(b) A half-range periodic function of period 27 is defined as: ( 4 0 ...
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(b) A half-range periodic function of period 27 is defined as: ( 4 0<1< ww(t) %3D \0 플<r<n i. Sketch the odd periodic extension of w(t) over the range [-T, 7]. ii. Determine the coefficients ko, an, b, for the Fourier series of the even periodic extension of w(t). iii. In general, which (if any) is preferable when dealing with a half-range func- tion - the Fourier series for an even periodic extension, for an odd periodic extension, or for a periodic extension that is neither even nor odd? Explain your reasoning. 1 mark 5 marks 4 marks (b) A half-range periodic function of period 27 is defined as: ( 4 0<1< ww(t) %3D \0 플<r<n i. Sketch the odd periodic extension of w(t) over the range [-T, 7]. ii. Determine the coefficients ko, an, b, for the Fourier series of the even periodic extension of w(t). iii. In general, which (if any) is preferable when dealing with a half-range func- tion - the Fourier series for an even periodic extension, for an odd periodic extension, or for a periodic extension that is neither even nor odd? Explain your reasoning. 1 mark 5 marks 4 marks
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