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August 27th, 2017, 02:17 PM   #1
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odd or even function

Hello dear,

I have a question in complex Fourier series:
Q:/ how do I know whether the function is even or odd? if after solving:
a$_0$ = 2$\pi$
a$_n$ = 0
b$_n$ = -2/$\pi$
C$_n$ = j/n
C$_{-n}$ = -j/n
Can you help me with that?

Last edited by skipjack; August 27th, 2017 at 05:40 PM.
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August 27th, 2017, 06:05 PM   #2
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Whether it's complex is irrelevant. Write the nth term (for non-zero n) in terms of sin and cos. For an odd function, the non-zero terms are all sin terms. For an even function, there are no non-zero sin terms.
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August 28th, 2017, 02:35 AM   #3
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clarify

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Originally Posted by skipjack View Post
Whether it's complex is irrelevant. Write the nth term (for non-zero n) in terms of sin and cos. For an odd function, the non-zero terms are all sin terms. For an even function, there are no non-zero sin terms.
Hello Dear,
can you clarify more ?
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August 28th, 2017, 03:50 AM   #4
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Originally Posted by aows61 View Post
Hello Dear,
Something is not quite right here
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August 28th, 2017, 03:54 AM   #5
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share answer

Quote:
Originally Posted by Joppy View Post
Something is not quite right here
Hello Dear,
can you share your answer?
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August 28th, 2017, 04:02 AM   #6
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Originally Posted by aows61 View Post
Hello Dear,
can you share your answer?
Sorry, i was actually referring to your use of the word 'dear'. Typically we use it when writing a formal letter. For example, "Dear aows61, how are you today?".

However use of 'dear' in the context here ('hello dear') refers to the other meaning of the word: "regarded with deep affection". One might engage with ones lover by saying "hello dear". I like skipjack too, but not that much! .
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August 28th, 2017, 06:52 AM   #7
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Quote:
Originally Posted by Joppy View Post
Sorry, i was actually referring to your use of the word 'dear'. Typically we use it when writing a formal letter. For example, "Dear aows61, how are you today?".

However use of 'dear' in the context here ('hello dear') refers to the other meaning of the word: "regarded with deep affection". One might engage with ones lover by saying "hello dear". I like skipjack too, but not that much! .
thanks for notifying and sharing this info with us,
if you have more info regarding the question, kindly share it with us...

regards,
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August 28th, 2017, 06:56 AM   #8
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Quote:
Originally Posted by aows61 View Post
Hello dear,

I have a question in complex Fourier series:
Q:/ how do I know whether the function is even or odd? if after solving:
a$_0$ = 2$\pi$
a$_n$ = 0
b$_n$ = -2/$\pi$
C$_n$ = j/n
C$_{-n}$ = -j/n
Can you help me with that?
You seem confused as to what a "Fourier series" is. The "$\displaystyle a_n, b_n$ and "$\displaystyle C_n, C_{-n}$" are different notations. We can write a Fourier series as $\displaystyle a_0+ a_1 \cos(x)+ b_1 \sin(x)+ a_2\cos(2x)+ b_2\sin(2x)+ \cdot\cdot\cdot$
The "$\displaystyle a_n$" terms are the coefficients of cos(nx) and the "$\displaystyle b_n$" terms are coefficients of sin(nx).

Since cos(nx) is an even function, for all n, and sin(nx) is an odd function, for all n, a Fourier series is "odd" if and only if "$\displaystyle b_n= 0$" for all n and "even" if and only if "$\displaystyle a_n= 0$" for all n.

We can also write a Fourier series as $\displaystyle \sum_{n=-\infty}^\infty C_ne^{inx}$. Since $\displaystyle e^{inx}= \cos(nx)+ j \sin(nx)$, $\displaystyle \cos(-nx)= \cos(nx)$ and $\displaystyle \sin(-nx)= -\sin(nx)$, that reduces to the previous case.
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Last edited by skipjack; August 28th, 2017 at 07:18 AM.
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August 28th, 2017, 07:22 AM   #9
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Isn't that the wrong way round?
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August 28th, 2017, 08:33 AM   #10
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thanks

Quote:
Originally Posted by Country Boy View Post
You seem confused as to what a "Fourier series" is. The "$\displaystyle a_n, b_n$ and "$\displaystyle C_n, C_{-n}$" are different notations. We can write a Fourier series as $\displaystyle a_0+ a_1 \cos(x)+ b_1 \sin(x)+ a_2\cos(2x)+ b_2\sin(2x)+ \cdot\cdot\cdot$
The "$\displaystyle a_n$" terms are the coefficients of cos(nx) and the "$\displaystyle b_n$" terms are coefficients of sin(nx).

Since cos(nx) is an even function, for all n, and sin(nx) is an odd function, for all n, a Fourier series is "odd" if and only if "$\displaystyle b_n= 0$" for all n and "even" if and only if "$\displaystyle a_n= 0$" for all n.

We can also write a Fourier series as $\displaystyle \sum_{n=-\infty}^\infty C_ne^{inx}$. Since $\displaystyle e^{inx}= \cos(nx)+ j \sin(nx)$, $\displaystyle \cos(-nx)= \cos(nx)$ and $\displaystyle \sin(-nx)= -\sin(nx)$, that reduces to the previous case.
I think you mean odd if a_n = 0.

and my function is this function:

$$ I(t)= \pi + \sum_{n=-\infty}^\infty \frac j n e^{jnt} $$
with the following given data:

$$ C_o=\pi $$
$$ \frac {ao} 2 = \pi $$
$$ C_n=\frac j n $$
$$C_{-n}= \frac {-j} n $$
$$ a_n=0 $$
$$ b_n=\frac {-2} n $$

and the solutions said it is neither odd nor even and I want to know why it is neither odd nor even .....

Last edited by skipjack; October 8th, 2017 at 05:09 AM.
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