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Question 1 Expand the following periodic signal into its trigonometric Fourier series. Recall, the trigonometric Fourier series takes the form infty infty f(t) = a_0 + sum_{n=1} a_n cos(2pi n f_0 t) + sum_{n=1} b_n sin(2pi n f_0 t) (1) 1 0.75 s(t) 0.5 0.25 0 -2 -1 0 1 2 t (seconds) (a) What does $a_0$ represent? Estimate $a_0$ from the plot. (b) Determine the fundamental frequency, $f_0$, then calculate $a_0$. Sketch $a_0$ over a single period. (c) Find the equation for a single period of s(t). (d) Calculate $b_n$. (e) Sketch $b_n sin(2pi n f_0 t)$, for $n in {1, 2, 3}$, then sketch $sum_{n=1}^3 b_n sin(2pi n f_0 t)$. (f) Calculate $a_n$, and sketch $sum_{n=1}^3 a_n cos(2pi n f_0 t)$ (g) Is the signal even or odd?

          Question 1
Expand the following periodic signal into its trigonometric Fourier series.
Recall, the trigonometric Fourier series takes the form
infty
infty
f(t) = a_0 + sum_{n=1} a_n cos(2pi n f_0 t) + sum_{n=1} b_n sin(2pi n f_0 t)
(1)
1
0.75
s(t) 0.5
0.25
0
-2
-1
0
1
2
t (seconds)
(a) What does $a_0$ represent? Estimate $a_0$ from the plot.
(b) Determine the fundamental frequency, $f_0$, then calculate $a_0$.
Sketch $a_0$ over a single period.
(c) Find the equation for a single period of s(t).
(d) Calculate $b_n$.
(e) Sketch $b_n sin(2pi n f_0 t)$, for $n in {1, 2, 3}$, then sketch $sum_{n=1}^3 b_n sin(2pi n f_0 t)$.
(f) Calculate $a_n$, and sketch $sum_{n=1}^3 a_n cos(2pi n f_0 t)$
(g) Is the signal even or odd?

Question 1
Expand the following periodic signal into its trigonometric Fourier series.
Recall, the trigonometric Fourier series takes the form
infty
infty
f(t) = a0 + sumn=1 an cos(2pi n f0 t) + sumn=1 bn sin(2pi n f0 t)
(1)
1
0.75
s(t) 0.5
0.25
0
-2
-1
0
1
2
t (seconds)
(a) What does a0 represent? Estimate a0 from the plot.
(b) Determine the fundamental frequency, f0, then calculate a0.
Sketch a0 over a single period.
(c) Find the equation for a single period of s(t).
(d) Calculate bn.
(e) Sketch bn sin(2pi n f0 t), for n in 1, 2, 3, then sketch sumn=1^3 bn sin(2pi n f0 t).
(f) Calculate an, and sketch sumn=1^3 an cos(2pi n f0 t)
(g) Is the signal even or odd?

Added by Kenneth R.

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