a) The Fourier series for the sawtooth wave, otherwise , has coefficients, i. Explain why the coefficients 𝑎𝑚 are all ze

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a) The Fourier series for the sawtooth wave,

A The Fourier Series For The Sawtooth Wave Otherwise Has Coefficients I Explain Why The Coefficients Am Are All Ze 1 (10.74 KiB) Viewed 39 times

otherwise , has coefficients,

A The Fourier Series For The Sawtooth Wave Otherwise Has Coefficients I Explain Why The Coefficients Am Are All Ze 2 (8.59 KiB) Viewed 39 times

i. Explain why the coefficients 𝑎𝑚 are all zero.ii. Write down: a) the period and b) the Fourier series of thefunction S(t). You must explain why you picked the period for fullmarks.iii. Give an expression for the coefficients 𝑐𝑛 in the belowseries.

A The Fourier Series For The Sawtooth Wave Otherwise Has Coefficients I Explain Why The Coefficients Am Are All Ze 3 (8.95 KiB) Viewed 39 times

A The Fourier Series For The Sawtooth Wave Otherwise Has Coefficients I Explain Why The Coefficients Am Are All Ze 4 (9.7 KiB) Viewed 39 times

What is the Fourier transform of

A The Fourier Series For The Sawtooth Wave Otherwise Has Coefficients I Explain Why The Coefficients Am Are All Ze 5 (8.58 KiB) Viewed 39 times

A The Fourier Series For The Sawtooth Wave Otherwise Has Coefficients I Explain Why The Coefficients Am Are All Ze 6 (9.11 KiB) Viewed 39 times

A The Fourier Series For The Sawtooth Wave Otherwise Has Coefficients I Explain Why The Coefficients Am Are All Ze 7 (9.87 KiB) Viewed 39 times

For full marks, find the width of the Gaussian obtained byconvolution of normalised Gaussians with widths 𝑎1 and 𝑎2.
S(t)={tS(t±2π)​−π≤t<π otherwise ​
bm​=m2(−1)m​
S(t)=−∞∑∞​cn​eint
f(t)=e−∣t∣ is F(ω)=1+ω22​
h(t)=e−∣t∣/3
g(x)=a2π​1​e−2a2x2​
G(k)=F[g(x)](k)=e−2a2k2​