-
Notifications
You must be signed in to change notification settings - Fork 1
Expand file tree
/
Copy pathFFT.java
More file actions
203 lines (168 loc) · 10.3 KB
/
FFT.java
File metadata and controls
203 lines (168 loc) · 10.3 KB
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
203
package java.fft;
public class FFT {
// compute the FFT of x[], assuming its length is a power of 2
public static Complex[] fft(Complex[] x) {
int N = x.length;
// base case
if (N == 1) return new Complex[] { x[0] };
// radix 2 Cooley-Tukey FFT
if (N % 2 != 0) { throw new RuntimeException("N is not a power of 2"); }
// fft of even terms
Complex[] even = new Complex[N/2];
for (int k = 0; k < N/2; k++) {
even[k] = x[2*k];
}
Complex[] q = fft(even);
// fft of odd terms
Complex[] odd = even; // reuse the array
for (int k = 0; k < N/2; k++) {
odd[k] = x[2*k + 1];
}
Complex[] r = fft(odd);
// combine
Complex[] y = new Complex[N];
for (int k = 0; k < N/2; k++) {
double kth = -2 * k * Math.PI / N;
Complex wk = new Complex(Math.cos(kth), Math.sin(kth));
y[k] = q[k].plus(wk.times(r[k]));
y[k + N/2] = q[k].minus(wk.times(r[k]));
}
return y;
}
// compute the inverse FFT of x[], assuming its length is a power of 2
public static Complex[] ifft(Complex[] x) {
int N = x.length;
Complex[] y = new Complex[N];
// take conjugate
for (int i = 0; i < N; i++) {
y[i] = x[i].conjugate();
}
// compute forward FFT
y = fft(y);
// take conjugate again
for (int i = 0; i < N; i++) {
y[i] = y[i].conjugate();
}
// divide by N
for (int i = 0; i < N; i++) {
y[i] = y[i].times(1.0 / N);
}
return y;
}
// compute the circular convolution of x and y
public static Complex[] cconvolve(Complex[] x, Complex[] y) {
// should probably pad x and y with 0s so that they have same length
// and are powers of 2
if (x.length != y.length) { throw new RuntimeException("Dimensions don't agree"); }
int N = x.length;
// compute FFT of each sequence
Complex[] a = fft(x);
Complex[] b = fft(y);
// point-wise multiply
Complex[] c = new Complex[N];
for (int i = 0; i < N; i++) {
c[i] = a[i].times(b[i]);
}
// compute inverse FFT
return ifft(c);
}
// compute the linear convolution of x and y
public static Complex[] convolve(Complex[] x, Complex[] y) {
Complex ZERO = new Complex(0, 0);
Complex[] a = new Complex[2*x.length];
for (int i = 0; i < x.length; i++) a[i] = x[i];
for (int i = x.length; i < 2*x.length; i++) a[i] = ZERO;
Complex[] b = new Complex[2*y.length];
for (int i = 0; i < y.length; i++) b[i] = y[i];
for (int i = y.length; i < 2*y.length; i++) b[i] = ZERO;
return cconvolve(a, b);
}
// display an array of Complex numbers to standard output
public static void show(Complex[] x, String title) {
System.out.println(title);
System.out.println("-------------------");
for (int i = 0; i < x.length; i++) {
System.out.println(x[i]);
}
System.out.println();
}
public static Complex[] YW_to_ComplexYW(double[] SZ)
{
int count = SZ.length;
Complex[] C_SZ = new Complex[count];
for (int i = 0; i < count; i++)
{
Complex d = new Complex(SZ[i],0);
C_SZ[i] = d;
}
return C_SZ;
}
/*********************************************************************
* Test client and sample execution
*
* % java FFT 4
* x
* -------------------
-0.03480425839330703 0.07910192950176387 0.7233322451735928 0.1659819820667019
*
* y = fft(x)
* -------------------
* 0.9336118983487516
* -0.7581365035668999 + 0.08688005256493803i
* 0.44344407521182005
* -0.7581365035668999 - 0.08688005256493803i
*
* z = ifft(y)
* -------------------
* -0.03480425839330703
* 0.07910192950176387 + 2.6599344570851287E-18i
* 0.7233322451735928
* 0.1659819820667019 - 2.6599344570851287E-18i
*
* c = cconvolve(x, x)
* -------------------
* 0.5506798633981853
* 0.23461407150576394 - 4.033186818023279E-18i
* -0.016542951108772352
* 0.10288019294318276 + 4.033186818023279E-18i
*
* d = convolve(x, x)
* -------------------
* 0.001211336402308083 - 3.122502256758253E-17i
* -0.005506167987577068 - 5.058885073636224E-17i
* -0.044092969479563274 + 2.1934338938072244E-18i
* 0.10288019294318276 - 3.6147323062478115E-17i
* 0.5494685269958772 + 3.122502256758253E-17i
* 0.240120239493341 + 4.655566391833896E-17i
* 0.02755001837079092 - 2.1934338938072244E-18i
* 4.01805098805014E-17i
*
*********************************************************************/
public static void main(String[] args) {
// int N = 4;
// Complex[] x = new Complex[N];
//
// // original data
// for (int i = 0; i < N; i++) {
// x[i] = new Complex(i, 0);
// x[i] = new Complex(-2*Math.random() + 1, 0);
// }
double[] realInA ={94, 94, 112, 112, 112, 94, 94, 94, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 130, 112, 112, 112, 130, 130, 130, 130, 130, 130, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 166, 148, 148, 148, 166, 166, 166, 148, 148, 148, 166, 166, 166, 166, 166, 166, 166, 166, 184, 166, 166, 166, 166, 166, 166, 166, 184, 166, 166, 166, 184, 184, 184, 184, 184, 166, 166, 166, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 166, 166, 184, 220, 184, 166, 184, 202, 184, 166, 166, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 166, 166, 166, 184, 166, 166, 166, 166, 166, 166, 166, 166, 148, 148, 148, 166, 166, 166, 166, 166, 148, 148, 148, 166, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 130, 130, 130, 148, 148, 148, 148, 148, 130, 130, 130, 148, 130, 130, 130, 130, 130, 130, 112, 112, 112, 112, 112, 112, 112, 112, 112, 130, 112, 112, 112, 112, 94, 94, 94, 112, 112, 112, 112, 112, 112, 112, 112, 112, 94, 94, 94, 112, 94, 94, 94, 94, 94, 112, 94, 94, 94, 94, 94, 112, 94, 94, 94, 112, 94, 94, 94, 94, 94, 94, 94, 94, 76, 76, 76, 76, 76, 76, 58, 58, 58, 76, 58, 58, 58, 58, 58, 58, 40, 40, 40, 40, 40, 40, 40, 58, 40, 40, 40, 58, 58, 76, 40, 22, 40, 76, 58, 40, 40, 40, 40, 58, 40, 40, 40, 58, 40, 40, 40, 58, 40, 40, 40, 58, 58, 58, 40, 40, 40, 58, 40, 40, 40, 58, 58, 58, 58, 58, 58, 58, 58, 76, 58, 58, 58, 76, 58, 58, 58, 76, 76, 76, 76, 76, 58, 58, 58, 76, 58, 58, 58, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 94, 76, 76, 76, 76, 76, 76, 76, 94, 94, 94, 94, 94, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 130, 112, 112, 112, 130, 112, 112, 112, 130, 130, 130, 130, 148, 130, 130, 130, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 166, 202, 166, 148, 166, 184, 166, 166, 166, 184, 166, 166, 166, 166, 166, 184, 166, 166, 166, 184, 184, 184, 166, 166, 166, 166, 166, 184, 184, 184, 166, 166, 166, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 166, 166, 166, 184, 166, 166, 166, 166, 166, 184, 166, 166, 166, 184, 166, 166, 166, 184, 166, 166, 166, 184, 184, 184, 184, 184, 184, 184, 184, 184, 166, 166, 166, 184, 184, 184, 184, 184, 166, 166, 166, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 166, 166, 166, 184, 166, 166, 166, 166, 166, 166, 166, 166, 166, 166, 148, 148, 148, 166, 166, 166, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 130, 130, 130, 148, 130, 112, 112, 130, 130, 130, 130, 130, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 94, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 76, 76, 76, 94, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 58, 58, 58, 76, 76, 76, 76, 76, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 76, 58, 58, 58, 76, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 40, 40, 40, 58, 58, 58, 58, 58, 58, 58, 40, 40, 40, 58, 40, 40, 58, 76, 58, 58, 58, 58, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 76, 76, 76, 58, 58, 58, 76, 58, 58, 58, 76, 58, 58, 58, 58, 58, 76, 76, 94, 76, 58, 76, 94, 76, 76, 94, 112, 112, 112, 94, 94, 94, 112, 94, 94, 94, 112, 94, 94, 112, 130, 112, 112, 94, 94, 94, 94, 94, 94, 94, 112, 112, 112, 112, 112, 112, 130, 112, 112, 112, 130, 112, 112, 112, 130, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 130, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 112, 130, 130, 130, 130, 130, 112, 112, 112, 130, 112, 112, 112, 130, 130, 130, 130, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 166, 166, 166, 148, 148, 148, 166, 166, 166, 166, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 202, 184, 184, 184, 184, 184, 202, 202, 202, 184, 184, 184, 202, 184, 184, 184, 202, 202, 202, 202, 220, 202, 184, 184, 202, 202, 202, 202, 202, 202, 202, 202, 202, 202, 202, 202, 202, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 166, 166, 166, 166, 166, 166, 166, 166, 166, 166, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 148, 130, 130, 130, 148, 130, 130, 130, 148, 130, 130, 130, 148, 130, 130, 130, 148, 130, 130, 130};
Complex[] x = YW_to_ComplexYW(realInA);
show(x, "x");
// FFT of original data
Complex[] y = fft(x);
show(y, "y = fft(x)");
// take inverse FFT
// Complex[] z = ifft(y);
// show(z, "z = ifft(y)");
//
// // circular convolution of x with itself
// Complex[] c = cconvolve(x, x);
// show(c, "c = cconvolve(x, x)");
//
// // linear convolution of x with itself
// Complex[] d = convolve(x, x);
// show(d, "d = convolve(x, x)");
}
}