- 'removed' files added to project

app/src/main/java/com/example/ueberwachungssystem/Detection/Accelerometer.java

@@ -0,0 +1,108 @@
+package com.example.ueberwachungssystem.Detection;
+
+import static java.lang.Math.sqrt;
+
+import android.content.Context;
+import android.hardware.Sensor;
+import android.hardware.SensorEvent;
+import android.hardware.SensorEventListener;
+import android.hardware.SensorManager;
+
+
+/**
+ * Accelerometer inherits some methods from abstract Detector class (more info there)
+ *
+ *
+ * USE FROM MAIN ACTIVITY:
+ *
+ * Accelerometer beschleunigungssensor = new Accelerometer(this);
+ * onCreate:
+ * //Accelerometer Setup
+ * beschleunigungssensor = new Accelerometer(this, logger, textViewLog);   //logger and textview only for debugging necessary
+ * beschleunigungssensor.getSensor();
+ *
+ * //Starting Detection:
+ * beschleunigungssensor.startDetection();
+ * //Stopping Detection: also recommended at onPause to avoid unnecessary battery consumption
+ * beschleunigungssensor.stopDetection();
+ *
+ * */
+
+public class Accelerometer extends Detector implements SensorEventListener {
+
+    public SensorManager sensorManager;
+    private static final int sensorType = Sensor.TYPE_LINEAR_ACCELERATION;
+    private Sensor accelerometer;
+    private Context context;
+    boolean alarm = false;
+    //Preallocate memory for the data of each axis of the acceleration sensor
+    float x;
+    float y;
+    float z;
+    float betrag; //Betrag aller drei Achsen sqrt(x*x + y*y + z*z)
+    private DetectionReport detectionReport;
+
+    // In constructor pass Activity, Context and TextView from MainActivity in Accelerometer class
+    public Accelerometer(Context context){
+        super(); //von Detektor
+        this.context = context;
+    }
+
+    public void getSensor(){
+        sensorManager = (SensorManager)context.getSystemService(Context.SENSOR_SERVICE);
+        if(sensorManager.getSensorList(sensorType).size()==0) {
+            accelerometer = null;
+        }
+        else {
+            accelerometer = sensorManager.getSensorList(sensorType).get(0);
+        }
+    }
+
+    @Override
+    public void onSensorChanged(SensorEvent event) {
+        try {
+            checkAlarm(event);
+        } catch (InterruptedException e) {
+            throw new RuntimeException(e);
+        }
+    }
+
+    public void checkAlarm (SensorEvent event) throws InterruptedException {
+        x = event.values[0];
+        y = event.values[1];
+        z = event.values[2];
+        betrag = (float) sqrt(x*x + y*y + z*z);
+        float threshold = 1.5F;
+
+        if (!alarm) {
+            if (betrag > threshold) {
+                alarm = true;
+                reportViolation("Bewegung", betrag);
+            }
+        } else {
+            if (betrag < threshold) {
+                alarm = false;
+            } else {
+            }
+        }
+    }
+
+    @Override
+    public void onAccuracyChanged(Sensor sensor, int accuracy) {
+    }
+
+    @Override
+    public void startDetection() {
+        // entspricht void start()
+        //getSensor();
+        if (accelerometer != null) {
+            sensorManager.registerListener(this, accelerometer, SensorManager.SENSOR_DELAY_GAME);
+        }
+    }
+
+    @Override
+    public void stopDetection() {
+        // entspricht void stop()
+        sensorManager.unregisterListener(this, accelerometer);
+    }
+}

app/src/main/java/com/example/ueberwachungssystem/Detection/AudioRecorder.java

@@ -0,0 +1,74 @@
+package com.example.ueberwachungssystem.Detection;
+
+import android.content.Context;
+import android.media.MediaPlayer;
+import android.media.MediaRecorder;
+import android.widget.Toast;
+
+import java.io.File;
+import java.io.IOException;
+import java.time.LocalDateTime;
+import java.time.format.DateTimeFormatter;
+
+public class AudioRecorder {
+    private final Context context;
+    private MediaRecorder mediaRecorder = null;
+    private boolean isRecording = false;
+    private File outputDir;      // Default: in app files directory
+
+
+    public AudioRecorder (Context context) {
+        this.context = context;
+        this.outputDir = context.getFilesDir();
+    }
+
+    public void startRecording() {
+        // Handle logic
+        if (outputDir == null)
+            return;
+        if (isRecording)
+            return;
+        isRecording = true;
+
+        // Setup Audio Recorder for output Format: 3GP
+        mediaRecorder = new MediaRecorder();
+        mediaRecorder.setAudioSource(MediaRecorder.AudioSource.MIC);
+        mediaRecorder.setOutputFormat(MediaRecorder.OutputFormat.THREE_GPP);
+        mediaRecorder.setOutputFile(outputDir + "/" + generateFileName() + ".3gp");
+        mediaRecorder.setAudioEncoder(MediaRecorder.AudioEncoder.AMR_NB);
+        try {
+            mediaRecorder.prepare();
+        } catch (IOException e) {
+            e.printStackTrace();
+        }
+        mediaRecorder.start();
+    }
+
+    public void stopRecording() {
+        if (mediaRecorder != null) {
+            mediaRecorder.stop();
+            mediaRecorder.reset();
+            mediaRecorder.release();
+            mediaRecorder = null;
+            isRecording = false;
+            Toast.makeText(context, "audio recording saved", Toast.LENGTH_SHORT).show();
+        }
+    }
+
+    public boolean isRecording(){
+        return isRecording;
+    }
+
+    public void setOutputDir(File outputDir) {
+        this.outputDir = outputDir;
+    }
+
+    private String generateFileName(){
+        // Get the current timestamp
+        LocalDateTime currentTime = LocalDateTime.now();
+        // Define the format for the timestamp
+        DateTimeFormatter formatter = DateTimeFormatter.ofPattern("yyyyMMdd_HHmmss");
+        // Return the timestamp as a string
+        return currentTime.format(formatter);
+    }
+}

app/src/main/java/com/example/ueberwachungssystem/Detection/Detector.java

@@ -0,0 +1,76 @@
+package com.example.ueberwachungssystem.Detection;
+
+import android.os.CountDownTimer;
+
+import androidx.annotation.NonNull;
+import androidx.camera.core.ExperimentalGetImage;
+
+
+abstract public class Detector {
+    private OnDetectionListener listener;
+    private boolean isDetecting = false;
+    private boolean extendViolation = false;
+
+    // Countdown parameters
+    private final int COUNTDOWN_TIME = 10000;          // milliseconds
+    private final int COUNTDOWN_POLLING_TIME = 100;   // milliseconds
+
+    /** Constructor - takes context of current activity */
+    public Detector() {}
+
+
+    /** On Detection Listener - runs when violation is reported */
+    public interface OnDetectionListener {
+        void onDetection(@NonNull DetectionReport detectionReport);
+    }
+    public void setOnDetectionListener(@NonNull OnDetectionListener listener) {
+        this.listener = listener;
+    }
+
+    /** Triggers onDetectionListener - call this to trigger violation/alarm */
+    public void reportViolation(String detectionType, float amplitude) {
+        if (listener != null) {
+            if (!isDetecting) {
+                isDetecting = true;
+                DetectionReport detectionReport = new DetectionReport(true, detectionType, amplitude);
+                listener.onDetection(detectionReport);
+                startDetectionTimer(detectionType, amplitude);
+            } else {
+                extendViolation = true;
+            }
+        } else {
+            isDetecting = false;
+            extendViolation = false;
+        }
+    }
+
+    private void startDetectionTimer(String detectionType, float amplitude) {
+        isDetecting = true;
+        new CountDownTimer((long) COUNTDOWN_TIME, COUNTDOWN_POLLING_TIME) {
+            @Override
+            public void onTick(long millisUntilFinished) {
+                if (extendViolation) {
+                    extendViolation = false;
+                    startDetectionTimer(detectionType, amplitude);
+                    this.cancel();
+                }
+            }
+            @Override
+            public void onFinish() {
+                isDetecting = false;
+                DetectionReport detectionReport = new DetectionReport(false, detectionType, amplitude);
+                listener.onDetection(detectionReport);
+            }
+        }.start();
+    }
+
+    public void extendViolation(){
+        this.extendViolation = true;
+    }
+
+    /** Starts Detection (abstract method: needs to be overridden in child class) */
+    public abstract void startDetection();
+
+    /** Stops Detection (abstract method: needs to be overridden in child class) */
+    public abstract void stopDetection();
+}

app/src/main/java/com/example/ueberwachungssystem/Detection/OpenCVHelper.java

@@ -0,0 +1,109 @@
+package com.example.ueberwachungssystem.Detection;
+
+import android.graphics.Bitmap;
+import android.media.Image;
+import android.widget.ImageView;
+
+import androidx.annotation.NonNull;
+import androidx.camera.core.ExperimentalGetImage;
+import androidx.camera.core.ImageProxy;
+
+import org.opencv.android.Utils;
+import org.opencv.core.Core;
+import org.opencv.core.CvType;
+import org.opencv.core.Mat;
+import org.opencv.core.MatOfPoint;
+import org.opencv.core.Scalar;
+import org.opencv.core.Size;
+import org.opencv.imgproc.Imgproc;
+
+import java.nio.ByteBuffer;
+import java.util.ArrayList;
+import java.util.Collections;
+import java.util.List;
+
+
+@ExperimentalGetImage
+public class OpenCVHelper {
+
+    /** OpenCV helper methods **/
+    public static Mat addGaussianBlur(Mat inputMat, Size kernelSize){
+        Mat outputMat = new Mat();
+        Imgproc.GaussianBlur(inputMat, outputMat, kernelSize, 0);
+        return outputMat;
+    }
+
+    public static Mat addBlur(Mat inputMat, Size kernelSize){
+        Mat outputMat = new Mat();
+        Imgproc.blur(inputMat, outputMat, kernelSize);
+        return outputMat;
+    }
+
+    public static Mat extractYChannel(@NonNull ImageProxy imgProxy) {
+        Image img = imgProxy.getImage();
+
+        assert img != null;
+        ByteBuffer yBuffer = img.getPlanes()[0].getBuffer();
+        byte[] yData = new byte[yBuffer.remaining()];
+        yBuffer.get(yData);
+
+        Mat yMat = new Mat(img.getHeight(), img.getWidth(), CvType.CV_8UC1);
+        yMat.put(0, 0, yData);
+
+        return yMat;
+    }
+
+    public static Mat thresholdPixels(Mat inputMat, Mat previousImage, int threshold){
+        Mat diffImage = new Mat();
+        Core.absdiff(inputMat, previousImage, diffImage);
+        Mat binaryMat = new Mat();
+        Imgproc.threshold(diffImage, binaryMat, threshold, 255, Imgproc.THRESH_BINARY);
+        return binaryMat;
+    }
+
+
+    public static Mat thresholdContourArea(Mat inputMat, float areaThreshold){
+        List<MatOfPoint> contours = new ArrayList<>();
+        Mat hierarchy = new Mat();
+        Imgproc.findContours(inputMat, contours, hierarchy, Imgproc.RETR_EXTERNAL, Imgproc.CHAIN_APPROX_SIMPLE);
+
+        Mat outputMat = new Mat(inputMat.size(), inputMat.type(), new Scalar(0));
+        // Iterate over the contours and draw only the larger contours on the outputMat
+        for (MatOfPoint contour : contours) {
+            double contourArea = Imgproc.contourArea(contour);
+            if (contourArea > areaThreshold) {
+                Imgproc.drawContours(outputMat, Collections.singletonList(contour), 0, new Scalar(255), -1);
+            }
+        }
+        // Apply the outputMat as a mask to the dilatedImage
+        Mat maskedImage = new Mat();
+        inputMat.copyTo(maskedImage, outputMat);
+        return outputMat;
+    }
+
+    public static Mat dilateBinaryMat(Mat inputMat, Size kernelSize){
+        Mat dilatedMat = new Mat();
+        Mat kernel = Imgproc.getStructuringElement(Imgproc.MORPH_ELLIPSE, kernelSize);
+        Imgproc.dilate(inputMat, dilatedMat, kernel);
+        return dilatedMat;
+    }
+
+    public static int countNonZeroPixels(Mat inputImage) {
+        if (inputImage != null)
+            return Core.countNonZero(inputImage);
+        else
+            return 0;
+    }
+
+
+    public static void debugMat(Mat mat, ImageView imageView) {
+        if (imageView == null || mat == null)
+            return;
+
+        Bitmap bitmap = Bitmap.createBitmap(mat.cols(), mat.rows(), Bitmap.Config.ARGB_8888);
+        Utils.matToBitmap(mat, bitmap);
+
+        // Display the bitmap in an ImageView
+        imageView.setImageBitmap(bitmap);
+    }
+}

app/src/main/java/com/example/ueberwachungssystem/Detection/Signalverarbeitung/Complex.java

@@ -0,0 +1,148 @@
+package com.example.ueberwachungssystem.Detection.Signalverarbeitung;
+
+import java.util.Objects;
+
+public class Complex {
+    private final double re;   // the real part
+    private final double im;   // the imaginary part
+
+    // create a new object with the given real and imaginary parts
+    public Complex(double real, double imag) {
+        re = real;
+        im = imag;
+    }
+
+    // return a string representation of the invoking com.example.ueberwachungssystem.Detection.Signalverarbeitung.Complex object
+    public String toString() {
+        if (im == 0) return re + "";
+        if (re == 0) return im + "i";
+        if (im < 0) return re + " - " + (-im) + "i";
+        return re + " + " + im + "i";
+    }
+
+    // return abs/modulus/magnitude
+    public double abs() {
+        return Math.hypot(re, im);
+    }
+
+    // return angle/phase/argument, normalized to be between -pi and pi
+    public double phase() {
+        return Math.atan2(im, re);
+    }
+
+    // return a new com.example.ueberwachungssystem.Detection.Signalverarbeitung.Complex object whose value is (this + b)
+    public Complex plus(Complex b) {
+        Complex a = this;             // invoking object
+        double real = a.re + b.re;
+        double imag = a.im + b.im;
+        return new Complex(real, imag);
+    }
+
+    // return a new com.example.ueberwachungssystem.Detection.Signalverarbeitung.Complex object whose value is (this - b)
+    public Complex minus(Complex b) {
+        Complex a = this;
+        double real = a.re - b.re;
+        double imag = a.im - b.im;
+        return new Complex(real, imag);
+    }
+
+    // return a new com.example.ueberwachungssystem.Detection.Signalverarbeitung.Complex object whose value is (this * b)
+    public Complex times(Complex b) {
+        Complex a = this;
+        double real = a.re * b.re - a.im * b.im;
+        double imag = a.re * b.im + a.im * b.re;
+        return new Complex(real, imag);
+    }
+
+    // return a new object whose value is (this * alpha)
+    public Complex scale(double alpha) {
+        return new Complex(alpha * re, alpha * im);
+    }
+
+    // return a new com.example.ueberwachungssystem.Detection.Signalverarbeitung.Complex object whose value is the conjugate of this
+    public Complex conjugate() {
+        return new Complex(re, -im);
+    }
+
+    // return a new com.example.ueberwachungssystem.Detection.Signalverarbeitung.Complex object whose value is the reciprocal of this
+    public Complex reciprocal() {
+        double scale = re * re + im * im;
+        return new Complex(re / scale, -im / scale);
+    }
+
+    // return the real or imaginary part
+    public double re() {
+        return re;
+    }
+
+    public double im() {
+        return im;
+    }
+
+    // return a / b
+    public Complex divides(Complex b) {
+        Complex a = this;
+        return a.times(b.reciprocal());
+    }
+
+    // return a new com.example.ueberwachungssystem.Detection.Signalverarbeitung.Complex object whose value is the complex exponential of this
+    public Complex exp() {
+        return new Complex(Math.exp(re) * Math.cos(im), Math.exp(re) * Math.sin(im));
+    }
+
+    // return a new com.example.ueberwachungssystem.Detection.Signalverarbeitung.Complex object whose value is the complex sine of this
+    public Complex sin() {
+        return new Complex(Math.sin(re) * Math.cosh(im), Math.cos(re) * Math.sinh(im));
+    }
+
+    // return a new com.example.ueberwachungssystem.Detection.Signalverarbeitung.Complex object whose value is the complex cosine of this
+    public Complex cos() {
+        return new Complex(Math.cos(re) * Math.cosh(im), -Math.sin(re) * Math.sinh(im));
+    }
+
+    // return a new com.example.ueberwachungssystem.Detection.Signalverarbeitung.Complex object whose value is the complex tangent of this
+    public Complex tan() {
+        return sin().divides(cos());
+    }
+
+    // a static version of plus
+    public static Complex plus(Complex a, Complex b) {
+        double real = a.re + b.re;
+        double imag = a.im + b.im;
+        Complex sum = new Complex(real, imag);
+        return sum;
+    }
+
+    // See Section 3.3.
+    public boolean equals(Object x) {
+        if (x == null) return false;
+        if (this.getClass() != x.getClass()) return false;
+        Complex that = (Complex) x;
+        return (this.re == that.re) && (this.im == that.im);
+    }
+
+    // See Section 3.3.
+    public int hashCode() {
+        return Objects.hash(re, im);
+    }
+
+    // sample client for testing
+    public static void main(String[] args) {
+        Complex a = new Complex(5.0, 6.0);
+        Complex b = new Complex(-3.0, 4.0);
+
+        System.out.println("a            = " + a);
+        System.out.println("b            = " + b);
+        System.out.println("Re(a)        = " + a.re());
+        System.out.println("Im(a)        = " + a.im());
+        System.out.println("b + a        = " + b.plus(a));
+        System.out.println("a - b        = " + a.minus(b));
+        System.out.println("a * b        = " + a.times(b));
+        System.out.println("b * a        = " + b.times(a));
+        System.out.println("a / b        = " + a.divides(b));
+        System.out.println("(a / b) * b  = " + a.divides(b).times(b));
+        System.out.println("conj(a)      = " + a.conjugate());
+        System.out.println("|a|          = " + a.abs());
+        System.out.println("tan(a)       = " + a.tan());
+    }
+}

app/src/main/java/com/example/ueberwachungssystem/Detection/Signalverarbeitung/FFT.java

@@ -0,0 +1,246 @@
+package com.example.ueberwachungssystem.Detection.Signalverarbeitung;
+// Source: https://introcs.cs.princeton.edu/java/97data/FFT.java.html
+
+/******************************************************************************
+ *  Compilation:  javac FFT.java
+ *  Execution:    java FFT n
+ *  Dependencies: com.example.ueberwachungssystem.Detection.Signalverarbeitung.Complex.java
+ *
+ *  Compute the FFT and inverse FFT of a length n complex sequence
+ *  using the radix 2 Cooley-Tukey algorithm.
+ *  Bare bones implementation that runs in O(n log n) time and O(n)
+ *  space. Our goal is to optimize the clarity of the code, rather
+ *  than performance.
+ *
+ *  This implementation uses the primitive root of unity w = e^(-2 pi i / n).
+ *  Some resources use w = e^(2 pi i / n).
+ *
+ *  Reference: https://www.cs.princeton.edu/~wayne/kleinberg-tardos/pdf/05DivideAndConquerII.pdf
+ *
+ *  Limitations
+ *  -----------
+ *   -  assumes n is a power of 2
+ *
+ *   -  not the most memory efficient algorithm (because it uses
+ *      an object type for representing complex numbers and because
+ *      it re-allocates memory for the subarray, instead of doing
+ *      in-place or reusing a single temporary array)
+ *
+ *  For an in-place radix 2 Cooley-Tukey FFT, see
+ *  https://introcs.cs.princeton.edu/java/97data/InplaceFFT.java.html
+ *
+ ******************************************************************************/
+
+public class FFT {
+
+    // compute the FFT of x[], assuming its length n 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 IllegalArgumentException("n is not a power of 2");
+        }
+
+        // compute FFT of even terms
+        Complex[] even = new Complex[n / 2];
+        for (int k = 0; k < n / 2; k++) {
+            even[k] = x[2 * k];
+        }
+        Complex[] evenFFT = fft(even);
+
+        // compute FFT of odd terms
+        Complex[] odd = even;  // reuse the array (to avoid n log n space)
+        for (int k = 0; k < n / 2; k++) {
+            odd[k] = x[2 * k + 1];
+        }
+        Complex[] oddFFT = 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] = evenFFT[k].plus(wk.times(oddFFT[k]));
+            y[k + n / 2] = evenFFT[k].minus(wk.times(oddFFT[k]));
+        }
+        return y;
+    }
+
+
+    // compute the inverse FFT of x[], assuming its length n 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].scale(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 IllegalArgumentException("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);
+    }
+
+    // compute the DFT of x[] via brute force (n^2 time)
+    public static Complex[] dft(Complex[] x) {
+        int n = x.length;
+        Complex ZERO = new Complex(0, 0);
+        Complex[] y = new Complex[n];
+        for (int k = 0; k < n; k++) {
+            y[k] = ZERO;
+            for (int j = 0; j < n; j++) {
+                int power = (k * j) % n;
+                double kth = -2 * power * Math.PI / n;
+                Complex wkj = new Complex(Math.cos(kth), Math.sin(kth));
+                y[k] = y[k].plus(x[j].times(wkj));
+            }
+        }
+        return y;
+    }
+
+    // display an array of com.example.ueberwachungssystem.Detection.Signalverarbeitung.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();
+    }
+
+    /***************************************************************************
+     *  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 = Integer.parseInt(args[0]);
+        Complex[] x = new Complex[n];
+
+        // original data
+        for (int i = 0; i < n; i++) {
+            x[i] = new Complex(i, 0);
+        }
+        show(x, "x");
+
+        // FFT of original data
+        Complex[] y = fft(x);
+        show(y, "y = fft(x)");
+
+        // FFT of original data
+        Complex[] y2 = dft(x);
+        show(y2, "y2 = dft(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)");
+    }
+}
+
+