Give me a explanation in simple and the definition also.

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## DIVAKAR N K

Fourier series is an expansion of periodic signal as a linear combination of sines and cosines while Fourier transform is the process or function used to convert signals from time domain in to frequency domain.

Fourier series is defined for periodic signals and the Fourier transform can be applied to aperiodic (occurring without periodicity) signals. As mentioned above, the study of Fourier series actually provides motivation for the Fourier transform.

## Ananthu007

I have attached a video listing the difference between Fourier series and Fourier transform ðŸ‘‡

## SRIBALAJY N S

The Fourier Transform is an integral transform of (complex) function defined over the entire set of real numbers. The result is the is a (likewise complex) function defined over the entire set of real numbers (frequency values).

The Fourier Series is the Fourier Transform of a periodic function. It ends up with non-trivial values only for integral multiples (harmonics) of the period of the function. There is no largest frequency value that will have a nonzero magnitude for most functions. However, for functions that are well behaved, the values at the larger harmonics drop off quickly. We normally restate the the defining integral in such a way as to draw attention to the fact that the independent variable only takes on integral values. If the function was only defined on a finite interval, we construct a function that is a periodic repetition of that interval.

The Discrete Fourier Transform (DFT) is the Fourier Transform of a function defined at integer valued points over an interval. Its results is also defined at integer valued points over the same sized interval. (That is, if the input interval is 167 samples, then the output transform has 167 frequencies.) We refer to the number of samples as the order of the transform.

Some computational peculiarities of the DFT allow us to calculate the DFT much faster if the order is a power of two. Therefore, we often either pad out input to a power of two, or collect a time series sample consisting of a power of two values. A DFT that leverages this advantage is called a Fast Fourier Transform (FFT).

## Manisha Singh

Fourier series is an expansion of periodic signal as a linear combination of sines and cosines while Fourier transform is the process or function used to convert signals from time domain in to frequency domain.

Fourier series is defined for periodic signals and the Fourier transform can be applied to aperiodic (occurring without periodicity) signals. As mentioned above, the study of Fourier series actually provides motivation for the Fourier transform.

## Gowtham2001

https://math.stackexchange.com/questions/221137/what-is-the-difference-between-fourier-series-and-fourier-transformation#:~:text=The%20Fourier%20series%20is%20used,or%20integral%20of%20complex%20exponentials.

## siva

The Fourier series is used to represent a periodic function by a discrete sum of complex exponentials, while the Fourier transform is then used to represent a general, nonperiodic function by a continuous superposition or integral of complex exponentials.

## Muhil123

definition is a statement of the meaning of a term (a word, phrase, or other set of symbols).[1][2] Definitions can be classified into two large categories, intensional definitions (which try to give the sense of a term) and extensional definitions (which try to list the objects that a term describes).[3] Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions.[4][a]

In mathematics, a definition is used to give a precise meaning to a new term, by describing a condition which unambiguously qualifies what a mathematical term is and is not.[5] Definitions and axioms form the basis on which all of modern mathematics is to be constructed.[6]