Merge of MicrophoneDetector

# Conflicts:
#	app/build.gradle
#	app/src/main/AndroidManifest.xml
#	app/src/main/java/com/example/ueberwachungssystem/MainActivity.java
#	app/src/main/res/layout/activity_main.xml
#	gradle.properties

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

@@ -0,0 +1,419 @@
+package com.example.ueberwachungssystem.Detection;
+
+import static java.lang.Math.*;
+
+import android.Manifest;
+import android.app.Activity;
+import android.content.Context;
+import android.content.pm.PackageManager;
+import android.media.AudioFormat;
+import android.media.AudioRecord;
+import android.media.MediaRecorder;
+import android.os.AsyncTask;
+import android.util.Log;
+
+import androidx.core.app.ActivityCompat;
+import androidx.core.content.ContextCompat;
+
+import com.example.ueberwachungssystem.Detection.Signalverarbeitung.Complex;
+import com.example.ueberwachungssystem.Detection.Signalverarbeitung.FFT;
+import com.example.ueberwachungssystem.Detector.DetectionReport;
+import com.example.ueberwachungssystem.Detector.Detector;
+
+public class MicrophoneDetector extends Detector {
+    /**
+     * Constructor - takes context of current activity
+     *
+     * @param context
+     */
+
+    private static final int RECHTEANFORDERUNG_MIKROFON = 1;
+
+    private AufnahmeTask aufnahmeTask;
+    public boolean armed = false;
+    public int Schwellwert_Alarm = 100;
+    private Activity MainActivityForClass;
+
+    public MicrophoneDetector(Context context) {
+        super(context);
+        MainActivityForClass = (Activity) context;
+
+        if (!istZugriffAufMikrofonErlaubt()) {
+            zugriffAufMikrofonAnfordern();
+        }
+    }
+
+    @Override
+    public void startDetection() {
+
+        if (!istZugriffAufMikrofonErlaubt()) {
+            zugriffAufMikrofonAnfordern();
+        }
+        if (istZugriffAufMikrofonErlaubt()) {
+            aufnahmeTask = new AufnahmeTask();
+            aufnahmeTask.execute();
+        }
+    }
+
+    @Override
+    public void stopDetection() {
+        if (aufnahmeTask != null) {
+            aufnahmeTask.cancel(true);
+        }
+    }
+
+    private boolean istZugriffAufMikrofonErlaubt() {
+        if (ContextCompat.checkSelfPermission(MainActivityForClass, android.Manifest.permission.RECORD_AUDIO) != PackageManager.PERMISSION_GRANTED) {
+            Log.d("0","Zugriff auf Mikrofon ist verboten.");
+            return false;
+        } else {
+            Log.d("0","Zugriff auf Mikrofon ist erlaubt.");
+            return true;
+        }
+    }
+
+    private void zugriffAufMikrofonAnfordern() {
+        ActivityCompat.requestPermissions(MainActivityForClass, new String[]{Manifest.permission.RECORD_AUDIO}, RECHTEANFORDERUNG_MIKROFON);
+    }
+
+    class AufnahmeTask extends AsyncTask<Long, Verarbeitungsergebnis, Void> {
+        private AudioRecord recorder;
+        private final int sampleRateInHz = 44100;
+        private final int channelConfig = AudioFormat.CHANNEL_IN_MONO;
+        private final int audioFormat = AudioFormat.ENCODING_PCM_16BIT;
+        private int minPufferGroesseInBytes;
+        private int pufferGroesseInBytes;
+        private RingPuffer ringPuffer = new RingPuffer(10);
+        private float kalibierWert;
+        private com.example.ueberwachungssystem.Detector.DetectionReport detectionReport;
+
+        AufnahmeTask() {
+            minPufferGroesseInBytes = AudioRecord.getMinBufferSize(sampleRateInHz, channelConfig, audioFormat);
+            pufferGroesseInBytes = minPufferGroesseInBytes * 2;
+            if (ActivityCompat.checkSelfPermission(MainActivityForClass, Manifest.permission.RECORD_AUDIO) != PackageManager.PERMISSION_GRANTED) {
+                // TODO: Consider calling
+                //    ActivityCompat#requestPermissions
+                // here to request the missing permissions, and then overriding
+                //   public void onRequestPermissionsResult(int requestCode, String[] permissions,
+                //                                          int[] grantResults)
+                // to handle the case where the user grants the permission. See the documentation
+                // for ActivityCompat#requestPermissions for more details.
+                ActivityCompat.requestPermissions(MainActivityForClass, new String[]{Manifest.permission.RECORD_AUDIO}, RECHTEANFORDERUNG_MIKROFON);
+            }
+
+            recorder = new AudioRecord(MediaRecorder.AudioSource.MIC, sampleRateInHz, channelConfig, audioFormat, pufferGroesseInBytes);
+
+            Log.d("0","Puffergroeße: "+ minPufferGroesseInBytes + " " + pufferGroesseInBytes);
+            Log.d("0","Recorder (SR, CH): "+ recorder.getSampleRate() + " " + recorder.getChannelCount());
+
+            int anzahlBytesProAbtastwert;
+            String s;
+            switch (recorder.getAudioFormat()) {
+                case AudioFormat.ENCODING_PCM_8BIT:
+                    s = "8 Bit PCM ";
+                    anzahlBytesProAbtastwert = 1;
+                    break;
+                case AudioFormat.ENCODING_PCM_16BIT:
+                    s = "16 Bit PCM";
+                    anzahlBytesProAbtastwert = 2;
+                    break;
+                case AudioFormat.ENCODING_PCM_FLOAT:
+                    s = "Float PCM";
+                    anzahlBytesProAbtastwert = 4;
+                    break;
+                default:
+                    throw new IllegalArgumentException();
+            }
+
+            switch (recorder.getChannelConfiguration()) {
+                case AudioFormat.CHANNEL_IN_MONO:
+                    s = "Mono";
+                    break;
+                case AudioFormat.CHANNEL_IN_STEREO:
+                    s = "Stereo";
+                    anzahlBytesProAbtastwert *= 2;
+                    break;
+                case AudioFormat.CHANNEL_INVALID:
+                    s = "ungültig";
+                    break;
+                default:
+                    throw new IllegalArgumentException();
+            }
+
+            Log.d("0","Konfiguration: "+ s);
+
+            int pufferGroesseInAnzahlAbtastwerten = pufferGroesseInBytes / anzahlBytesProAbtastwert;
+            int pufferGroesseInMillisekunden = 1000 * pufferGroesseInAnzahlAbtastwerten / recorder.getSampleRate();
+
+        }
+
+        @Override
+        protected Void doInBackground(Long... params) {
+            recorder.startRecording();
+            short[] puffer = new short[pufferGroesseInBytes / 2];
+            long lastTime = System.currentTimeMillis();
+            float verarbeitungsrate = 0;
+            final int maxZaehlerZeitMessung = 10;
+            int zaehlerZeitMessung = 0;
+            int anzahlVerarbeitet = 0;
+            GleitenderMittelwert gleitenderMittelwert = new GleitenderMittelwert(0.3f);
+
+            //Kalibrierung
+            try {
+                Thread.sleep(3000); // Time to lay down the phone
+            } catch (InterruptedException e) {
+                e.printStackTrace();
+            }
+            int i = 0;
+            for (i = 0; i < 20; i++) {
+                int n = recorder.read(puffer, 0, puffer.length);
+                Verarbeitungsergebnis kalibrierErgebnis = verarbeiten(puffer, n);
+                kalibierWert += kalibrierErgebnis.maxAmp;
+                try {
+                    Thread.sleep(50);
+                } catch (InterruptedException e) {
+                    e.printStackTrace();
+                }
+            }
+            kalibierWert = kalibierWert/i;
+
+//            __Part of FFT__
+//            Complex[] zeitSignal = new Complex[puffer.length];
+//            for (int j = 0; j < puffer.length; j++) {
+//                zeitSignal[j] = new Complex(puffer[j], 0);
+//            }
+//            Complex[] spektrum = FFT.fft(zeitSignal);
+//            double[] spektrum = calculateFFT(puffer);
+//            DataPoint AddPoint;
+//            LineGraphSeries<DataPoint> series = new LineGraphSeries<DataPoint>(new DataPoint[]{});
+//            for (i = 0; i < spektrum.length; i++) {
+//                AddPoint = new DataPoint(i, spektrum[i]);
+//                series.appendData(AddPoint, true, spektrum.length);
+//            }
+//            graph.addSeries(series);
+
+            for (; ; ) {
+                if (aufnahmeTask.isCancelled()) {
+                    break;
+                } else {
+                    int n = recorder.read(puffer, 0, puffer.length);
+                    Verarbeitungsergebnis ergebnis = verarbeiten(puffer, n);
+                    anzahlVerarbeitet += n;
+//                    __Part of FFT__
+//                    spektrum = calculateFFT(puffer);
+//                    LineGraphSeries<DataPoint> newseries = new LineGraphSeries<DataPoint>(new DataPoint[]{});
+//                    for (i = 0; i < spektrum.length; i++) {
+//                        AddPoint = new DataPoint(i, spektrum[i]);
+//                        newseries.appendData(AddPoint, true, spektrum.length);
+//                    }
+
+                    zaehlerZeitMessung++;
+                    if (zaehlerZeitMessung == maxZaehlerZeitMessung) {
+                        long time = System.currentTimeMillis();
+                        long deltaTime = time - lastTime;
+                        verarbeitungsrate = 1000.0f * anzahlVerarbeitet / deltaTime;
+                        verarbeitungsrate = gleitenderMittelwert.mittel(verarbeitungsrate);
+                        zaehlerZeitMessung = 0;
+                        anzahlVerarbeitet = 0;
+                        lastTime = time;
+                    }
+
+
+                    ergebnis.verarbeitungsrate = (int) verarbeitungsrate;
+                    publishProgress(ergebnis);
+
+                    try {
+                        Thread.sleep(10);
+                    } catch (InterruptedException e) {
+                        e.printStackTrace();
+                    }
+                }
+            }
+            recorder.release();
+            return null;
+        }
+
+        private Verarbeitungsergebnis verarbeiten(short[] daten, int n) {
+            String status;
+            short maxAmp = -1;
+            if (n == AudioRecord.ERROR_INVALID_OPERATION) {
+                status = "ERROR_INVALID_OPERATION";
+            } else if (n == AudioRecord.ERROR_BAD_VALUE) {
+                status = "ERROR_BAD_VALUE";
+            } else {
+                status = "OK";
+                short max = 0;
+                for (int i = 0; i < n; i++) {
+                    if (daten[i] > max) {
+                        max = daten[i];
+                    }
+                }
+
+                ringPuffer.hinzufuegen(max);
+                maxAmp = ringPuffer.maximum();
+                if (maxAmp <= Schwellwert_Alarm+kalibierWert) {
+                    armed = true;
+                }
+            }
+
+            return new Verarbeitungsergebnis(status, maxAmp, 0);
+        }
+
+        @Override
+        protected void onProgressUpdate(Verarbeitungsergebnis... progress) {
+            super.onProgressUpdate(progress);
+            float maxAmpPrint = round(20*log10(abs(progress[0].maxAmp/1.0)));
+            float kalibierWertPrint = round(20*log10(abs(kalibierWert)));
+            Log.d("0","VR, Max, Kal:" + progress[0].verarbeitungsrate + ", " + maxAmpPrint
+            + " dB, " + kalibierWertPrint + " dB");
+
+            if (progress[0].maxAmp >= Schwellwert_Alarm+kalibierWert && armed == true) {
+                armed = false;
+                detectionReport = new DetectionReport("Mic1", "Audio", maxAmpPrint);
+                reportViolation("Mic1", "Audio", maxAmpPrint);
+                Log.d("1",detectionReport.toString());
+            }
+        }
+    }
+
+    private double[] calculateFFT(short[] zeitsignal)
+    {
+        byte signal[] = new byte[zeitsignal.length];
+        // loops through all the values of a Short
+        for (int i = 0; i < zeitsignal.length-1; i++) {
+            signal[i] = (byte) (zeitsignal[i]);
+            signal[i+1] = (byte) (zeitsignal[i] >> 8);
+        }
+
+        final int mNumberOfFFTPoints =1024;
+        double mMaxFFTSample;
+
+        double temp;
+        Complex[] y;
+        Complex[] complexSignal = new Complex[mNumberOfFFTPoints];
+        double[] absSignal = new double[mNumberOfFFTPoints/2];
+
+        for(int i = 0; i < mNumberOfFFTPoints; i++){
+            temp = (double)((signal[2*i] & 0xFF) | (signal[2*i+1] << 8)) / 32768.0F;
+            complexSignal[i] = new Complex(temp,0.0);
+        }
+
+        y = FFT.fft(complexSignal);
+
+        mMaxFFTSample = 0.0;
+        for(int i = 0; i < (mNumberOfFFTPoints/2); i++)
+        {
+            absSignal[i] = y[i].abs();
+//            absSignal[i] = Math.sqrt(Math.pow(y[i].re(), 2) + Math.pow(y[i].im(), 2));
+//            if(absSignal[i] > mMaxFFTSample)
+//            {
+//                mMaxFFTSample = absSignal[i];
+//            }
+        }
+
+        return absSignal;
+
+    }
+
+    class Verarbeitungsergebnis {
+        String status;
+        short maxAmp;
+        int verarbeitungsrate;
+        Verarbeitungsergebnis(String status, short maxAmp, int verarbeitungsrate) {
+            this.status = status;
+            this.maxAmp = maxAmp;
+            this.verarbeitungsrate = verarbeitungsrate;
+        }
+    }
+
+    class RingPuffer {
+        private short[] puffer;
+        private final int laenge;
+        private int anzahlEnthaltenerDaten;
+        private int position;
+
+        public RingPuffer(int n) {
+            laenge = n;
+            anzahlEnthaltenerDaten = 0;
+            position = 0;
+            puffer = new short[laenge];
+        }
+
+        public void hinzufuegen(short wert) {
+            puffer[position] = wert;
+            position++;
+            if (position >= laenge) {
+                position = 0;
+            }
+            if (anzahlEnthaltenerDaten < laenge) {
+                anzahlEnthaltenerDaten++;
+            }
+        }
+
+        public void hinzufuegen(short[] daten) {
+            for (short d : daten) {
+                puffer[position] = d;
+                position++;
+                if (position >= laenge) {
+                    position = 0;
+                }
+            }
+            if (anzahlEnthaltenerDaten < laenge) {
+                anzahlEnthaltenerDaten += daten.length;
+                if (anzahlEnthaltenerDaten >= laenge) {
+                    anzahlEnthaltenerDaten = laenge;
+                }
+            }
+        }
+
+        public short maximum() {
+            short max = 0;
+            for (int i = 0; i < anzahlEnthaltenerDaten; i++) {
+                if (puffer[i] > max) {
+                    max = puffer[i];
+                }
+            }
+            return max;
+        }
+
+        public float mittelwert() {
+            float summe = 0;
+            for (int i = 0; i < anzahlEnthaltenerDaten; i++) {
+                summe += puffer[i];
+            }
+            return summe / anzahlEnthaltenerDaten;
+        }
+    }
+
+    class GleitenderMittelwert {
+        private final float wichtungNeuerWert;
+        private final float wichtungAlterWert;
+        private float mittelwert = 0;
+        private boolean istMittelwertGesetzt = false;
+
+        GleitenderMittelwert(float wichtungNeuerWert) {
+            this.wichtungNeuerWert = wichtungNeuerWert;
+            this.wichtungAlterWert = 1 - this.wichtungNeuerWert;
+        }
+
+        float MittelwertPuffer(short[] puffer) {
+
+            for (int i = 0; i < puffer.length; i++) {
+                mittelwert = Math.abs(puffer[i]);
+            }
+            mittelwert = mittelwert/puffer.length;
+
+            return mittelwert;
+        }
+
+        float mittel(float wert) {
+            if (istMittelwertGesetzt) {
+                mittelwert = wert * wichtungNeuerWert + mittelwert * wichtungAlterWert;
+            } else {
+                mittelwert = wert;
+                istMittelwertGesetzt = true;
+            }
+            return mittelwert;
+        }
+    }
+}

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)");
+    }
+}
+
+