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MDT5_1_Ueberwachungssystem_G1
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Merge branch 'tw' into master 

# 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
copie
Tobias Wolz 1 year ago
parent
b9c66f7533 c60a14b6ac
commit
8e47934beb
5 changed files with 890 additions and 0 deletions
Split View Show Diff Stats
  1. 36
    0
      app/src/main/java/com/example/ueberwachungssystem/Detector/DetectionReport.java
  2. 39
    0
      app/src/main/java/com/example/ueberwachungssystem/Detector/Detector.java
  3. 421
    0
      app/src/main/java/com/example/ueberwachungssystem/Detector/MicrophoneDetector.java
  4. 148
    0
      app/src/main/java/com/example/ueberwachungssystem/Detector/Signalverarbeitung/Complex.java
  5. 246
    0
      app/src/main/java/com/example/ueberwachungssystem/Detector/Signalverarbeitung/FFT.java

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app/src/main/java/com/example/ueberwachungssystem/Detector/DetectionReport.java View File

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package com.example.ueberwachungssystem.Detector;

import android.util.Log;

import java.util.Calendar;

/** Detection Report Class */
public class DetectionReport {
public String timeStamp;
public String detectionType;
public float detectedValue;
public String detectorID;

public DetectionReport(String detectorID, String detectionType, float detectedAmplitude) {
this.timeStamp = String.valueOf(Calendar.getInstance().getTime());
this.detectionType = detectionType;
this.detectedValue = detectedAmplitude;
this.detectorID = detectorID;
}


/** Get Detection Report in String format */
public String toString() {
String time = "Time: " + "[" + this.timeStamp + "]";
String type = "Type: " + "[" + this.detectionType + "]";
String value = "Value: " + "[" + this.detectedValue + "]";
String id = "ID: " + "[" + this.detectorID + "]";

return String.join("\t", time, type, value, id);
}

/** Debug Report */
public void log(String tag) {
Log.d(tag, this.toString());
}
}

+ 39
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app/src/main/java/com/example/ueberwachungssystem/Detector/Detector.java View File

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package com.example.ueberwachungssystem.Detector;

import android.content.Context;
import androidx.annotation.NonNull;


abstract public class Detector {
private OnDetectionListener listener;

/** Constructor - takes context of current activity */
public Detector(Context context) {};


/** 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 detectorID, String detectionType, float amplitude) {
if (listener != null) {
DetectionReport detectionReport = new DetectionReport(detectorID, detectionType, amplitude);
listener.onDetection(detectionReport);
} else {
throw new IllegalStateException("No listener set for violation reporting");
}
}


/** 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();
}

+ 421
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app/src/main/java/com/example/ueberwachungssystem/Detector/MicrophoneDetector.java View File

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package com.example.ueberwachungssystem.Detector;

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.Detector.Signalverarbeitung.Complex;
import com.example.ueberwachungssystem.Detector.Signalverarbeitung.FFT;
import com.example.ueberwachungssystem.Detector.logger.Logger;
import com.jjoe64.graphview.GraphView;
import com.jjoe64.graphview.series.DataPoint;
import com.jjoe64.graphview.series.LineGraphSeries;

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 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;
}
}
}

+ 148
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app/src/main/java/com/example/ueberwachungssystem/Detector/Signalverarbeitung/Complex.java View File

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package com.example.ueberwachungssystem.Detector.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.Detector.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.Detector.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.Detector.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.Detector.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.Detector.Signalverarbeitung.Complex object whose value is the conjugate of this
public Complex conjugate() {
return new Complex(re, -im);
}

// return a new com.example.ueberwachungssystem.Detector.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.Detector.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.Detector.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.Detector.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.Detector.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());
}
}

+ 246
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app/src/main/java/com/example/ueberwachungssystem/Detector/Signalverarbeitung/FFT.java View File

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package com.example.ueberwachungssystem.Detector.Signalverarbeitung;
// Source: https://introcs.cs.princeton.edu/java/97data/FFT.java.html

/******************************************************************************
* Compilation: javac FFT.java
* Execution: java FFT n
* Dependencies: com.example.ueberwachungssystem.Detector.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.Detector.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)");
}
}



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