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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 23 "Looking for Periodicity
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 36 "The c
ell below compares the function" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 259 "" 0 "" {TEXT -1 22 "f(t) = \+
sin(2 Pi 440 t)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 25 "and the clipped  function
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 43 "g(t
) = max(-0.5, min(0.5, sin(2 Pi 440 t)))" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 258 "" 0 "" {TEXT -1 17 "Evaluate it now. " }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "f := \+
t -> sin(2 * Pi * 440 * t):\ng := t -> max(-0.5, min(0.5, f(t))):\n\np
lot(\{f(t), g(t)\}, t=0..1/440);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 68 "The following cell illustrates how
 the Maple integration procedure  " }{TEXT 256 4 "int " }{TEXT -1 57 "
 can be used to work with the exercises in this module.  " }{TEXT 257 
15 "Evaluate it now" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 330 "w := 440:\nf := t -> 3 * \+
sin(2 * Pi * (440 * t + 0.15)):\n\nc := 0:\nd := 1/440:\n\na := (2/(d \+
- c)) * evalf(int(f(t) * cos(2 * Pi * w * t), t = c..d));\nb := (2/(d \+
- c)) * evalf(int(f(t) * sin(2 * Pi * w * t), t = c..d));\nA := sqrt(a
^2 + b^2);\n\ng := t -> a * cos(2 * Pi * w * t) + b * sin(2 * Pi * w *
 t):\n\nplot(\{f(t), g(t)\}, t = c..d);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 140 "The cell below carries o
ut similar computations for a \"clipped\" signal.  These computations \+
are numerically difficult.  Notice that we use  " }{TEXT 258 9 "evalf(
Int" }{TEXT -1 28 "  with an extra parameter --" }{TEXT 259 2 " 4" }
{TEXT -1 47 " -- that indicates we only need a rough answer." }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 344 "
w := 440:\nf := t -> max(-0.5, min(0.5, sin(2 * Pi * 440 * t))):\n\nc \+
:= 0:\nd := 1/440:\n\na := (2/(d - c)) * evalf(Int(f(t) * cos(2 * Pi *
 w * t), t = c..d, 4));\nb := (2/(d - c)) * evalf(Int(f(t) * sin(2 * P
i * w * t), t = c..d, 4));\nA := sqrt(a^2 + b^2);\n\ng := t -> a * cos
(2 * Pi * w * t) + b * sin(2 * Pi * w * t):\n\nplot(\{f(t), g(t)\}, t \+
= c..d);" }}}}{MARK "0 2 0" 36 }{VIEWOPTS 1 1 0 1 1 1803 }