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 August 27th, 2017, 01:17 PM #1 Newbie   Joined: Jul 2017 From: Iraq Posts: 18 Thanks: 0 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 04:40 PM. August 27th, 2017, 05:05 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,933 Thanks: 2207 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. Thanks from aows61 August 28th, 2017, 01:35 AM   #3
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 Originally Posted by skipjack 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 ? August 28th, 2017, 02:50 AM   #4
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 Originally Posted by aows61 Hello Dear,
Something is not quite right here  August 28th, 2017, 02:54 AM   #5
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 Originally Posted by Joppy Something is not quite right here Hello Dear,
can you share your answer? August 28th, 2017, 03:02 AM   #6
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 Originally Posted by aows61 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! . August 28th, 2017, 05:52 AM   #7
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 Originally Posted by Joppy 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, August 28th, 2017, 05:56 AM   #8
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 Originally Posted by aows61 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.

Last edited by skipjack; August 28th, 2017 at 06:18 AM. August 28th, 2017, 06:22 AM #9 Global Moderator   Joined: Dec 2006 Posts: 20,933 Thanks: 2207 Isn't that the wrong way round? August 28th, 2017, 07:33 AM   #10
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 Originally Posted by Country Boy 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 04:09 AM. Tags function, odd Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post vlekje5 Pre-Calculus 11 March 27th, 2017 12:58 PM Rramos2 Advanced Statistics 5 February 11th, 2017 11:38 AM Adam Ledger Number Theory 19 May 7th, 2016 01:52 AM msgelyn Number Theory 2 January 12th, 2014 03:13 AM deSitter Algebra 4 April 10th, 2013 01:17 PM

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