# Test1_THans - Take Home Part of Test I The Answers(Using...

This preview shows pages 1–4. Sign up to view the full content.

Take Home Part of Test I The Answers (Using Mathcad) Problems I & II (combined): The period: p 3 The function: First define f0(t) to be the given function for t between 0 and p, and zero elsewhere. f0 t ( ) t 0 t 1 < if 1 1 t 2 < if 3 t 2 t 3 < if 0 otherwise This "shift by np" functions uses MathCad's mod function to compute the x between 0 and p such that t=x+np for some integer n. shift_by_np t ( ) if mod t p , ( ) 0 mod t p , ( ) , p mod t p , ( ) , ( ) So f(t) is the composition of f0 with the "shift by np" function: f t ( ) f0 shift_by_np t ( ) ( ) Maximum number of terms in the Fourier partial sum : M 25 Compute the Fourier Coefficients: A 0 1 p 0 p t f t ( ) d . Note: I've set q k = 2 pw k since 2 k appears in so many of the following computations. k 1 M .. w k k p q k 2 p . w k . a k 2 p 0 p t f t ( ) cos q k t . . d . b k 2 p 0 p t f t ( ) sin q k t . . d .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
FS N t , ( ) A 0 1 N k a k cos q k t . . b k sin q k t . . = b k 0.073 0.067 0.026 0.013 0.015 9.297 10 3 . 6.131 10 3 . 7.152 10 3 . 5.083 10 3 . 3.71 10 3 . 4.331 10 3 . 3.309 10 3 . 2.557 10 3 . 2.972 10 3 . 2.371 10 3 . 4.604 10 15 . 2.198 10 3 . 1.807 10 3 . 1.486 10 3 . 1.709 10 3 . 1.437 10 3 . 1.203 10 3 . 1.378 10 3 . 1.18 10 3 . 1.002 10 3 . a k 0.39 0.117 0.018 0.034 0.023 7.441 10 3 . 0.013 0.01 4.227 10 3 . 7.189 10 3 . 6.048 10 3 . 2.846 10 3 . 4.561 10 3 . 4.014 10 3 . 2.056 10 3 . 3.21 10 3 . 2.91 10 3 . 1.628 10 3 . 2.646 10 3 . 2.271 10 3 . 1.488 10 3 . 1.933 10 3 . 1.818 10 3 . 1.096 10 3 . 1.549 10 3 . The Fourier Coefficients: k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 A 0 0.722 =
Graphs of the Function and Various Partial Sums of the Fourier Series : The Function and the 4 th Partial Sum: f t ( ) FS 4 t , ( ) t 1 0 1 2

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 11

Test1_THans - Take Home Part of Test I The Answers(Using...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online