python实战01FFT快速傅里叶变换

本科小作业,快速傅里叶变换
python3.2

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
# Copyright (C) 2011-2012 YuanJh
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.

"""yuanJh's fft and ifft module.
the detail about fft you can see "http://en.wikipedia.org/wiki/Fast_Fourier_transform"
Main functions:
fft(a)
ifft(a)
"""
from math import *
from cmath import *
import sys
from numpy import *
pi=3.1414926

#version infomation
__version__ = '1.0'

#################### function recursive FFT ####################
def RECURSIVE_FFT(a):
"Use recursive method to realize FFT"
n=len(a)
if n==1:
return a
wn=complex(cos(-2*pi/n),sin(-2*pi/n)) #create the complex number wn=cos(-2pi/n)+sin(-2pi/n)i
w=1

a0=[]
a1=[]
for i in range(0,n-1,2):
a0.append(a[i]) #pick up the even number
a1.append(a[i+1]) #pick up the odd number

y0=RECURSIVE_FFT(a0) #translate the even part
y1=RECURSIVE_FFT(a1) #translate the odd part

y=[0 for i in range(n)]
for k in range(0,int(n/2)): #combine the even part and the odd part
y[k]=y0[k]+w*y1[k]
y[k+int(n/2)]=y0[k]-w*y1[k]
w*=wn
return y
#################### end function recursive FFT ####################

#################### function recursive IFFT ####################
def RECURSIVE_IFFT(a):
"Use recursive method to realize IFFT"
n=len(a)
if n==1:
return a
wn=complex(cos(2*pi/n),sin(2*pi/n)) #create the complex number wn=cos(2pi/n)+sin(2pi/n)i
w=1

a0=[]
a1=[]
for i in range(0,n-1,2):
a0.append(a[i]) #pick up the even number
a1.append(a[i+1]) #pick up the odd number

y0=RECURSIVE_IFFT(a0)
y1=RECURSIVE_IFFT(a1)

y=[0 for i in range(n)]
for k in range(0,int(n/2)): #combine the even part and the odd part
y[k]=y0[k]+w*y1[k]
y[k+int(n/2)]=y0[k]-w*y1[k]
w*=wn
return y
#################### end function recursive IFFT ####################

#################### got data and verify the program ####################
a=input("please input the number (use ',' split):")
a=a.split(',')
n=len(a)
#tempn=ceil(log2(n))
#tempn=tempn**2

for i in range(0,n):
a[i]=int(a[i])

#################### verify the FFT ####################
print ("the results of my program fft")
b=RECURSIVE_FFT(a)
for i in range(0,n):
print ("%4d: %4.4f+%4.4fi"%(a[i],b[i].real,b[i].imag))

print ("the results of the numpy program fft") #Use the function in the package numpy
b=fft.fft(a)
for i in range(0,n):
print ("%4d: %4.4f+%4.4fi"%(a[i],b[i].real,b[i].imag))

#################### verify the IFFT ####################
#test the my ifft program is right or not by compare with the ifft function in numpy package
print ("the results of my program ifft")
lenb=len(b)
a=RECURSIVE_IFFT(b)
for i in range(0,n):
print("%4.4f+%4.4fi: %4.4f+%4.4fi"%(b[i].real,b[i].imag,a[i].real/lenb,a[i].imag/lenb))

print ("the results of the numpy program ifft")
a=fft.ifft(b)
for i in range(0,n):
print("%4.4f+%4.4fi: %4.4f+%4.4fi"%(b[i].real,b[i].imag,a[i].real,a[i].imag))

文件名:fft.py
实现语言:PYTHON
1,系统概述
利用递归的方法实现快速傅里叶变化(FFT)和快速傅里叶逆变换(IFFT)。
2,模块层次
主要包含三部分:
1,递归实现快速傅里叶变换(FFT)。
2,快速傅里叶逆变换(IFFT)。
3,数据录入以及结果正确性验证。
3,函数声明表
def RECURSIVE_FFT(a):
功能说明:递归实现快速傅里叶变换。
参数说明:
a:需要进行快速傅里叶变换的数据,以列表(类似C,JAVA中数组)形式存储。
def RECURSIVE_IFFT(a):
功能说明:递归实现快速傅里叶逆变换,
参数说明:
a:需要进行快速傅里叶逆变换的数据,以列表(类似C,JAVA中数组)形式存储。

filename:fft.py
language:python
1,System overview
Using recursive method to realize Fast Fourier Transform (FFT) and inverse Fast Fourier Transform (IFFT).
2,Module and level
Mainly includes three parts:
1, The recursive Fast Fourier Transform(FFT).
2, Inverse Fast Fourier Transform(IFFT).
3, Got data and verify the results.
3,Function declaration table
def RECURSIVE_FFT (a):
Function introduction:recursive realize Fast Fourier Transform.
Parameters:
a: the data need for Fast Fourier Transform store as a list (similar to C, JAVA the array).
def RECURSIVE_IFFT (a):
Function introduction: recursive inverse Fast Fourier Transform.
Parameters:
a: the data need for inverse Fast Fourier Transform store as a list.
Your browser is out-of-date!

Update your browser to view this website correctly. Update my browser now

×