notebook.community

Edit and run



In [9]:

    
%pylab inline
pylab.rcParams['figure.figsize'] = (15, 3)









    



Populating the interactive namespace from numpy and matplotlib



In [10]:

    
phase_inc = 2 * pi / 100;
l = 400

Calculate a buffer of sine values.



In [11]:

    
p = 0
v = []
for i in range(l):
    v.append(sin(p))
    p += phase_inc

plot(v)
grid(True)
show()
print(v[0], v[-1])









    












    



0.0 -0.06279051952942746

Fast version that caclulates followup values using one multiplication and one subtraction



In [12]:

    
si0 = sin(-phase_inc)
si1 = 0.0
fc = 2.0 * cos(phase_inc)
v = []
for i in range(l//2):
    v.append(si1)
    si0 = fc * si1 - si0
    v.append(si0)
    si1 = fc * si0 - si1

plot(v)
grid(True)
show()
print(v[0], v[-1])









    












    



0.0 -0.0627905195293102



In [18]:

    
sk = 0.0
ck = 1.0
s1 = sin(phase_inc) 
c1 = cos(phase_inc)
v = []
for i in range(l):
    v.append(sk)
    skk = c1 * sk + s1 * ck
    ck = c1 * ck - s1 * sk
    sk = skk

plot(v)
grid(True)
show()
print(v[0], v[-1])









    












    



0.0 -0.0627905195293153

Same as before but demonstrating how initializie the series with a phase != 0



In [22]:

    
phase = pi / 2.0
si0 = sin(phase - phase_inc)
si1 = sin(phase)
fc = 2.0 * cos(phase_inc)
v = []
for i in range(l//2):
    v.append(si1)
    si0 = fc * si1 - si0
    v.append(si0)
    si1 = fc * si0 - si1

plot(v)
grid(True)
show()



In [21]:

    
phase = pi / 2.0
sk = sin(-phase)
ck = cos(-phase)
s1 = sin(phase_inc) 
c1 = cos(phase_inc)
v = []
for i in range(l):
    v.append(sk)
    skk = c1 * sk + s1 * ck
    ck = c1 * ck - s1 * sk
    sk = skk

plot(v)
grid(True)
show()

Variant that demonstrates changing the frequency without reseting the phase.



In [16]:

    
sk = 0.0
ck = 1.0
s1 = sin(phase_inc) 
c1 = cos(phase_inc)
v = []
l1 = l // 3
l2 = l - l1
for i in range(l1):
    v.append(sk)
    skk = c1 * sk + s1 * ck
    ckk = c1 * ck - s1 * sk
    sk = skk
    ck = ckk
s1 = sin(phase_inc*2.0) 
c1 = cos(phase_inc*2.0)
for i in range(l2):
    v.append(sk)
    skk = c1 * sk + s1 * ck
    ckk = c1 * ck - s1 * sk
    sk = skk
    ck = ckk
    
plot(v)
grid(True)
show()



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