Consider the function f(t) defined for t [0; 16] 0

Consider the function f(t) defined for t ∈ [0; 16]

 

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0<t<8 t+9 8<t<16 f(t)= Using integration by parts, derive a closed form expression for the following integral. It cos(at) dt a 40 You may use this expression to help with other parts of this question. Using integration by parts, derive a closed form expression for the following integral. ft sin(at) dt a 40 You may use this expression to help with other parts of this question. ods. Sketch the full-range periodic extension of f(t), showing three peri- Determine the full-range Fourier series of f(t). Sketch the even periodic extension of f(t), showing three periods. Determine the half-range cosine expansion of f(t). Sketch the odd periodic extension of f(t), showing three periods. Determine the half-range sine expansion of f(t). Which of the Fourier series converges fastest? Give a brief explana- tion for this observation. 0<t<8 t+9 8<t<16 f(t)= Using integration by parts, derive a closed form expression for the following integral. It cos(at) dt a 40 You may use this expression to help with other parts of this question. Using integration by parts, derive a closed form expression for the following integral. ft sin(at) dt a 40 You may use this expression to help with other parts of this question. ods. Sketch the full-range periodic extension of f(t), showing three peri- Determine the full-range Fourier series of f(t). Sketch the even periodic extension of f(t), showing three periods. Determine the half-range cosine expansion of f(t). Sketch the odd periodic extension of f(t), showing three periods. Determine the half-range sine expansion of f(t). Which of the Fourier series converges fastest? Give a brief explana- tion for this observation.

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Answer 1 Using integration by parts the closed form expression for the integral of cosatdt can be derived as follows cosatdt sinat asinatdt Integratin... View the full answer