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Reverse summation of a complex exponential
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In the equation below:
$$s_l(t)=sum_k=-lfloorN_sc^RB/2rfloor^lceilN_sc^RB/2rceil-1a_k^(-),l^,.e^j2pi(k+1/2)Delta f(t-N_CP,lT_s)$$
where: $0le tlt (N_CP,l+N)times T_s$ , $k^(-)=k+lfloorN_sc^RB/2rfloor$, $N = 2048$, $Delta f=15kHz$
I know the values of: $N_sc^RB$, $N_CP,l$ and $T_s$.
Simply put, I want to solve for $a_k^(-),l$ which is a vector of values. And I know all the values of the other parameters. $s_l(t)$ is a vector as well which values I know.
Is it possible to reverse the order of the equation to calculate for $a_k^(-),l$ ?
complex-analysis summation exponential-function exponential-sum
asked Jul 16 at 13:53
Khaled Ismail
61
add a comment |Â
up vote
1
down vote
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In the equation below:
$$s_l(t)=sum_k=-lfloorN_sc^RB/2rfloor^lceilN_sc^RB/2rceil-1a_k^(-),l^,.e^j2pi(k+1/2)Delta f(t-N_CP,lT_s)$$
where: $0le tlt (N_CP,l+N)times T_s$ , $k^(-)=k+lfloorN_sc^RB/2rfloor$, $N = 2048$, $Delta f=15kHz$
I know the values of: $N_sc^RB$, $N_CP,l$ and $T_s$.
Simply put, I want to solve for $a_k^(-),l$ which is a vector of values. And I know all the values of the other parameters. $s_l(t)$ is a vector as well which values I know.
Is it possible to reverse the order of the equation to calculate for $a_k^(-),l$ ?
complex-analysis summation exponential-function exponential-sum
asked Jul 16 at 13:53
Khaled Ismail
61
you are using way too many letters
– mercio
Jul 16 at 15:04
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
In the equation below:
$$s_l(t)=sum_k=-lfloorN_sc^RB/2rfloor^lceilN_sc^RB/2rceil-1a_k^(-),l^,.e^j2pi(k+1/2)Delta f(t-N_CP,lT_s)$$
where: $0le tlt (N_CP,l+N)times T_s$ , $k^(-)=k+lfloorN_sc^RB/2rfloor$, $N = 2048$, $Delta f=15kHz$
I know the values of: $N_sc^RB$, $N_CP,l$ and $T_s$.
Simply put, I want to solve for $a_k^(-),l$ which is a vector of values. And I know all the values of the other parameters. $s_l(t)$ is a vector as well which values I know.
Is it possible to reverse the order of the equation to calculate for $a_k^(-),l$ ?
complex-analysis summation exponential-function exponential-sum
asked Jul 16 at 13:53
Khaled Ismail
61
In the equation below:
$$s_l(t)=sum_k=-lfloorN_sc^RB/2rfloor^lceilN_sc^RB/2rceil-1a_k^(-),l^,.e^j2pi(k+1/2)Delta f(t-N_CP,lT_s)$$
where: $0le tlt (N_CP,l+N)times T_s$ , $k^(-)=k+lfloorN_sc^RB/2rfloor$, $N = 2048$, $Delta f=15kHz$
I know the values of: $N_sc^RB$, $N_CP,l$ and $T_s$.
Simply put, I want to solve for $a_k^(-),l$ which is a vector of values. And I know all the values of the other parameters. $s_l(t)$ is a vector as well which values I know.
Is it possible to reverse the order of the equation to calculate for $a_k^(-),l$ ?
complex-analysis summation exponential-function exponential-sum
asked Jul 16 at 13:53
Khaled Ismail
61
asked Jul 16 at 13:53
Khaled Ismail
61
asked Jul 16 at 13:53
Khaled Ismail
61
asked Jul 16 at 13:53
Khaled Ismail
61
61
you are using way too many letters
– mercio
Jul 16 at 15:04
add a comment |Â
you are using way too many letters
– mercio
Jul 16 at 15:04
you are using way too many letters
– mercio
Jul 16 at 15:04
you are using way too many letters
– mercio
Jul 16 at 15:04
add a comment |Â
1 Answer
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This is a long comment, that's why I put it as an answer. By the looks of it, this is some sort of Discrete Fourier Transform. To reverse it, you would just use the Inverse Discrete Fourier Transform.
$$X_k = sum_n=0^N-1 x_ncdot e^-frac 2pi iNkn ,$$
$$x_n = frac1N sum_k=0^N-1 X_kcdot e^i 2 pi k n / N .$$
Also, based on the facts that you used $j$ for the unit of imaginary numbers, and having units of $Hz$; I believe the context of this equation is Electrical Engineering. And Fourier Transforms are widely used in EE.
answered Jul 16 at 17:00
Ali
1,144924
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
This is a long comment, that's why I put it as an answer. By the looks of it, this is some sort of Discrete Fourier Transform. To reverse it, you would just use the Inverse Discrete Fourier Transform.
$$X_k = sum_n=0^N-1 x_ncdot e^-frac 2pi iNkn ,$$
$$x_n = frac1N sum_k=0^N-1 X_kcdot e^i 2 pi k n / N .$$
Also, based on the facts that you used $j$ for the unit of imaginary numbers, and having units of $Hz$; I believe the context of this equation is Electrical Engineering. And Fourier Transforms are widely used in EE.
answered Jul 16 at 17:00
Ali
1,144924
add a comment |Â
up vote
0
down vote
This is a long comment, that's why I put it as an answer. By the looks of it, this is some sort of Discrete Fourier Transform. To reverse it, you would just use the Inverse Discrete Fourier Transform.
$$X_k = sum_n=0^N-1 x_ncdot e^-frac 2pi iNkn ,$$
$$x_n = frac1N sum_k=0^N-1 X_kcdot e^i 2 pi k n / N .$$
Also, based on the facts that you used $j$ for the unit of imaginary numbers, and having units of $Hz$; I believe the context of this equation is Electrical Engineering. And Fourier Transforms are widely used in EE.
answered Jul 16 at 17:00
Ali
1,144924
add a comment |Â
up vote
0
down vote
up vote
0
down vote
This is a long comment, that's why I put it as an answer. By the looks of it, this is some sort of Discrete Fourier Transform. To reverse it, you would just use the Inverse Discrete Fourier Transform.
$$X_k = sum_n=0^N-1 x_ncdot e^-frac 2pi iNkn ,$$
$$x_n = frac1N sum_k=0^N-1 X_kcdot e^i 2 pi k n / N .$$
Also, based on the facts that you used $j$ for the unit of imaginary numbers, and having units of $Hz$; I believe the context of this equation is Electrical Engineering. And Fourier Transforms are widely used in EE.
answered Jul 16 at 17:00
Ali
1,144924
This is a long comment, that's why I put it as an answer. By the looks of it, this is some sort of Discrete Fourier Transform. To reverse it, you would just use the Inverse Discrete Fourier Transform.
$$X_k = sum_n=0^N-1 x_ncdot e^-frac 2pi iNkn ,$$
$$x_n = frac1N sum_k=0^N-1 X_kcdot e^i 2 pi k n / N .$$
Also, based on the facts that you used $j$ for the unit of imaginary numbers, and having units of $Hz$; I believe the context of this equation is Electrical Engineering. And Fourier Transforms are widely used in EE.
answered Jul 16 at 17:00
Ali
1,144924
answered Jul 16 at 17:00
Ali
1,144924
answered Jul 16 at 17:00
Ali
1,144924
answered Jul 16 at 17:00
Ali
1,144924
1,144924
add a comment |Â
add a comment |Â
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you are using way too many letters
– mercio
Jul 16 at 15:04