Chris' Page for HW 4 (Fourier Transforms): Difference between revisions
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The Fourier Transform is a process or formula that converts a signal from one domain to another. Often it is used to go between the time domain and the frequency domain. | The Fourier Transform is a process or formula that converts a signal from one domain to another. Often it is used to go between the time domain and the frequency domain. | ||
Developed by Frenchman, Jean Baptiste Joseph Fourier (1768 - 1830), the Fourier Transform stems from the more general Fourier Analysis, which is the representation of a function with sine and cosine terms. | |||
Developed by Frenchman, Jean Baptiste Joseph Fourier (1768 - 1830), the Fourier Transform stems from the more general Fourier Analysis, which is the representation of a function with sine and cosine terms. Unlike the Fourier Series the Fourier Transform is capable of representing aperiodic signals. | |||
== Mathematical Description == | == Mathematical Description == | ||
:<math>X(f) = \int_{-\infty}^{\infty} x(t)\ e^{-i 2\pi f t}\,dt, </math> for every [[real number]] <math>f.\,</math> | |||
== Relation to Laplace Transform == | == Relation to Laplace Transform == | ||
== Examples == | == Examples == | ||
Revision as of 00:27, 3 November 2007
The Fourier Transform is a process or formula that converts a signal from one domain to another. Often it is used to go between the time domain and the frequency domain.
Developed by Frenchman, Jean Baptiste Joseph Fourier (1768 - 1830), the Fourier Transform stems from the more general Fourier Analysis, which is the representation of a function with sine and cosine terms. Unlike the Fourier Series the Fourier Transform is capable of representing aperiodic signals.
Mathematical Description
- for every real number