import numpy as np

import matplotlib.pyplot as plt

%matplotlib inline
plt.rcParams['figure.figsize'] = (12.0, 9.0)

import random

t=np.arange(0.0,10.0,1.0/15)

tData=np.zeros(t.size,np.float32)

for i in range(t.size):
    if t[i]<2:
        tData[i]=0
    elif t[i]<3:
        tData[i]=t[i]-2
    elif t[i]<5:
        tData[i]=1
    elif t[i]<8:
        tData[i]=np.cos(0.5*np.pi*(t[i]-5));
    else:
        tData[i]=0

plt.plot(t,tData)
plt.ylim(-1.0,1.2)

oData=np.zeros(t.size,np.float32)

for i in range(oData.size):
    oData[i] = tData[i] + random.gauss(0,0.05)

plt.plot(t,tData)
plt.plot(t,oData,'.')

def SimpleAverage(data,N):
    filtered = np.zeros(data.size)
    for i in range(N):
        filtered[i]=data[i]
    for i in range(data.size):
        if i>N:
            sum=0
            for j in range(N):
                sum = sum + data[i-j]
            filtered[i] = sum/N
    return filtered

pData1=SimpleAverage(oData,5)
plt.plot(t,tData,"b")
plt.plot(t,oData,'.g')
plt.plot(t,pData1,"r")

def DoubleMovingAverage(data,N):
    filtered1 = np.zeros(data.size)
    filtered2 = np.zeros(data.size)
    for i in range(N):
        filtered1[i]=data[i]
    for i in range(N):
        filtered2[i]=filtered1[i]
    for i in range(data.size):
        if i>N:
            sum=0
            for j in range(N):
                sum = sum + data[i-j]
            filtered1[i] = sum/N
    for i in range(data.size):
        if i>N:
            sum=0
            for j in range(N):
                sum = sum + filtered1[i-j]
            filtered2[i] = sum/N
    #return filtered1*2-filtered2
    return filtered2

pData2=DoubleMovingAverage(oData,4)
pData1=SimpleAverage(oData,4)
plt.plot(t,tData,'b')
plt.plot(t,oData,'.g')
plt.plot(t,pData2,'r')
plt.plot(t,pData1,'y')

pData3=2*SimpleAverage(oData,4)-DoubleMovingAverage(oData,4)
plt.plot(t,tData,'b')
plt.plot(t,oData,'.g')
plt.plot(t,pData3,'r')

def ExponentialSmoothing(data,alpha):
    filtered = np.zeros(data.size)
    filtered[0]=alpha*data[0]
    for i in range(data.size):
        if i>0:
            filtered[i]=alpha*data[i]+(1-alpha)*filtered[i-1]
    return filtered

pData4=ExponentialSmoothing(oData,0.9)
pData5=ExponentialSmoothing(oData,0.5)
pData6=ExponentialSmoothing(oData,0.1)
plt.plot(t,tData,'b')
plt.plot(t,oData,'.g')
plt.plot(t,pData4,'r')
plt.plot(t,pData5,'k')
plt.plot(t,pData6,'y')

def DoubleExponentialSmoothing(data,alpha,gamma):
    filtered=np.zeros(data.size)
    b=np.zeros(data.size)
    b[0]=data[1]-data[0]
    filtered[0]=data[0]
    for i in range(data.size):
        filtered[i]=alpha*data[i]+(1-alpha)*(filtered[i-1]+b[i-1])
        b[i]=gamma*(filtered[i]-filtered[i-1])+(1-gamma)*b[i-1]
    return filtered

pData5=ExponentialSmoothing(oData,0.4)
pData6=DoubleExponentialSmoothing(oData,0.4,0.5)
plt.plot(t,tData,'b')
plt.plot(t,oData,'.g')
plt.plot(t,pData6,'r')
plt.plot(t,pData5,'y')