8 Given the following function 0

A, b, and c

8 Given the following function<br>0<t< p<br>x(t) =<br>0. p<t <2<br>x(t) = x(t+T).<br>Here T = 2<br>(8-2)<br>a) Explain why the Fourier expansion of this function does not have a term of sin(t/3 t)<br>b) Calculate the expansion of x(t), when p →0.<br>c) Discuss the issue of domain for this function (hint, show the possible domain(s)).<br>d) Instead of (8-2), if T → 00, can you have a Fourier transform of x(t) and why?<br>e) Under the condition of d), when p →0, show your Laplace transform and discuss your<br>Laplace variable.<br>

Extracted text: 8 Given the following function 0<>< p="" x(t)="0."><2 x(t)="x(t+T)." here="" t="2" (8-2)="" a)="" explain="" why="" the="" fourier="" expansion="" of="" this="" function="" does="" not="" have="" a="" term="" of="" sin(t/3="" t)="" b)="" calculate="" the="" expansion="" of="" x(t),="" when="" p="" →0.="" c)="" discuss="" the="" issue="" of="" domain="" for="" this="" function="" (hint,="" show="" the="" possible="" domain(s)).="" d)="" instead="" of="" (8-2),="" if="" t="" →="" 00,="" can="" you="" have="" a="" fourier="" transform="" of="" x(t)="" and="" why?="" e)="" under="" the="" condition="" of="" d),="" when="" p="" →0,="" show="" your="" laplace="" transform="" and="" discuss="" your="" laplace="">

Jun 05, 2022

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8 Given the following function 0

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