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In [36]:



    


f(x) = sin(2pi*x)+sin(4pi*x)+sin(6pi*x)



    


















    
Out[36]:








f (generic function with 1 method)

















In [37]:



    


r = 0:0.01:1.0



    


















    
Out[37]:








0.0:0.01:1.0

















In [38]:



    


A = f(r);



    











In [39]:



    


Af=fft(A)



    


















    
Out[39]:








101-element Array{Complex{Float64},1}:
 -8.77076e-15+0.0im     
      1.59432-51.2399im 
      3.15224-50.6058im 
      4.52486-48.3496im 
     -0.33826+2.70466im 
    -0.256238+1.63427im 
    -0.229232+1.21398im 
    -0.216161+0.977037im
    -0.208648+0.821107im
    -0.203871+0.709134im
    -0.200624+0.624054im
    -0.198305+0.556783im
    -0.196588+0.50199im 
             ⋮          
    -0.196588-0.50199im 
    -0.198305-0.556783im
    -0.200624-0.624054im
    -0.203871-0.709134im
    -0.208648-0.821107im
    -0.216161-0.977037im
    -0.229232-1.21398im 
    -0.256238-1.63427im 
     -0.33826-2.70466im 
      4.52486+48.3496im 
      3.15224+50.6058im 
      1.59432+51.2399im 

















In [40]:



    


using Gadfly



    











In [41]:



    


plot(x=r, y=A)



    


















    
Out[41]:









  
    x
  
  
    -1.5
    -1.0
    -0.5
    0.0
    0.5
    1.0
    1.5
    2.0
    2.5
    -1.00
    -0.95
    -0.90
    -0.85
    -0.80
    -0.75
    -0.70
    -0.65
    -0.60
    -0.55
    -0.50
    -0.45
    -0.40
    -0.35
    -0.30
    -0.25
    -0.20
    -0.15
    -0.10
    -0.05
    0.00
    0.05
    0.10
    0.15
    0.20
    0.25
    0.30
    0.35
    0.40
    0.45
    0.50
    0.55
    0.60
    0.65
    0.70
    0.75
    0.80
    0.85
    0.90
    0.95
    1.00
    1.05
    1.10
    1.15
    1.20
    1.25
    1.30
    1.35
    1.40
    1.45
    1.50
    1.55
    1.60
    1.65
    1.70
    1.75
    1.80
    1.85
    1.90
    1.95
    2.00
    -1
    0
    1
    2
    -1.0
    -0.9
    -0.8
    -0.7
    -0.6
    -0.5
    -0.4
    -0.3
    -0.2
    -0.1
    0.0
    0.1
    0.2
    0.3
    0.4
    0.5
    0.6
    0.7
    0.8
    0.9
    1.0
    1.1
    1.2
    1.3
    1.4
    1.5
    1.6
    1.7
    1.8
    1.9
    2.0
  

  
    
      
    
    
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
    
    
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
    
    
      
        
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
        
      
    
    
      
        
        
      
      
        
      
      
        
      
      
        
        
      
    
  

  
    -10
    -9
    -8
    -7
    -6
    -5
    -4
    -3
    -2
    -1
    0
    1
    2
    3
    4
    5
    6
    7
    8
    9
    10
    -9.0
    -8.8
    -8.6
    -8.4
    -8.2
    -8.0
    -7.8
    -7.6
    -7.4
    -7.2
    -7.0
    -6.8
    -6.6
    -6.4
    -6.2
    -6.0
    -5.8
    -5.6
    -5.4
    -5.2
    -5.0
    -4.8
    -4.6
    -4.4
    -4.2
    -4.0
    -3.8
    -3.6
    -3.4
    -3.2
    -3.0
    -2.8
    -2.6
    -2.4
    -2.2
    -2.0
    -1.8
    -1.6
    -1.4
    -1.2
    -1.0
    -0.8
    -0.6
    -0.4
    -0.2
    0.0
    0.2
    0.4
    0.6
    0.8
    1.0
    1.2
    1.4
    1.6
    1.8
    2.0
    2.2
    2.4
    2.6
    2.8
    3.0
    3.2
    3.4
    3.6
    3.8
    4.0
    4.2
    4.4
    4.6
    4.8
    5.0
    5.2
    5.4
    5.6
    5.8
    6.0
    6.2
    6.4
    6.6
    6.8
    7.0
    7.2
    7.4
    7.6
    7.8
    8.0
    8.2
    8.4
    8.6
    8.8
    9.0
    -10
    -5
    0
    5
    10
    -9.0
    -8.5
    -8.0
    -7.5
    -7.0
    -6.5
    -6.0
    -5.5
    -5.0
    -4.5
    -4.0
    -3.5
    -3.0
    -2.5
    -2.0
    -1.5
    -1.0
    -0.5
    0.0
    0.5
    1.0
    1.5
    2.0
    2.5
    3.0
    3.5
    4.0
    4.5
    5.0
    5.5
    6.0
    6.5
    7.0
    7.5
    8.0
    8.5
    9.0
  
  
    y
  


  
  

  
    
  





















In [46]:



    


plot(x=r, y=real(Af)/(2pi))



    


















    
Out[46]:









  
    x
  
  
    -1.5
    -1.0
    -0.5
    0.0
    0.5
    1.0
    1.5
    2.0
    2.5
    -1.00
    -0.95
    -0.90
    -0.85
    -0.80
    -0.75
    -0.70
    -0.65
    -0.60
    -0.55
    -0.50
    -0.45
    -0.40
    -0.35
    -0.30
    -0.25
    -0.20
    -0.15
    -0.10
    -0.05
    0.00
    0.05
    0.10
    0.15
    0.20
    0.25
    0.30
    0.35
    0.40
    0.45
    0.50
    0.55
    0.60
    0.65
    0.70
    0.75
    0.80
    0.85
    0.90
    0.95
    1.00
    1.05
    1.10
    1.15
    1.20
    1.25
    1.30
    1.35
    1.40
    1.45
    1.50
    1.55
    1.60
    1.65
    1.70
    1.75
    1.80
    1.85
    1.90
    1.95
    2.00
    -1
    0
    1
    2
    -1.0
    -0.9
    -0.8
    -0.7
    -0.6
    -0.5
    -0.4
    -0.3
    -0.2
    -0.1
    0.0
    0.1
    0.2
    0.3
    0.4
    0.5
    0.6
    0.7
    0.8
    0.9
    1.0
    1.1
    1.2
    1.3
    1.4
    1.5
    1.6
    1.7
    1.8
    1.9
    2.0
  

  
    
      
    
    
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
    
    
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
    
    
      
        
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
          
        
      
    
    
      
        
        
      
      
        
      
      
        
      
      
        
        
      
    
  

  
    -1.50
    -1.25
    -1.00
    -0.75
    -0.50
    -0.25
    0.00
    0.25
    0.50
    0.75
    1.00
    1.25
    1.50
    1.75
    2.00
    -1.25
    -1.20
    -1.15
    -1.10
    -1.05
    -1.00
    -0.95
    -0.90
    -0.85
    -0.80
    -0.75
    -0.70
    -0.65
    -0.60
    -0.55
    -0.50
    -0.45
    -0.40
    -0.35
    -0.30
    -0.25
    -0.20
    -0.15
    -0.10
    -0.05
    0.00
    0.05
    0.10
    0.15
    0.20
    0.25
    0.30
    0.35
    0.40
    0.45
    0.50
    0.55
    0.60
    0.65
    0.70
    0.75
    0.80
    0.85
    0.90
    0.95
    1.00
    1.05
    1.10
    1.15
    1.20
    1.25
    1.30
    1.35
    1.40
    1.45
    1.50
    1.55
    1.60
    1.65
    1.70
    1.75
    -2
    -1
    0
    1
    2
    -1.3
    -1.2
    -1.1
    -1.0
    -0.9
    -0.8
    -0.7
    -0.6
    -0.5
    -0.4
    -0.3
    -0.2
    -0.1
    0.0
    0.1
    0.2
    0.3
    0.4
    0.5
    0.6
    0.7
    0.8
    0.9
    1.0
    1.1
    1.2
    1.3
    1.4
    1.5
    1.6
    1.7
    1.8
  
  
    y
  


  
  

  
    
  





















In [ ]:

Content source: goedman/RobGoedmansNotebooks.jl

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