56 lines
1.8 KiB
Java
56 lines
1.8 KiB
Java
package com.maths;
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import java.util.ArrayList;
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/**
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* Class for circular convolution of two discrete signals using the convolution theorem.
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*
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* @author Ioannis Karavitsis
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* @version 1.0
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*/
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public class CircularConvolutionFFT {
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/**
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* This method pads the signal with zeros until it reaches the new size.
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*
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* @param x The signal to be padded.
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* @param newSize The new size of the signal.
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*/
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private static void padding(ArrayList<FFT.Complex> x, int newSize) {
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if (x.size() < newSize) {
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int diff = newSize - x.size();
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for (int i = 0; i < diff; i++) x.add(new FFT.Complex());
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}
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}
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/**
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* Discrete circular convolution function. It uses the convolution theorem for discrete signals:
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* convolved = IDFT(DFT(a)*DFT(b)). Then we use the FFT algorithm for faster calculations of the
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* two DFTs and the final IDFT.
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*
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* <p>More info: https://en.wikipedia.org/wiki/Convolution_theorem
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*
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* @param a The first signal.
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* @param b The other signal.
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* @return The convolved signal.
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*/
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public static ArrayList<FFT.Complex> fftCircularConvolution(
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ArrayList<FFT.Complex> a, ArrayList<FFT.Complex> b) {
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int convolvedSize =
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Math.max(
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a.size(), b.size()); // The two signals must have the same size equal to the bigger one
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padding(a, convolvedSize); // Zero padding the smaller signal
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padding(b, convolvedSize);
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/* 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 */
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FFTBluestein.fftBluestein(a, false);
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FFTBluestein.fftBluestein(b, false);
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ArrayList<FFT.Complex> convolved = new ArrayList<>();
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for (int i = 0; i < a.size(); i++) convolved.add(a.get(i).multiply(b.get(i))); // FFT(a)*FFT(b)
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FFTBluestein.fftBluestein(convolved, true); // IFFT
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return convolved;
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}
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}
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