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Java/Maths/CircularConvolutionFFT.java at master · primary-code-test/Java · GitHub
primary-code-test
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CircularConvolutionFFT.java
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Maths
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CircularConvolutionFFT.java
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package
com
.
maths
;
import
java
.
util
.
ArrayList
;
/**
* Class for circular convolution of two discrete signals using the convolution theorem.
*
* @author Ioannis Karavitsis
* @version 1.0
*/
public
class
CircularConvolutionFFT
{
/**
* This method pads the signal with zeros until it reaches the new size.
*
* @param x The signal to be padded.
* @param newSize The new size of the signal.
*/
private
static
void
padding
(
ArrayList
<
FFT
.
Complex
>
x
,
int
newSize
) {
if
(
x
.
size
() <
newSize
) {
int
diff
=
newSize
-
x
.
size
();
for
(
int
i
=
0
;
i
<
diff
;
i
++)
x
.
add
(
new
FFT
.
Complex
());
}
}
/**
* Discrete circular convolution function. It uses the convolution theorem for discrete signals:
* convolved = IDFT(DFT(a)*DFT(b)). Then we use the FFT algorithm for faster calculations of the
* two DFTs and the final IDFT.
*
* <p>More info: https://en.wikipedia.org/wiki/Convolution_theorem
*
* @param a The first signal.
* @param b The other signal.
* @return The convolved signal.
*/
public
static
ArrayList
<
FFT
.
Complex
>
fftCircularConvolution
(
ArrayList
<
FFT
.
Complex
>
a
,
ArrayList
<
FFT
.
Complex
>
b
) {
int
convolvedSize
=
Math
.
max
(
a
.
size
(),
b
.
size
());
// The two signals must have the same size equal to the bigger one
padding
(
a
,
convolvedSize
);
// Zero padding the smaller signal
padding
(
b
,
convolvedSize
);
/* Find the FFTs of both signal. Here we use the Bluestein algorithm because we want the FFT to have the same length with the signal and not bigger */
FFTBluestein
.
fftBluestein
(
a
,
false
);
FFTBluestein
.
fftBluestein
(
b
,
false
);
ArrayList
<
FFT
.
Complex
>
convolved
=
new
ArrayList
<>();
for
(
int
i
=
0
;
i
<
a
.
size
();
i
++)
convolved
.
add
(
a
.
get
(
i
).
multiply
(
b
.
get
(
i
)));
// FFT(a)*FFT(b)
FFTBluestein
.
fftBluestein
(
convolved
,
true
);
// IFFT
return
convolved
;
}
}
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