Very Basic Fourier Transform Equation

In summary, the conversation discussed the two equations for the Fourier transform, which convert a function from time to frequency and vice versa. The first equation includes a negative sign in the exponent, while the second does not. The person searched online and found a video that explains the difference in signs. They also express their preference for the video's definition and mention the helpfulness of Brian Douglas's videos. Finally, they question the accuracy of the equation given in class.
  • #1
DiamondV
103
0

Homework Statement


So well, in class we were shown this equation for the Fourier transform:
http://puu.sh/nHsWo/042d1d01ba.png
First equation turns a function of time into frequency(notice there's no - in the exponent of e)
Second one does the opposite(notice there is a - in the exponent of e)

I searched online and found this video:

3f6aa20cac.jpg


the first equation on the left transforms function of time into frequency but there is a - this time why so?
arent they meant to be the same

Homework Equations

The Attempt at a Solution

 
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  • #2
It's just the sign of f. The video definition is more sensible. Can you guess why I say that ?
 
  • #3
Brian Douglas's videos are great.

He is the only reason why I passed Modern Control Systems. I'd watch the videos and understand the material. Prof was useless.
 
  • #4
I think the formula you were given in class is wrong. Even if it works it's completely at variance with every other transform pair I've ever encountered, and I've encountered many.
 

1. What is the basic Fourier transform equation?

The basic Fourier transform equation is an integral equation that relates a function in the time domain to its representation in the frequency domain. It is written as F(k) = ∫f(x)e-2πikxdx, where F(k) is the frequency domain representation and f(x) is the time domain representation of the function.

2. How is the Fourier transform used in signal processing?

The Fourier transform is used in signal processing to convert a signal from the time domain to the frequency domain. This allows for analysis and manipulation of the signal in terms of its frequency components, which can be useful in tasks such as filtering, compression, and noise reduction.

3. What is the difference between a Fourier transform and a Fourier series?

A Fourier transform is used for continuous signals, while a Fourier series is used for periodic signals. The Fourier transform represents a signal as a continuous spectrum of frequencies, while a Fourier series decomposes a periodic signal into a sum of sinusoidal components.

4. What are the applications of the Fourier transform in science and engineering?

The Fourier transform has a wide range of applications in science and engineering, including signal processing, image processing, data compression, and solving differential equations. It is also used in fields such as astronomy, physics, and chemistry to analyze and understand complex systems and phenomena.

5. Can the Fourier transform be computed numerically?

Yes, the Fourier transform can be computed numerically using algorithms such as the Fast Fourier Transform (FFT). These algorithms can efficiently compute the Fourier transform of a signal or data set, making it possible to use the Fourier transform in real-time applications and large-scale data analysis.

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