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Thread: Fourier serier on a engiineering pulse.

  1. #16
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    Re: Fourier serier on a engiineering pulse.

    You don't seem to have n anywhere in your expressions.
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  2. #17
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    Re: Fourier serier on a engiineering pulse.

    i've used the formula

    An=(2/T) int f(t) cos (N2pit/2)dt

    This is the same as romsek as I seem to under stand that one better. I have come out with

    For int(3t+3)cos(ntpi/2) between -1 & 0

    I come out with -12(cos(pi*n/2)-1)/(pi^2*n^2)

    Please tell me this is correct. I have been round the houses with this one.
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  3. #18
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    Re: Fourier serier on a engiineering pulse.

    Last edited by Archie; Jan 16th 2017 at 07:42 AM.
    Thanks from jblakes
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  4. #19
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    Re: Fourier serier on a engiineering pulse.

    hrm, last night's post doesn't seem to have gone through...

    Fourier serier on a engiineering pulse.-clipboard01.jpg

    Fourier serier on a engiineering pulse.-clipboard02.jpg

    Fourier serier on a engiineering pulse.-clipboard03.jpg
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  5. #20
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    Re: Fourier serier on a engiineering pulse.

    that what I got in the end i think.

    An = ((16πnsin(3πn/2)+ (12cos(3πn/2))-(16cos(tn/2)-8)) / π^2 * n^2

    Bn= 12sin(3πn/2) - 16πncos(3πn/2) – 4sin(πn/2) / π^2 * n^2

    The only difference between my answers and yours i can see is the An you got 4 and i got 8. Slightly different from you beg formula one i used is 2/T which is 2/4, you have put 1/4, not sure which one is correct.

    Next step i guess is to sketch in the frequency domain to show that the wave is out between 600 & 800hz?

    regards
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  6. #21
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    Re: Fourier serier on a engiineering pulse.

    Quote Originally Posted by jblakes View Post
    that what I got in the end i think.

    An = ((16πnsin(3πn/2)+ (12cos(3πn/2))-(16cos(tn/2)-8)) / π^2 * n^2

    Bn= 12sin(3πn/2) - 16πncos(3πn/2) 4sin(πn/2) / π^2 * n^2

    The only difference between my answers and yours i can see is the An you got 4 and i got 8. Slightly different from you beg formula one i used is 2/T which is 2/4, you have put 1/4, not sure which one is correct.

    Next step i guess is to sketch in the frequency domain to show that the wave is out between 600 & 800hz?

    regards
    it's $\dfrac 2 T$ for $n\neq 0$

    for $a_0$ you use $\dfrac 1 T$ as $a_0$ is half the integral of the signal over a period.
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  7. #22
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    Re: Fourier serier on a engiineering pulse.

    Ah thanks that clears it up, I think i actually am starting to understand this. Apart from now i need the next bit.

    Find the amplitude at the fundamental frequency and at the next six higher harmonics.
    Make a plot of this waveform in the frequency domain, showing amplitude against frequency in Hertz.

    Can you give me an idea of how to attempt this bit?

    regards
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  8. #23
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    Re: Fourier serier on a engiineering pulse.

    Quote Originally Posted by jblakes View Post
    Ah thanks that clears it up, I think i actually am starting to understand this. Apart from now i need the next bit.

    Find the amplitude at the fundamental frequency and at the next six higher harmonics.
    Make a plot of this waveform in the frequency domain, showing amplitude against frequency in Hertz.

    Can you give me an idea of how to attempt this bit?

    regards
    the sheet I posted has all this.

    Having evaluated the general formula for the sine and cosine series in terms of $n$ simply plug in $n$.

    The fundamental frequency is $n=0$

    the final table has $\omega_n$ in KHz, the a's and b's, and then the magnitude

    I guess you should divide the $\omega$'s by $2\pi$ to get the frequency. Sorry about that.
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  9. #24
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    Re: Fourier serier on a engiineering pulse.

    Is the ω's definitely devided by 2π, i've seem some comment on net saying it souldn't be to get a frequency domain.

    regards
    Last edited by jblakes; Jan 16th 2017 at 12:47 PM. Reason: updating question
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  10. #25
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    Re: Fourier serier on a engiineering pulse.

    Quote Originally Posted by jblakes View Post
    I'm not really sure what this table is showing. How did you get the amp & frequency? what is the different values or An & Bn? i'm sure im being thick. My guess you plug n=1,2,3,4,5,6 (as per the six higher harmonics) and get the values of An & Bn, i'm guessing you then stick them in a formula to get the amp and freq?

    regards
    your period is 4ms

    so the fundamental frequency is $f_0 = 1/T = 0.25 KHz$

    the left column of the table is $2 \pi n f_0$ where $f_0$ is in KHz.

    I should have just made this $n f_0$. I apologize.

    the second column is $a_n$, the third $b_n$, the 4th $\sqrt{a_n^2 + b_n^2}$ which is the magnitude of the frequency response at $n f_0$
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  11. #26
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    Re: Fourier serier on a engiineering pulse.

    Thanks for that. Last bit of the question is,
    Does the above waveform comply with this restriction ?
    If not , can you suggest a way of circumventing this problem ?

    I'm guessing as when n=0 then frequency will be 0, i assume this means that amp will be zero. But how do i accuratly plot this to confirm out of tollerance?

    I know there is a problem and you have to increase the time range by 2.

    I'm guessing i need to just increase all the ranges i.e -2<t<0, 0<t<2, 2<t<6? and do the same as you have to get the results.

    regards
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  12. #27
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    Re: Fourier serier on a engiineering pulse.

    Quote Originally Posted by jblakes View Post
    Thanks for that. Last bit of the question is,
    Does the above waveform comply with this restriction ?
    If not , can you suggest a way of circumventing this problem ?

    I'm guessing as when n=0 then frequency will be 0, i assume this means that amp will be zero. But how do i accuratly plot this to confirm out of tollerance?

    I know there is a problem and you have to increase the time range by 2.

    I'm guessing i need to just increase all the ranges i.e -2<t<0, 0<t<2, 2<t<6? and do the same as you have to get the results.

    regards
    amplitude is given in microns

    0.1mm = 100 microns

    so you need to make sure your coefficients have amplitude less than 100
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  13. #28
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    Re: Fourier serier on a engiineering pulse.

    so from what you are saying looking at you results

    freq Amp
    0.25
    0.5 2.55453
    0.7 1.75197
    1 1.27324

    So between 500 and 1000hz the value for the amp is between 2.55453 & 1.27324 therefore doesnt comply with the restriction?.

    regards
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  14. #29
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    Re: Fourier serier on a engiineering pulse.

    Quote Originally Posted by jblakes View Post
    so from what you are saying looking at you results

    freq Amp
    0.25
    0.5 2.55453
    0.7 1.75197
    1 1.27324

    So between 500 and 1000hz the value for the amp is between 2.55453 & 1.27324 therefore doesnt comply with the restriction?.

    regards
    2.55 and 1.27 seem comfortably below 100 to me :P
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  15. #30
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    Re: Fourier serier on a engiineering pulse.

    I can only assume that the amp of 2.55 & 1.27 should be 255 & 127 respectively as I know it falls out of that range and i have to increase the time period.
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