Consider the periodic function given on the interval - ≤t≤ by the equation: y(t) = { I T 3 - n ≤ t ≤0; Ost≤n. 4 Q2a. Plo

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Consider The Periodic Function Given On The Interval T By The Equation Y T I T 3 N T 0 Ost N 4 Q2a Plo 1 (116.21 KiB) Viewed 51 times

Consider the periodic function given on the interval - ≤t≤ by the equation: y(t) = { I T 3 - n ≤ t ≤0; Ost≤n. 4 Q2a. Plot this function on the interval-3л≤t≤3. Q2b. Determine whether the function is odd, even or neither. Q2c. Determine the average value of the function on the period. Q2d. Find coefficients of the Fourier series for that function. Q2e. Present the Fourier series of the function in terms of the E-notation. Q2f. Present the first four terms of the Fourier series plus the zero term in the explicit form. Q2g. Find the Fourier spectrum 4 = √√² + b² where an and b, are the amplitudes of the cosine and sine Fourier harmonics respectively and plot it against n in the log-log scale. Q2h. Show that the Fourier spectrum is the decaying function of the harmonic number n and find the character of decay (exponential, power type, logarithmic-type, etc). Q2i. Plot again function y(t) together with its two approximations based on the Fourier series i) with only first harmonic and ii) with three first harmonics. Q2j. Estimate the relative accuracy of approximations in percents at the function maximum.