# Thread: Fourier serier on a engiineering pulse.

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

You don't seem to have $n$ anywhere in your expressions.

2. ## 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.

4. ## Re: Fourier serier on a engiineering pulse.

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

5. ## 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

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

Originally Posted by jblakes
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.

7. ## 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

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

Originally Posted by jblakes
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.

9. ## 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

10. ## Re: Fourier serier on a engiineering pulse.

Originally Posted by jblakes
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

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 $n f_0$

11. ## 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

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

Originally Posted by jblakes
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

13. ## 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

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

Originally Posted by jblakes
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

15. ## 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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