Inverse Fourier transform of decaying function

Thread starter redundant6939
Start date Nov 18, 2014
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Fourier Fourier transform Function Inverse inverse fourier Transform

In summary, an inverse Fourier transform is a mathematical operation that converts a function from the frequency domain to the time domain. A decaying function is a mathematical function that decreases in amplitude or magnitude over time or distance. The inverse Fourier transform of a decaying function will produce a function in the time domain that represents the original function with a decaying component. This means that the amplitude or magnitude of the function will decrease over time. The inverse Fourier transform of a decaying function is calculated by integrating the function over all frequencies using the inverse Fourier transform formula. This can be done analytically or numerically using software or programming languages. Some practical applications of the inverse Fourier transform of decaying functions include signal processing, audio and image processing, and

Nov 18, 2014

redundant6939

Homework Statement

Find the inverse Fourier transform of
X(e^jw = 1/(1-ae^-jw)²
using the convolution theorem.

Homework Equations

The Attempt at a Solution

I tried finding the partial fraction coefficients but without success.

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Nov 18, 2014

marcusl

Science Advisor

Gold Member

I assume that you left out a right parenthesis before the equal sign. I don't know what the answer is, but this is oscillatory not decaying.

What is an inverse Fourier transform?

An inverse Fourier transform is a mathematical operation that converts a function from the frequency domain to the time domain. It is the reverse process of a Fourier transform, which converts a function from the time domain to the frequency domain.

What is a decaying function?

A decaying function is a mathematical function that decreases in amplitude or magnitude over time or distance. It can be represented by an exponential decay curve, where the rate of decrease is determined by a decay constant.

What is the relationship between a decaying function and the inverse Fourier transform?

The inverse Fourier transform of a decaying function will produce a function in the time domain that represents the original function with a decaying component. This means that the amplitude or magnitude of the function will decrease over time.

How is the inverse Fourier transform of a decaying function calculated?

The inverse Fourier transform of a decaying function is calculated by using the inverse Fourier transform formula, which involves integrating the function over all frequencies. This can be done analytically or numerically using software or programming languages.

What are some practical applications of the inverse Fourier transform of decaying functions?

The inverse Fourier transform of decaying functions is commonly used in signal processing, audio and image processing, and in the study of vibrations and oscillations. It is also used in scientific and engineering fields to analyze and interpret data collected from experiments or simulations.