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Discrete Fourier transform terms derivation

0

$begingroup$

According to the paper Lecture 7 - Discrete Fourier Transform we can approximate a Fourier transform
$$F(omega ) = int_ - infty ^infty f(t)e^ - jomega t$$
by the series
$$F(omega ) = sumlimits_k = 0^N - 1 f[k]e^ - jomega kT,$$

where $T$ is the sampling period, $kT$ is the $k$-th time moment. But why do they not multiply the terms of the series by the $dt = T$? And why are there no negative frequencies?

numerical-methods fourier-analysis fourier-series fourier-transform

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edited Apr 8 at 13:56

Masacroso

13.1k41748

asked Apr 8 at 12:15

James FlashJames Flash

1

New contributor

James Flash is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment | 

0

$begingroup$

According to the paper Lecture 7 - Discrete Fourier Transform we can approximate a Fourier transform
$$F(omega ) = int_ - infty ^infty f(t)e^ - jomega t$$
by the series
$$F(omega ) = sumlimits_k = 0^N - 1 f[k]e^ - jomega kT,$$

where $T$ is the sampling period, $kT$ is the $k$-th time moment. But why do they not multiply the terms of the series by the $dt = T$? And why are there no negative frequencies?

numerical-methods fourier-analysis fourier-series fourier-transform

share|cite|improve this question

edited Apr 8 at 13:56

Masacroso

13.1k41748

asked Apr 8 at 12:15

James FlashJames Flash

1

New contributor

James Flash is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

$begingroup$

According to the paper Lecture 7 - Discrete Fourier Transform we can approximate a Fourier transform
$$F(omega ) = int_ - infty ^infty f(t)e^ - jomega t$$
by the series
$$F(omega ) = sumlimits_k = 0^N - 1 f[k]e^ - jomega kT,$$

where $T$ is the sampling period, $kT$ is the $k$-th time moment. But why do they not multiply the terms of the series by the $dt = T$? And why are there no negative frequencies?

numerical-methods fourier-analysis fourier-series fourier-transform

share|cite|improve this question

edited Apr 8 at 13:56

Masacroso

13.1k41748

asked Apr 8 at 12:15

James FlashJames Flash

1

New contributor

James Flash is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

edited Apr 8 at 13:56

Masacroso

13.1k41748

asked Apr 8 at 12:15

James FlashJames Flash

1

New contributor

James Flash is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

edited Apr 8 at 13:56

Masacroso

13.1k41748

asked Apr 8 at 12:15

James FlashJames Flash

1

New contributor

James Flash is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

edited Apr 8 at 13:56

Masacroso

13.1k41748

edited Apr 8 at 13:56

Masacroso

13.1k41748

asked Apr 8 at 12:15

James FlashJames Flash

1

New contributor

James Flash is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked Apr 8 at 12:15

James FlashJames Flash

1