function ...
{{id}} {{{paragraph}}}
Example: bachelor of science
Example: the Fourier Transform of a rectangle function ...
Example: the Fourier Transform of a rectangle function : rect(t). 1/ 2. 1. F ( ) = . 1/ 2. exp( i t )dt =. i . [exp( i t )]1/ 1/2 2. 1. = [exp( i / 2) exp(i /2)]. i . 1 exp(i / 2) exp( i /2). =. ( /2) 2i sin( /2) F(w) =. ( /2). F ( ) = sinc( /2) Imaginary Component = 0. w Example: the Fourier Transform of a Gaussian, exp(-at2), is itself! . F {exp( at 2 )} = ) exp( i t ) dt 2. exp( at . exp( / 4a). 2. The details are a HW problem! exp( at 2 ) exp( 2 / 4a). 0 t 0 w Fourier Series & The Fourier Transform What is the Fourier Transform ? Fourier Cosine Series for even functions and Sine Series for odd functions The continuous limit: the Fourier Transform (and its inverse). The spectrum Some examples and theorems .. 1. f (t ) = F ( ) exp(i t ) d F ( ) = f (t ) exp( i t ) dt 2.
The Fourier Transform and its Inverse The Fourier Transform and its Inverse: So we can transform to the frequency domain and back. Interestingly, these transformations are very similar. There are different definitions of these transforms. The 2π can occur in several places, but the idea is generally the same. Inverse Fourier Transform
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: