├── .gitattributes
├── .gitignore
├── README.md
└── makesomenoise.py


/.gitattributes:
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1 | # Auto detect text files and perform LF normalization
2 | * text=auto
3 | 


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/.gitignore:
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1 | 
2 | __pycache__/makesomenoise.cpython-38.pyc
3 | .ipynb_checkpoints/make-some-noise-checkpoint.ipynb
4 | 


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/README.md:
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1 | # Make some noise!
2 | By André van Schaik, \
3 | International Centre for Neuromorphic Systems, \
4 | Western Sydney University, \
5 | January 2021\
6 | \
7 | This notebook shows how to generate noise with a user defined distribution AND a user defined autocorrelation.
8 | 


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/makesomenoise.py:
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 1 | 
 2 | def makesomenoise(xi, acf, fs):
 3 |     '''
 4 |     Produces noise with a specified autocorrelation function
 5 |     
 6 |     Parameters:
 7 |     
 8 |     xi   - input noise sequence
 9 |     acf  - desired autocorrelation of the noise as a numpy array
10 |     fs.  - sample frequency of the autocorrelation and the noise
11 |     
12 |     Returns:
13 |     xo   - reordered version of xi to produce the desired acf
14 |     '''
15 |     
16 |     import numpy as np
17 | 
18 |     N = xi.shape[0]          # Get number of samples
19 |     psd = np.fft.fft(acf, N) # Calculate PSD (Power Spectral Density) from ACF
20 |     psd[0] = 0               # Zero out the DC component (remove mean)
21 |     
22 |     Af = np.sqrt(2 * np.pi * fs * N * psd) # Convert PSD to Fourier amplitudes
23 |     mx = np.mean(xi)         # Calculate mean of samples 
24 |     x  = xi - mx             # Make zero mean
25 |     xs = np.sort(x)          # Store sorted signal xs with correct PDF
26 |     k  = 1 
27 |     idxr = np.zeros(N)       # Reference index array
28 |     while(k != 0):
29 |         Fx  = np.fft.fft(x)  # Compute FT of noise
30 |         Px  = np.arctan2(np.imag(Fx), np.real(Fx))  # Get phases
31 |         # Create a signal with correct PSD and original phases
32 |         xg  = np.real(np.fft.ifft((np.exp(1.j*Px)) * np.abs(Af))) 
33 |         idx = np.argsort(xg) # Get rank indices of signal with correct PSD
34 |         x[idx] = xs          # Put original noise samples in desired rank order. 
35 |         k = k+1              # Increment counter
36 |         if (idx == idxr).all() :
37 |             print(f'Number of iterations = {k}')
38 |             k = 0            # If we converged, stop
39 |         else:
40 |             if k%500 == 0: print(f'Number of iterations = {k} ...')
41 |             idxr = idx       # Re-set ordering for next iter
42 |     x = x + mx               # Restore the original mean
43 |     return(x)
44 | 
45 | 
46 | 
47 | 
48 | 
49 | def plot_noise(xi, xo, pdf, acf, fs, range1):
50 |     '''
51 |     Helper function to plot the output noise and targets.
52 |     '''
53 |     
54 |     import matplotlib.pyplot as plt 
55 |     import numpy as np
56 |     
57 |     if 'fig' in locals():
58 |         plt.close(fig)
59 |     fig = plt.figure(figsize = (8, 8))
60 |     
61 |     dt  = 1/fs
62 |     N   = xi.size
63 |     M   = acf.size - 1
64 |     
65 |     ax1 = plt.subplot(2,1,1)
66 |     if xi.size>1000:
67 |         time = np.arange(1000)*dt
68 |         ax1.plot(time, xi[:1000], 'C0', label='input')
69 |         ax1.plot(time, xo[:1000], 'C1', label='output')
70 |     else:
71 |         time = np.arange(xi.size)*dt
72 |         ax1.plot(time, xi, 'C0', label='input')
73 |         ax1.plot(time, xo, 'C1', label='output')        
74 |     ax1.legend()
75 |     ax1.set_xlabel('time (s)')
76 |     ax1.set_title('noise sequency')
77 | 
78 |     ax2 = plt.subplot(2,2,3)
79 |     ax2.hist(xo, bins=range1, density=True, color='C0', label='output')
80 |     ax2.plot(range1, pdf, color='C1', linestyle='--', label='target')
81 |     ax2.hist(xi, bins=range1, density=True, label='input', color='C3', alpha=0.2)
82 |     ax2.legend()
83 |     ax2.set_xlabel('amplitude (AU)')
84 |     ax2.set_title('pdf')
85 | 
86 |     ax3 = plt.subplot(2,2,4)
87 |     range2 = int(M/2)
88 |     lags = np.linspace(-range2-1,range2,2*range2+1)
89 |     xcor = np.correlate(xo, xo, mode='full')/N
90 |     xcor = xcor/xcor.max()
91 |     ax3.plot(lags*dt, xcor[N-range2-1:N+range2], color='C0', label='output')
92 |     ax3.plot(lags*dt, acf, color='C1', linestyle='--', label='target') 
93 |     ax3.legend()
94 |     ax3.set_xlabel('lag (s)')
95 |     ax3.set_title('acf')


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