-
Notifications
You must be signed in to change notification settings - Fork 2
/
exampleTF.py
202 lines (181 loc) · 6.6 KB
/
exampleTF.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
# -*- coding: utf-8 -*-
"""
Created on Wed Mar 21 00:23:19 2018
Practice using Scipy functions
@author: Daryl
https://stackoverflow.com/questions/12233702/fitting-transfer-function-models-in-scipy-signal
https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.deconvolve.html
https://stackoverflow.com/questions/38146985/inverse-filtering-using-python
https://stackoverflow.com/questions/20036663/understanding-numpys-convolve
"""
from scipy.optimize import curve_fit
import scipy.signal as signal
import matplotlib.pyplot as plt
import numpy as np
plt.close('all')
def buildWFM(ftext, amptext, srate=1e5, plot=True):
wfm=np.zeros(0)
stor=np.zeros(0)
aptr=0
fstring = unicode(ftext).split()
ampString = unicode(amptext).split() #convert amplitude strings
# amp1=map(float,ampString) #map amplitude data to numbers
# fdata = map(float, fstring)
for i in range(len(fstring)):
func = fstring[i][:2]; #read first 2 strings for func
data = map(float,fstring[i][2:].split(',')); #read remainder for constant
amp1 = map(float,ampString[i].split(','))
if func == 'rm': #ramp
if data==0: print('ramp0');continue;
samp=abs(int(amp1[0]*srate/data[0]))
newpt=aptr+float(data[0])*samp/srate
stor=np.linspace(aptr,newpt,num=samp)
# print('ramp')
aptr=newpt
elif func == 'dl': #delay
samp=abs(int(srate*data[0]))
newpt=aptr+float(amp1[0]) #Amp jump during delay section
stor=np.linspace(newpt,newpt,num=samp) #Amp level during delay
# print('delay')
aptr=newpt
elif func == 'er': #build exponential rise f(t1,ttotal)=A-A*exp(-t1)
if len(data)!=2: print('Exp. needs 2 inputs (E.g.: er5,10)'); continue;
samp=abs(int(srate*data[1]))
x=np.linspace(0,data[1],num=samp)
stor=-amp1[0]*np.exp(-data[0]*x)+aptr+amp1[0]
aptr=stor[-1]
elif func == 'dr': #double exp. rise, f(t1,t2,ttotal)=A1*exp(t1)+A2*exp(t2)
if len(data)!=3: print('Exp. needs 3 inputs (E.g.: dr5,10,0.1)'); continue;
samp=abs(int(srate*data[2]))
x=np.linspace(0,data[2],num=samp)
stor=-amp1[0]*np.exp(-data[0]*x) - amp1[1]*np.exp(-data[1]*x) + aptr + (amp1[0]+amp1[1]);
aptr=stor[-1]
else: print('Badly formed function at pos%s'%(i+1))
wfm=np.hstack((wfm,stor))
wfmT=np.linspace(0, len(wfm)/srate, num=len(wfm))
if plot:
plt.figure()
plt.plot(wfmT, wfm)
return wfmT, wfm
#
def buildWave(wfm, num=3, start=0, srate=1e5, plot=True):
wfm = np.tile(wfm,num)
wfmT=np.linspace(0, len(wfm)/srate, num=len(wfm))
if plot:
plt.figure()
plt.plot(wfmT, wfm)
return wfmT, wfm
def convolveWFM(impulse, wfm, plot=True):
wfmcon = signal.convolve(impulse, wfm);
wfmT=np.linspace(0, len(wfmcon)/srate, num=len(wfmcon))
if plot:
plt.figure()
plt.plot(wfmT, wfmcon)
return wfmT, wfmcon
def buildFFT(wfm, srate=1e5, plot=True):
n = len(wfm)
d = 1./srate
hs = np.fft.fft(wfm)
hs = np.fft.fftshift(hs)
amps = np.abs(hs)
fs = np.fft.fftfreq(n, d)
fs = np.fft.fftshift(fs)
if plot:
plt.figure()
plt.semilogx(fs, 20*np.log10(amps), '.-', markersize=2)
plt.ylim([-100, plt.ylim()[1]])
return fs, hs
def deconvolveWFM(wfm, impulse_resp, plot=True):
padL = len(impulse_resp)-1
wfm = np.pad(wfm, (0,padL), 'constant')
precomp, remainder = signal.deconvolve(wfm, impulse_resp)
if plot:
plt.figure()
plt.plot(wfm)
plt.plot(precomp)
plt.xlabel('Sample')
plt.ylabel('Amplitude')
return precomp, remainder
srate=1.0e2
c = np.exp(-np.arange(10)/10)
wfmT, wfm = buildWFM('dl2 rm5 dl2 rm-.2 dl1', '0 2.5 0 2.5 0', srate=srate)
wavT, wav = buildWave(wfm, num=5, srate=srate)
wfmT, wfmcon = convolveWFM(c, wav)
buildFFT(wav, srate=srate)
#%% Smooth square wave
sig = wfm
#sig = np.repeat([0., 1.,1., 1., 0.], 1000)
sigfs, sighs = buildFFT(sig)
plt.xlabel('Freq. (Hz)')
plt.ylabel('Filter Amp. Response (dB)')
#win = signal.exponential(int(10*srate), center=0, sym=0, tau=int(1*srate))
win=signal.hann(int(10000/srate), sym=1)+1e-2*np.ones(int(10000/srate))
win=win[len(win)/2:]
win=win/sum(win)
precomp, remainder = deconvolveWFM(sig, win)
filtered = signal.convolve(sig, win, mode='full')# / sum(win)
adjusted = signal.convolve(precomp, win, mode='full')
import matplotlib.pyplot as plt
fig, (ax_orig, ax_win, ax_filt, ax_prec, ax_adjusted) = plt.subplots(5, 1, sharex=True)
ax_orig.plot(sig)
ax_orig.set_title('Original pulse')
ax_orig.margins(0, 0.1)
ax_win.plot(win)
ax_win.set_title('Filter impulse response')
ax_win.margins(0, 0.1)
ax_filt.plot(filtered)
ax_filt.set_title('Filtered signal')
ax_filt.margins(0, 0.1)
ax_prec.plot(precomp)
ax_prec.set_title('Precompensate signal')
ax_prec.margins(0, 0.1)
ax_adjusted.plot(adjusted)
ax_adjusted.set_title('Adjusted signal')
ax_adjusted.margins(0, 0.1)
fig.tight_layout()
fig.show()
#%% Convolve function, ptsC = n1+n2-1 (for n2>n1); also: 1+ |n1-n2| + 2*(min(n1,n2)-1)
original = [0, 1, 0, 0, 1, 1, 0, 0]
#original = np.ones(8)
impulse_response = [2, 1, 0]
#impulse_response = np.pad(impulse_response, (0,len(original)-len(impulse_response)), 'constant')
recorded = signal.convolve(impulse_response, original, mode='full')
recovered, remainder = signal.deconvolve(recorded, impulse_response)
print([original,recorded,recovered])
plt.figure();
plt.plot(original)
plt.plot(recorded)
plt.plot(recovered)
#%% Deconvolve function, ptsD = 1+|na-nb|. Zeropad orginal (longer wave) by nb-1
original = [0, 1, 0, 0, 1, 1, 0, 0]
#original = np.ones(8)
impulse_response = [2, 1, 0]
padL = len(impulse_response)-1
originalpd = np.pad(original, (padL,padL), 'constant')
#precomp, remainder = signal.deconvolve(original, impulse_response)
precomp, remainder = deconvolveWFM(original, impulse_response)
recorded = signal.convolve(impulse_response, precomp, mode='full')
print([original,recorded,recovered])
plt.figure();
plt.plot(original[:-padL])
plt.plot(precomp)
plt.plot(recorded[:-padL])
#%%% Impulse example 2
imp = signal.unit_impulse(100, 'mid')
b, a = signal.butter(4, 0.2)
response = signal.lfilter(b, a, imp)
plt.figure();
plt.plot(np.arange(-50, 50), imp)
plt.plot(np.arange(-50, 50), response)
plt.margins(0.1, 0.1)
plt.xlabel('Time [samples]')
plt.ylabel('Amplitude')
plt.grid(True)
plt.show()
#%% Plots
w, h = signal.freqresp(b)
plt.figure()
plt.semilogx(w, 20*np.log10(abs(h)))
ax1=plt.gca()
ax2=ax1.twinx()
plt.semilogx(w, 180./np.pi*np.unwrap(np.angle(h)), 'g')