Lesson_3 - Lesson3:Sinusoids Challenge2:Fibonacci...

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Lesson 3 Lesson 3:  Sinusoids Challenge 2: Fibonacci Lesson 3: Sinusoids (Chapter 2) What’s it all about   Sinusoid, complex exponentials, and phasors (Oh my)   Sinusoidal signal properties   Sinusoidal signal representation Challenge 3: Phasors
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  Lesson 3 Challenge 2 The  Fibonacci sequence  is given by  Fn  =  Fn-1 + Fn-2  for the initial  conditions  F0 =1 , F-1 =0.  F[n]={1,1,2,3,5,8,13,21,34, 55,…}.  There are some interesting  subtleties associated Fibonacci  numbers.  One is the ratio of two  successive Fibonacci integers  converges to the  golden ratio .   Experimentally determine the golden  ratio. 
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  Lesson 3 Challenge 2 Fibonacci Series production x=zeros(17) x[1]=1; x[2]=1 for (i=3:16) x[i]=x[i-1]+x[i-2] end x Columns 0 - 8    0:      0       1       1       2       3       5       8      13      21 Columns 9 - 16    0:     34      55      89     144     233     377     610     987 r=zeros(17) for (i=2:16) r[i]=x[i]/x[i-1] end r Columns 0 - 8    0:      0       0       1       2     1.5   1.667     1.6   1.625   1.615 Columns 9 - 16    0:  1.619   1.618   1.618   1.618   1.618   1.618   1.618   1.618 graph(r)
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  Lesson 3 Challenge 2 Fibonacci Ratio Converges in essentially 10 iterations: r 10 =r[10]/r[9]=1.618 (good enough)
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  Lesson 3 Lesson 3: Sinusoids Sinusoidal signal have the form x(t)= A sin( ϖ 0 t+ φ 0 ) where: A = amplitude ϖ 0  = frequency (rad./sec.) φ = phase shift (rad.) Equivalences: Fundamental frequency  f 0  =  ϖ 0 /2 π  (Hz) Fundamental period  T 0 =1/f 0  (sec.) Table 2-1 and 2-2 have useful indentities.
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This note was uploaded on 08/21/2010 for the course EEL 3135 taught by Professor ? during the Spring '08 term at University of Florida.

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Lesson_3 - Lesson3:Sinusoids Challenge2:Fibonacci...

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