Add tests for ConvolutionFFT

DIRECTORY.md

@@ -907,6 +907,7 @@
             * [CeilTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/CeilTest.java)
             * [CollatzConjectureTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/CollatzConjectureTest.java)
             * [CombinationsTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/CombinationsTest.java)
+            * [ConvolutionFFTTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/ConvolutionFFTTest.java)
             * [CrossCorrelationTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/CrossCorrelationTest.java)
             * [DeterminantOfMatrixTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/DeterminantOfMatrixTest.java)
             * [DigitalRootTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/DigitalRootTest.java)

src/main/java/com/thealgorithms/maths/FFT.java

@@ -164,6 +164,14 @@ public Complex divide(double n) {
             temp.img = this.img / n;
             return temp;
         }
+
+        public double real() {
+            return real;
+        }
+
+        public double imaginary() {
+            return img;
+        }
     }
 
     /**

src/test/java/com/thealgorithms/maths/ConvolutionFFTTest.java

@@ -0,0 +1,98 @@
+package com.thealgorithms.maths;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import java.util.ArrayList;
+import org.junit.jupiter.api.Test;
+
+public class ConvolutionFFTTest {
+
+    /**
+     * Helper method to create a complex signal from an array of doubles.
+     */
+    private ArrayList<FFT.Complex> createComplexSignal(double[] values) {
+        ArrayList<FFT.Complex> signal = new ArrayList<>();
+        for (double value : values) {
+            signal.add(new FFT.Complex(value, 0));
+        }
+        return signal;
+    }
+
+    /**
+     * Helper method to compare two complex signals for equality within a small margin of error.
+     */
+    private void assertComplexArrayEquals(ArrayList<FFT.Complex> expected, ArrayList<FFT.Complex> result, double delta) {
+        assertEquals(expected.size(), result.size(), "Signal lengths are not equal.");
+        for (int i = 0; i < expected.size(); i++) {
+            FFT.Complex expectedValue = expected.get(i);
+            FFT.Complex resultValue = result.get(i);
+            assertEquals(expectedValue.real(), resultValue.real(), delta, "Real part mismatch at index " + i);
+            assertEquals(expectedValue.imaginary(), resultValue.imaginary(), delta, "Imaginary part mismatch at index " + i);
+        }
+    }
+
+    @Test
+    public void testConvolutionFFTBasic() {
+        double[] a = {1, 2, 3};
+        double[] b = {4, 5, 6};
+        ArrayList<FFT.Complex> signalA = createComplexSignal(a);
+        ArrayList<FFT.Complex> signalB = createComplexSignal(b);
+
+        ArrayList<FFT.Complex> expected = createComplexSignal(new double[] {4, 13, 28, 27, 18}); // Expected output
+        ArrayList<FFT.Complex> result = ConvolutionFFT.convolutionFFT(signalA, signalB);
+
+        assertComplexArrayEquals(expected, result, 1e-9); // Allow small margin of error
+    }
+
+    @Test
+    public void testConvolutionFFTWithZeroElements() {
+        double[] a = {0, 0, 0};
+        double[] b = {1, 2, 3};
+        ArrayList<FFT.Complex> signalA = createComplexSignal(a);
+        ArrayList<FFT.Complex> signalB = createComplexSignal(b);
+
+        ArrayList<FFT.Complex> expected = createComplexSignal(new double[] {0, 0, 0, 0, 0}); // All values should be zero
+        ArrayList<FFT.Complex> result = ConvolutionFFT.convolutionFFT(signalA, signalB);
+
+        assertComplexArrayEquals(expected, result, 1e-9);
+    }
+
+    @Test
+    public void testConvolutionFFTWithDifferentSizes() {
+        double[] a = {1, 2};
+        double[] b = {3, 4, 5};
+        ArrayList<FFT.Complex> signalA = createComplexSignal(a);
+        ArrayList<FFT.Complex> signalB = createComplexSignal(b);
+
+        ArrayList<FFT.Complex> expected = createComplexSignal(new double[] {3, 10, 13, 10});
+        ArrayList<FFT.Complex> result = ConvolutionFFT.convolutionFFT(signalA, signalB);
+
+        assertComplexArrayEquals(expected, result, 1e-9);
+    }
+
+    @Test
+    public void testConvolutionFFTWithSingleElement() {
+        double[] a = {5};
+        double[] b = {2};
+        ArrayList<FFT.Complex> signalA = createComplexSignal(a);
+        ArrayList<FFT.Complex> signalB = createComplexSignal(b);
+
+        ArrayList<FFT.Complex> expected = createComplexSignal(new double[] {10});
+        ArrayList<FFT.Complex> result = ConvolutionFFT.convolutionFFT(signalA, signalB);
+
+        assertComplexArrayEquals(expected, result, 1e-9);
+    }
+
+    @Test
+    public void testConvolutionFFTWithNegativeValues() {
+        double[] a = {1, -2, 3};
+        double[] b = {-1, 2, -3};
+        ArrayList<FFT.Complex> signalA = createComplexSignal(a);
+        ArrayList<FFT.Complex> signalB = createComplexSignal(b);
+
+        ArrayList<FFT.Complex> expected = createComplexSignal(new double[] {-1, 4, -10, 12, -9});
+        ArrayList<FFT.Complex> result = ConvolutionFFT.convolutionFFT(signalA, signalB);
+
+        assertComplexArrayEquals(expected, result, 1e-9);
+    }
+}