-
Notifications
You must be signed in to change notification settings - Fork 179
/
filters.py
186 lines (137 loc) · 4.6 KB
/
filters.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
# Authors: CommPy contributors
# License: BSD 3-Clause
"""
=============================================
Pulse Shaping Filters (:mod:`commpy.filters`)
=============================================
.. autosummary::
:toctree: generated/
rcosfilter -- Raised Cosine (RC) Filter.
rrcosfilter -- Root Raised Cosine (RRC) Filter.
gaussianfilter -- Gaussian Filter.
rectfilter -- Rectangular Filter.
"""
import numpy as np
__all__=['rcosfilter', 'rrcosfilter', 'gaussianfilter', 'rectfilter']
def rcosfilter(N, alpha, Ts, Fs):
"""
Generates a raised cosine (RC) filter (FIR) impulse response.
Parameters
----------
N : int
Length of the filter in samples.
alpha : float
Roll off factor (Valid values are [0, 1]).
Ts : float
Symbol period in seconds.
Fs : float
Sampling Rate in Hz.
Returns
-------
time_idx : 1-D ndarray (float)
Array containing the time indices, in seconds, for the impulse response.
h_rc : 1-D ndarray (float)
Impulse response of the raised cosine filter.
"""
T_delta = 1/float(Fs)
time_idx = ((np.arange(N)-N/2))*T_delta
sample_num = np.arange(N)
h_rc = np.zeros(N, dtype=float)
for x in sample_num:
t = (x-N/2)*T_delta
if t == 0.0:
h_rc[x] = 1.0
elif alpha != 0 and t == Ts/(2*alpha):
h_rc[x] = (np.pi/4)*(np.sin(np.pi*t/Ts)/(np.pi*t/Ts))
elif alpha != 0 and t == -Ts/(2*alpha):
h_rc[x] = (np.pi/4)*(np.sin(np.pi*t/Ts)/(np.pi*t/Ts))
else:
h_rc[x] = (np.sin(np.pi*t/Ts)/(np.pi*t/Ts))* \
(np.cos(np.pi*alpha*t/Ts)/(1-(((2*alpha*t)/Ts)*((2*alpha*t)/Ts))))
return time_idx, h_rc
def rrcosfilter(N, alpha, Ts, Fs):
"""
Generates a root raised cosine (RRC) filter (FIR) impulse response.
Parameters
----------
N : int
Length of the filter in samples.
alpha : float
Roll off factor (Valid values are [0, 1]).
Ts : float
Symbol period in seconds.
Fs : float
Sampling Rate in Hz.
Returns
---------
time_idx : 1-D ndarray of floats
Array containing the time indices, in seconds, for
the impulse response.
h_rrc : 1-D ndarray of floats
Impulse response of the root raised cosine filter.
"""
T_delta = 1/float(Fs)
time_idx = ((np.arange(N)-N/2))*T_delta
sample_num = np.arange(N)
h_rrc = np.zeros(N, dtype=float)
for x in sample_num:
t = (x-N/2)*T_delta
if t == 0.0:
h_rrc[x] = 1.0 - alpha + (4*alpha/np.pi)
elif alpha != 0 and t == Ts/(4*alpha):
h_rrc[x] = (alpha/np.sqrt(2))*(((1+2/np.pi)* \
(np.sin(np.pi/(4*alpha)))) + ((1-2/np.pi)*(np.cos(np.pi/(4*alpha)))))
elif alpha != 0 and t == -Ts/(4*alpha):
h_rrc[x] = (alpha/np.sqrt(2))*(((1+2/np.pi)* \
(np.sin(np.pi/(4*alpha)))) + ((1-2/np.pi)*(np.cos(np.pi/(4*alpha)))))
else:
h_rrc[x] = (np.sin(np.pi*t*(1-alpha)/Ts) + \
4*alpha*(t/Ts)*np.cos(np.pi*t*(1+alpha)/Ts))/ \
(np.pi*t*(1-(4*alpha*t/Ts)*(4*alpha*t/Ts))/Ts)
return time_idx, h_rrc
def gaussianfilter(N, alpha, Ts, Fs):
"""
Generates a gaussian filter (FIR) impulse response.
Parameters
----------
N : int
Length of the filter in samples.
alpha : float
Roll off factor (Valid values are [0, 1]).
Ts : float
Symbol period in seconds.
Fs : float
Sampling Rate in Hz.
Returns
-------
time_index : 1-D ndarray of floats
Array containing the time indices for the impulse response.
h_gaussian : 1-D ndarray of floats
Impulse response of the gaussian filter.
"""
T_delta = 1/float(Fs)
time_idx = ((np.arange(N)-N/2))*T_delta
h_gaussian = (np.sqrt(np.pi)/alpha)*np.exp(-((np.pi*time_idx/alpha)*(np.pi*time_idx/alpha)))
return time_idx, h_gaussian
def rectfilter(N, Ts, Fs):
"""
Generates a rectangular filter (FIR) impulse response.
Parameters
----------
N : int
Length of the filter in samples.
Ts : float
Symbol period in seconds.
Fs : float
Sampling Rate in Hz.
Returns
-------
time_index : 1-D ndarray of floats
Array containing the time indices for the impulse response.
h_rect : 1-D ndarray of floats
Impulse response of the rectangular filter.
"""
h_rect = np.ones(N)
T_delta = 1/float(Fs)
time_idx = ((np.arange(N)-N/2))*T_delta
return time_idx, h_rect