Difference between revisions of "Fourier Transform"
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{{WikiEntry|key=Fourier Transform|qCode=6520159}} | {{WikiEntry|key=Fourier Transform|qCode=6520159}} | ||
[[Fourier | [[Fourier Transform]] <ref> {{:Video/Introduction to the Fourier Transform}}</ref> is the next level of the Fourier Series, it comes up with a way to approximate hole functions by using exponentials <math>e^{ikx}</math> that means, unlike Fourier Series can only approximate a function on an interval, now we can approximate functions that are infinitely long. | ||
Example for Fourier transform: | Example for Fourier transform: | ||
We have a signal called <math>x(t)</math> we will represent it in terms of the time domain. We also can represent it in another way which is called <math>x(f)</math> we will represent it in terms of the frequency domain and This is why we called transformation. Fourier Transform is an equivalent representation of the signal. | We have a signal called <math>x(t)</math> we will represent it in terms of the time domain. We also can represent it in another way which is called <math>x(f)</math> we will represent it in terms of the frequency domain and This is why we called transformation. Fourier Transform is an equivalent representation of the signal. | ||
Fourier Series equation <math> f(\omega)= \int f(x) e^{-i \omega x } dx </math> <ref>{{:Video/The Fourier Series and Fourier Transform Demystified}}</ref> | Fourier Series equation <math> f(\omega)= \int f(x) e^{-i \omega x } dx </math> <ref>{{:Video/The Fourier Series and Fourier Transform Demystified}}</ref> | ||
Revision as of 11:47, 31 July 2022
Fourier Transform [1] is the next level of the Fourier Series, it comes up with a way to approximate hole functions by using exponentials that means, unlike Fourier Series can only approximate a function on an interval, now we can approximate functions that are infinitely long.
Example for Fourier transform: We have a signal called we will represent it in terms of the time domain. We also can represent it in another way which is called we will represent it in terms of the frequency domain and This is why we called transformation. Fourier Transform is an equivalent representation of the signal.
Fourier Series equation [2]
Eulers formula [3]
References
- ↑ Douglas, Brian (Jan 11, 2013). Introduction to the Fourier Transform. local page: Brian Douglas.
- ↑ Tan-Holmes, Jade (Jun 30, 2022). The Fourier Series and Fourier Transform Demystified. local page: Up and Atom.
- ↑ Tan-Holmes, Jade (Jun 30, 2022). The Fourier Series and Fourier Transform Demystified. local page: Up and Atom.
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