General formal for complex symmetric part of sequence x[n]
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Given:
(1) Complex Symmetric Sequence has the property:
$$x[n]=x^{*}[-n]$$
What’s the general formula for the Complex Symmetric Component of the sequence x[n], in terms of x[n] and x*[n]?
I'm guessing it's this:
$$x_{complex symetric}[n] =frac{1}{2}left(xleft[nright]+x^*left[-nright]right)$$
How to prove this equation is true or false?
sequences-and-series complex-numbers
asked Nov 13 at 19:05
Bill Moore
1176
|
show 9 more comments
up vote
0
down vote
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Given:
(1) Complex Symmetric Sequence has the property:
$$x[n]=x^{*}[-n]$$
What’s the general formula for the Complex Symmetric Component of the sequence x[n], in terms of x[n] and x*[n]?
I'm guessing it's this:
$$x_{complex symetric}[n] =frac{1}{2}left(xleft[nright]+x^*left[-nright]right)$$
How to prove this equation is true or false?
sequences-and-series complex-numbers
asked Nov 13 at 19:05
Bill Moore
1176
What does $;x^*;$ mean here? And what is $;[n];$ ?
– DonAntonio
Nov 13 at 19:08
x*[n] means the complex conjugate of x[n]. if x[n]=a[n] + i b[n], then x*[n] = a[n] - i b[n].
– Bill Moore
Nov 13 at 19:13
x[n] means that its a discrete function, that is, its only defined at integer values of n. This is in contrast to a continuous function: x(t) that can be defined at any real number t.
– Bill Moore
Nov 13 at 19:24
But then $;-x^*[n]=-a[n]+ib[n] neq a[n]+ib[n];$ ...! By the way, with $;x[n];$, do you mean $;x_n;$ ?
– DonAntonio
Nov 13 at 19:24
And if $;x;$ is a function defined on integers or naturals, what is the problem to denote its values by $;x(n);$ instead of the confusing $;x[n];$ ?
– DonAntonio
Nov 13 at 19:26
|
show 9 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Given:
(1) Complex Symmetric Sequence has the property:
$$x[n]=x^{*}[-n]$$
What’s the general formula for the Complex Symmetric Component of the sequence x[n], in terms of x[n] and x*[n]?
I'm guessing it's this:
$$x_{complex symetric}[n] =frac{1}{2}left(xleft[nright]+x^*left[-nright]right)$$
How to prove this equation is true or false?
sequences-and-series complex-numbers
asked Nov 13 at 19:05
Bill Moore
1176
Given:
(1) Complex Symmetric Sequence has the property:
$$x[n]=x^{*}[-n]$$
What’s the general formula for the Complex Symmetric Component of the sequence x[n], in terms of x[n] and x*[n]?
I'm guessing it's this:
$$x_{complex symetric}[n] =frac{1}{2}left(xleft[nright]+x^*left[-nright]right)$$
How to prove this equation is true or false?
sequences-and-series complex-numbers
sequences-and-series complex-numbers
asked Nov 13 at 19:05
Bill Moore
1176
asked Nov 13 at 19:05
Bill Moore
1176
edited Nov 21 at 16:56
asked Nov 13 at 19:05
Bill Moore
1176
asked Nov 13 at 19:05
Bill Moore
1176
asked Nov 13 at 19:05
Bill Moore
1176
1176
What does $;x^*;$ mean here? And what is $;[n];$ ?
– DonAntonio
Nov 13 at 19:08
x*[n] means the complex conjugate of x[n]. if x[n]=a[n] + i b[n], then x*[n] = a[n] - i b[n].
– Bill Moore
Nov 13 at 19:13
x[n] means that its a discrete function, that is, its only defined at integer values of n. This is in contrast to a continuous function: x(t) that can be defined at any real number t.
– Bill Moore
Nov 13 at 19:24
But then $;-x^*[n]=-a[n]+ib[n] neq a[n]+ib[n];$ ...! By the way, with $;x[n];$, do you mean $;x_n;$ ?
– DonAntonio
Nov 13 at 19:24
And if $;x;$ is a function defined on integers or naturals, what is the problem to denote its values by $;x(n);$ instead of the confusing $;x[n];$ ?
– DonAntonio
Nov 13 at 19:26
|
show 9 more comments
What does $;x^*;$ mean here? And what is $;[n];$ ?
– DonAntonio
Nov 13 at 19:08
x*[n] means the complex conjugate of x[n]. if x[n]=a[n] + i b[n], then x*[n] = a[n] - i b[n].
– Bill Moore
Nov 13 at 19:13
x[n] means that its a discrete function, that is, its only defined at integer values of n. This is in contrast to a continuous function: x(t) that can be defined at any real number t.
– Bill Moore
Nov 13 at 19:24
But then $;-x^*[n]=-a[n]+ib[n] neq a[n]+ib[n];$ ...! By the way, with $;x[n];$, do you mean $;x_n;$ ?
– DonAntonio
Nov 13 at 19:24
And if $;x;$ is a function defined on integers or naturals, what is the problem to denote its values by $;x(n);$ instead of the confusing $;x[n];$ ?
– DonAntonio
Nov 13 at 19:26
What does $;x^*;$ mean here? And what is $;[n];$ ?
– DonAntonio
Nov 13 at 19:08
What does $;x^*;$ mean here? And what is $;[n];$ ?
– DonAntonio
Nov 13 at 19:08
x*[n] means the complex conjugate of x[n]. if x[n]=a[n] + i b[n], then x*[n] = a[n] - i b[n].
– Bill Moore
Nov 13 at 19:13
x*[n] means the complex conjugate of x[n]. if x[n]=a[n] + i b[n], then x*[n] = a[n] - i b[n].
– Bill Moore
Nov 13 at 19:13
x[n] means that its a discrete function, that is, its only defined at integer values of n. This is in contrast to a continuous function: x(t) that can be defined at any real number t.
– Bill Moore
Nov 13 at 19:24
x[n] means that its a discrete function, that is, its only defined at integer values of n. This is in contrast to a continuous function: x(t) that can be defined at any real number t.
– Bill Moore
Nov 13 at 19:24
But then $;-x^*[n]=-a[n]+ib[n] neq a[n]+ib[n];$ ...! By the way, with $;x[n];$, do you mean $;x_n;$ ?
– DonAntonio
Nov 13 at 19:24
But then $;-x^*[n]=-a[n]+ib[n] neq a[n]+ib[n];$ ...! By the way, with $;x[n];$, do you mean $;x_n;$ ?
– DonAntonio
Nov 13 at 19:24
And if $;x;$ is a function defined on integers or naturals, what is the problem to denote its values by $;x(n);$ instead of the confusing $;x[n];$ ?
– DonAntonio
Nov 13 at 19:26
And if $;x;$ is a function defined on integers or naturals, what is the problem to denote its values by $;x(n);$ instead of the confusing $;x[n];$ ?
– DonAntonio
Nov 13 at 19:26
|
show 9 more comments
1 Answer
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A Conjugate Symmetric Sequence (CSS) is defined as:
$$x[n] = x^{*}[-n]$$
A Anti-Conjugate Symmetric Sequence (CAS) is defined as:
$$x[n] = - x^{*}[-n]$$
It can be shown that any sequence can be written as the sum of an CSS sequence and an CAS sequence as follows:
$$x[n] = x_{css}[n] + x_{cas}[n] $$
$$x[n] = (0.5)(x[n] + X^{*}[-n]) + (0.5)(x[n] - X^{*}[-n])$$
$$x[n] = x[n] $$
we can see that CSS Sequence is equal to:
$$x_{css}[n] = (0.5) (x[n] + x^{*}[n])$$
answered Nov 21 at 17:06
Bill Moore
1176
add a comment |
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1 Answer
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A Conjugate Symmetric Sequence (CSS) is defined as:
$$x[n] = x^{*}[-n]$$
A Anti-Conjugate Symmetric Sequence (CAS) is defined as:
$$x[n] = - x^{*}[-n]$$
It can be shown that any sequence can be written as the sum of an CSS sequence and an CAS sequence as follows:
$$x[n] = x_{css}[n] + x_{cas}[n] $$
$$x[n] = (0.5)(x[n] + X^{*}[-n]) + (0.5)(x[n] - X^{*}[-n])$$
$$x[n] = x[n] $$
we can see that CSS Sequence is equal to:
$$x_{css}[n] = (0.5) (x[n] + x^{*}[n])$$
answered Nov 21 at 17:06
Bill Moore
1176
add a comment |
up vote
0
down vote
A Conjugate Symmetric Sequence (CSS) is defined as:
$$x[n] = x^{*}[-n]$$
A Anti-Conjugate Symmetric Sequence (CAS) is defined as:
$$x[n] = - x^{*}[-n]$$
It can be shown that any sequence can be written as the sum of an CSS sequence and an CAS sequence as follows:
$$x[n] = x_{css}[n] + x_{cas}[n] $$
$$x[n] = (0.5)(x[n] + X^{*}[-n]) + (0.5)(x[n] - X^{*}[-n])$$
$$x[n] = x[n] $$
we can see that CSS Sequence is equal to:
$$x_{css}[n] = (0.5) (x[n] + x^{*}[n])$$
answered Nov 21 at 17:06
Bill Moore
1176
add a comment |
up vote
0
down vote
up vote
0
down vote
A Conjugate Symmetric Sequence (CSS) is defined as:
$$x[n] = x^{*}[-n]$$
A Anti-Conjugate Symmetric Sequence (CAS) is defined as:
$$x[n] = - x^{*}[-n]$$
It can be shown that any sequence can be written as the sum of an CSS sequence and an CAS sequence as follows:
$$x[n] = x_{css}[n] + x_{cas}[n] $$
$$x[n] = (0.5)(x[n] + X^{*}[-n]) + (0.5)(x[n] - X^{*}[-n])$$
$$x[n] = x[n] $$
we can see that CSS Sequence is equal to:
$$x_{css}[n] = (0.5) (x[n] + x^{*}[n])$$
answered Nov 21 at 17:06
Bill Moore
1176
A Conjugate Symmetric Sequence (CSS) is defined as:
$$x[n] = x^{*}[-n]$$
A Anti-Conjugate Symmetric Sequence (CAS) is defined as:
$$x[n] = - x^{*}[-n]$$
It can be shown that any sequence can be written as the sum of an CSS sequence and an CAS sequence as follows:
$$x[n] = x_{css}[n] + x_{cas}[n] $$
$$x[n] = (0.5)(x[n] + X^{*}[-n]) + (0.5)(x[n] - X^{*}[-n])$$
$$x[n] = x[n] $$
we can see that CSS Sequence is equal to:
$$x_{css}[n] = (0.5) (x[n] + x^{*}[n])$$
answered Nov 21 at 17:06
Bill Moore
1176
answered Nov 21 at 17:06
Bill Moore
1176
answered Nov 21 at 17:06
Bill Moore
1176
answered Nov 21 at 17:06
Bill Moore
1176
1176
add a comment |
add a comment |
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What does $;x^*;$ mean here? And what is $;[n];$ ?
– DonAntonio
Nov 13 at 19:08
x*[n] means the complex conjugate of x[n]. if x[n]=a[n] + i b[n], then x*[n] = a[n] - i b[n].
– Bill Moore
Nov 13 at 19:13
x[n] means that its a discrete function, that is, its only defined at integer values of n. This is in contrast to a continuous function: x(t) that can be defined at any real number t.
– Bill Moore
Nov 13 at 19:24
But then $;-x^*[n]=-a[n]+ib[n] neq a[n]+ib[n];$ ...! By the way, with $;x[n];$, do you mean $;x_n;$ ?
– DonAntonio
Nov 13 at 19:24
And if $;x;$ is a function defined on integers or naturals, what is the problem to denote its values by $;x(n);$ instead of the confusing $;x[n];$ ?
– DonAntonio
Nov 13 at 19:26