In [2]:

    

import numpy as np
import matplotlib.pyplot as plt
import scipy.signal as signal
%matplotlib inline


    

In [3]:

    

x=np.arange(0,1000,0.1)
y=np.sin(x*np.pi)<0


    

In [4]:

    

k=np.ones(5)
win = signal.gaussian(6,1.0)
#filtered = signal.convolve(y, win, mode='same') / sum(win)
plt.plot(win)


    

    
Out[4]:





[<matplotlib.lines.Line2D at 0x1c0d45ecc0>]






    

In [5]:

    

sigma=np.arange(0.0,20,0.5)
sd = []
mu = []
signals = []
for s in sigma :
    win = signal.gaussian(int(6*s+1),s)
    filtered = signal.convolve(y, win, mode='same') / sum(win)
    signals.append(filtered[40:80])
    mu.append(np.mean(filtered))
    sd.append(np.std(filtered))
    
plt.figure(figsize=(15,8))
plt.subplot(1,2,2)    
plt.plot(sigma,sd)
plt.plot([0,sigma[-1]],[0,0])
plt.legend(['Measurement', 'Zero level'])
plt.title('Standard deviation as function of unsharpness')
plt.xlabel('Width of Gaussian window $\sigma_G$')
plt.ylabel('Standard deviation')
plt.subplot(1,2,1)
plt.plot(np.transpose(signals[0:20:3]))
plt.title('Filtered square wave signal')
plt.xlabel('Position')
plt.ylabel('Amplitude')
plt.legend(sigma[0:20:3])
plt.savefig('stddev_smooth_signal.png')


    

In [40]:

    

sigma=np.arange(0.0,20,0.5)
ssd = []
mmu = []

noiselevels = np.linspace(0,0.5,6)
for idx,noise in enumerate(noiselevels) :
    sd = []
    mu = []
    n=np.random.normal(0,noise,x.size)
    for s in sigma :
        
        win = signal.gaussian(int(6*s+1),s)
        filtered = signal.convolve(y, win, mode='same') / sum(win)+n
        mu.append(np.mean(filtered))
        sd.append(np.std(filtered))

    ssd.append(sd)
    mmu.append(mu)
    
plt.figure(figsize=(8,8))

for idx,sd in enumerate(ssd) :
    lbl = "$\sigma$={:0.2}".format(noiselevels[idx])
    plt.plot(sigma,sd,label=lbl)
    
plt.plot([0,sigma[-1]],[0,0],label="Zero level")
plt.legend()
plt.title('Standard deviation as function of unsharpness')
plt.xlabel('Width of Gaussian window $\sigma_G$')
plt.ylabel('Standard deviation')
plt.savefig('stddev_smooth_signal_noise.png')


    

In [13]:

    

x.size


    

    
Out[13]:





10000

In [ ]: