DSP tutorial: SSB modulation using the Hartley method

Last modified: November 16th, 2011

This example records audio and generates a lower sideband signal using the Hartley method, and saves it to a .wav file.

This method can be simulated very efficiently and easily in software. To generate an SSB signal with this method, two versions of the original signal are generated, mutually 90° out of phase. Each one of these signals is then mixed with carrier waves that are also 90° out of phase with each other. By either adding or subtracting the resulting signals, a lower or upper sideband signal results.

90 degrees phase delay can be realized with a Hilbert transformer. You can design one using this great page.

You can see an output example (LSB signal, 10kHz carrier, 4kHz modulator bandwidth) here:

More info:

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public class SSBHartley implements Runnable {
    private final static int SAMPLERATE = 44100;
    private final static int BUFFERSIZE = SAMPLERATE * 2;

    private final static int HILBERT_NZEROS = 512;
    private final static double HILBERT_GAIN = 1.570483967e+00;
    private double[] hilbert_xv;

    private final double hilbert_xcoeffs[] = { +0.0000000000, +0.0003138613, +0.0000000000, +0.0003174376, +0.0000000000, +0.0003221740, +0.0000000000, +0.0003280972, +0.0000000000, +0.0003352340, +0.0000000000, +0.0003436114, +0.0000000000, +0.0003532566, +0.0000000000, +0.0003641970, +0.0000000000, +0.0003764603, +0.0000000000, +0.0003900744, +0.0000000000, +0.0004050673, +0.0000000000, +0.0004214676, +0.0000000000, +0.0004393040, +0.0000000000, +0.0004586054, +0.0000000000, +0.0004794011, +0.0000000000, +0.0005017209, +0.0000000000, +0.0005255947, +0.0000000000, +0.0005510531, +0.0000000000, +0.0005781267, +0.0000000000, +0.0006068469, +0.0000000000, +0.0006372454, +0.0000000000, +0.0006693544, +0.0000000000, +0.0007032067, +0.0000000000, +0.0007388356, +0.0000000000, +0.0007762750, +0.0000000000, +0.0008155595, +0.0000000000, +0.0008567243, +0.0000000000, +0.0008998053, +0.0000000000, +0.0009448395, +0.0000000000, +0.0009918643, +0.0000000000, +0.0010409181, +0.0000000000,
            +0.0010920405, +0.0000000000, +0.0011452719, +0.0000000000, +0.0012006537, +0.0000000000, +0.0012582286, +0.0000000000, +0.0013180405, +0.0000000000, +0.0013801346, +0.0000000000, +0.0014445576, +0.0000000000, +0.0015113575, +0.0000000000, +0.0015805840, +0.0000000000, +0.0016522886, +0.0000000000, +0.0017265245, +0.0000000000, +0.0018033470, +0.0000000000, +0.0018828134, +0.0000000000, +0.0019649832, +0.0000000000, +0.0020499184, +0.0000000000, +0.0021376834, +0.0000000000, +0.0022283457, +0.0000000000, +0.0023219754, +0.0000000000, +0.0024186459, +0.0000000000, +0.0025184340, +0.0000000000, +0.0026214200, +0.0000000000, +0.0027276884, +0.0000000000, +0.0028373275, +0.0000000000, +0.0029504304, +0.0000000000, +0.0030670949, +0.0000000000, +0.0031874241, +0.0000000000, +0.0033115266, +0.0000000000, +0.0034395171, +0.0000000000, +0.0035715167, +0.0000000000, +0.0037076536, +0.0000000000, +0.0038480636, +0.0000000000, +0.0039928907, +0.0000000000, +0.0041422875,
            +0.0000000000, +0.0042964166, +0.0000000000, +0.0044554506, +0.0000000000, +0.0046195735, +0.0000000000, +0.0047889815, +0.0000000000, +0.0049638842, +0.0000000000, +0.0051445053, +0.0000000000, +0.0053310847, +0.0000000000, +0.0055238792, +0.0000000000, +0.0057231643, +0.0000000000, +0.0059292361, +0.0000000000, +0.0061424131, +0.0000000000, +0.0063630386, +0.0000000000, +0.0065914829, +0.0000000000, +0.0068281459, +0.0000000000, +0.0070734605, +0.0000000000, +0.0073278960, +0.0000000000, +0.0075919615, +0.0000000000, +0.0078662107, +0.0000000000, +0.0081512469, +0.0000000000, +0.0084477282, +0.0000000000, +0.0087563740, +0.0000000000, +0.0090779724, +0.0000000000, +0.0094133886, +0.0000000000, +0.0097635740, +0.0000000000, +0.0101295776, +0.0000000000, +0.0105125586, +0.0000000000, +0.0109138011, +0.0000000000, +0.0113347310, +0.0000000000, +0.0117769368, +0.0000000000, +0.0122421921, +0.0000000000, +0.0127324845, +0.0000000000, +0.0132500473, +0.0000000000,
            +0.0137973997, +0.0000000000, +0.0143773929, +0.0000000000, +0.0149932668, +0.0000000000, +0.0156487183, +0.0000000000, +0.0163479841, +0.0000000000, +0.0170959429, +0.0000000000, +0.0178982414, +0.0000000000, +0.0187614506, +0.0000000000, +0.0196932631, +0.0000000000, +0.0207027420, +0.0000000000, +0.0218006399, +0.0000000000, +0.0229998108, +0.0000000000, +0.0243157494, +0.0000000000, +0.0257673042, +0.0000000000, +0.0273776363, +0.0000000000, +0.0291755264, +0.0000000000, +0.0311971870, +0.0000000000, +0.0334888257, +0.0000000000, +0.0361103470, +0.0000000000, +0.0391408311, +0.0000000000, +0.0426868713, +0.0000000000, +0.0468956751, +0.0000000000, +0.0519764409, +0.0000000000, +0.0582368230, +0.0000000000, +0.0661485683, +0.0000000000, +0.0764737425, +0.0000000000, +0.0905286557, +0.0000000000, +0.1107996896, +0.0000000000, +0.1426148288, +0.0000000000, +0.1998268664, +0.0000000000, +0.3332294323, +0.0000000000, +0.9999653629, +0.0000000000, -0.9999653629,
            -0.0000000000, -0.3332294323, -0.0000000000, -0.1998268664, -0.0000000000, -0.1426148288, -0.0000000000, -0.1107996896, -0.0000000000, -0.0905286557, -0.0000000000, -0.0764737425, -0.0000000000, -0.0661485683, -0.0000000000, -0.0582368230, -0.0000000000, -0.0519764409, -0.0000000000, -0.0468956751, -0.0000000000, -0.0426868713, -0.0000000000, -0.0391408311, -0.0000000000, -0.0361103470, -0.0000000000, -0.0334888257, -0.0000000000, -0.0311971870, -0.0000000000, -0.0291755264, -0.0000000000, -0.0273776363, -0.0000000000, -0.0257673042, -0.0000000000, -0.0243157494, -0.0000000000, -0.0229998108, -0.0000000000, -0.0218006399, -0.0000000000, -0.0207027420, -0.0000000000, -0.0196932631, -0.0000000000, -0.0187614506, -0.0000000000, -0.0178982414, -0.0000000000, -0.0170959429, -0.0000000000, -0.0163479841, -0.0000000000, -0.0156487183, -0.0000000000, -0.0149932668, -0.0000000000, -0.0143773929, -0.0000000000, -0.0137973997, -0.0000000000, -0.0132500473, -0.0000000000,
            -0.0127324845, -0.0000000000, -0.0122421921, -0.0000000000, -0.0117769368, -0.0000000000, -0.0113347310, -0.0000000000, -0.0109138011, -0.0000000000, -0.0105125586, -0.0000000000, -0.0101295776, -0.0000000000, -0.0097635740, -0.0000000000, -0.0094133886, -0.0000000000, -0.0090779724, -0.0000000000, -0.0087563740, -0.0000000000, -0.0084477282, -0.0000000000, -0.0081512469, -0.0000000000, -0.0078662107, -0.0000000000, -0.0075919615, -0.0000000000, -0.0073278960, -0.0000000000, -0.0070734605, -0.0000000000, -0.0068281459, -0.0000000000, -0.0065914829, -0.0000000000, -0.0063630386, -0.0000000000, -0.0061424131, -0.0000000000, -0.0059292361, -0.0000000000, -0.0057231643, -0.0000000000, -0.0055238792, -0.0000000000, -0.0053310847, -0.0000000000, -0.0051445053, -0.0000000000, -0.0049638842, -0.0000000000, -0.0047889815, -0.0000000000, -0.0046195735, -0.0000000000, -0.0044554506, -0.0000000000, -0.0042964166, -0.0000000000, -0.0041422875, -0.0000000000, -0.0039928907,
            -0.0000000000, -0.0038480636, -0.0000000000, -0.0037076536, -0.0000000000, -0.0035715167, -0.0000000000, -0.0034395171, -0.0000000000, -0.0033115266, -0.0000000000, -0.0031874241, -0.0000000000, -0.0030670949, -0.0000000000, -0.0029504304, -0.0000000000, -0.0028373275, -0.0000000000, -0.0027276884, -0.0000000000, -0.0026214200, -0.0000000000, -0.0025184340, -0.0000000000, -0.0024186459, -0.0000000000, -0.0023219754, -0.0000000000, -0.0022283457, -0.0000000000, -0.0021376834, -0.0000000000, -0.0020499184, -0.0000000000, -0.0019649832, -0.0000000000, -0.0018828134, -0.0000000000, -0.0018033470, -0.0000000000, -0.0017265245, -0.0000000000, -0.0016522886, -0.0000000000, -0.0015805840, -0.0000000000, -0.0015113575, -0.0000000000, -0.0014445576, -0.0000000000, -0.0013801346, -0.0000000000, -0.0013180405, -0.0000000000, -0.0012582286, -0.0000000000, -0.0012006537, -0.0000000000, -0.0011452719, -0.0000000000, -0.0010920405, -0.0000000000, -0.0010409181, -0.0000000000,
            -0.0009918643, -0.0000000000, -0.0009448395, -0.0000000000, -0.0008998053, -0.0000000000, -0.0008567243, -0.0000000000, -0.0008155595, -0.0000000000, -0.0007762750, -0.0000000000, -0.0007388356, -0.0000000000, -0.0007032067, -0.0000000000, -0.0006693544, -0.0000000000, -0.0006372454, -0.0000000000, -0.0006068469, -0.0000000000, -0.0005781267, -0.0000000000, -0.0005510531, -0.0000000000, -0.0005255947, -0.0000000000, -0.0005017209, -0.0000000000, -0.0004794011, -0.0000000000, -0.0004586054, -0.0000000000, -0.0004393040, -0.0000000000, -0.0004214676, -0.0000000000, -0.0004050673, -0.0000000000, -0.0003900744, -0.0000000000, -0.0003764603, -0.0000000000, -0.0003641970, -0.0000000000, -0.0003532566, -0.0000000000, -0.0003436114, -0.0000000000, -0.0003352340, -0.0000000000, -0.0003280972, -0.0000000000, -0.0003221740, -0.0000000000, -0.0003174376, -0.0000000000, -0.0003138613, -0.0000000000, };

    private TargetDataLine tdl;

    SSBHartley(TargetDataLine tdl) {
        this.tdl = tdl;
        hilbert_xv = new double[HILBERT_NZEROS + 1];
    }

    private double hilbertTransform(double in) {
        for (int j = 0; j < HILBERT_NZEROS; j++)
            hilbert_xv[j] = hilbert_xv[j + 1];
        hilbert_xv[HILBERT_NZEROS] = in / HILBERT_GAIN;

        double sum = 0;
        for (int j = 0; j <= HILBERT_NZEROS; j++)
            sum += hilbert_xcoeffs[j] * hilbert_xv[j];

        return sum;
    }

    // converts float array to byte array
    private byte[] getBytesFromDoubles(final double[] audioData, final int storedSamples) {
        byte[] audioDataBytes = new byte[storedSamples * 2];

        for (int i = 0; i < storedSamples; i++) {
            // saturation
            audioData[i] = Math.min(1.0, Math.max(-1.0, audioData[i]));

            // scaling and conversion to integer
            int sample = (int) Math.round((audioData[i] + 1.0) * 32767.5) - 32768;

            byte high = (byte) ((sample >> 8) & 0xFF);
            byte low = (byte) (sample & 0xFF);
            audioDataBytes[i * 2] = low;
            audioDataBytes[i * 2 + 1] = high;
        }

        return audioDataBytes;
    }

    // saves the audio data given in audioDataBytes to a .wav file
    private void writeWavFile(final byte[] audioDataBytes, final int storedSamples, final String fileName) {
        AudioFormat audioFormat = new AudioFormat(AudioFormat.Encoding.PCM_SIGNED, SAMPLERATE, 16, 1, 2, SAMPLERATE, false);
        AudioInputStream audioInputStream = new AudioInputStream(new ByteArrayInputStream(audioDataBytes), audioFormat, storedSamples);

        try {
            FileOutputStream fileOutputStream = new FileOutputStream(fileName);
            AudioSystem.write(audioInputStream, AudioFileFormat.Type.WAVE, fileOutputStream);
            audioInputStream.close();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    @Override
    public void run() {
        byte[] abBuffer = new byte[tdl.getBufferSize()];
        double[] abBufferDouble = new double[abBuffer.length / 2];
        ByteArrayOutputStream baos = new ByteArrayOutputStream(); // this will store sound data
        double oscPhase = 0;
        double carrierFreq = 10000;
        double[] delay = new double[HILBERT_NZEROS / 2 + 1];

        tdl.start();

        try {
            while (!Thread.interrupted()) {
                // waiting for the buffer to get filled
                while (tdl.available() < tdl.getBufferSize() * 0.5)
                    Thread.sleep(0, 1); // without this, the audio will be choppy

                int bytesRead = tdl.read(abBuffer, 0, tdl.available());

                // converting frames stored as bytes to double values
                int samplesRead = bytesRead / tdl.getFormat().getFrameSize();
                for (int i = 0; i < samplesRead; i++)
                    abBufferDouble[i] = ((abBuffer[i * 2] & 0xFF) | (abBuffer[i * 2 + 1] << 8)) / 32768.0;

                for (int samplePos = 0; samplePos < samplesRead; samplePos++) {
                    oscPhase += (2 * Math.PI * carrierFreq) / SAMPLERATE;

                    // delay line
                    for (int j = 0; j < HILBERT_NZEROS / 2; j++)
                        delay[j] = delay[j + 1];
                    delay[HILBERT_NZEROS / 2] = abBufferDouble[samplePos];

                    abBufferDouble[samplePos] = delay[0] * Math.cos(oscPhase) + hilbertTransform(abBufferDouble[samplePos]) * Math.sin(oscPhase);

                    if (oscPhase >= 2 * Math.PI)
                        oscPhase -= 2 * Math.PI;
                }

                // demodulating (multiplying samples with the carrier again)
                /*oscPhase = 0;
                for (int samplePos = 0; samplePos < samplesRead; samplePos++) {
                    oscPhase += (2 * Math.PI * carrierFreq) / SAMPLERATE;
                    abBufferDouble[samplePos] *= Math.sin(oscPhase);

                    if (oscPhase >= 2 * Math.PI)
                        oscPhase -= 2 * Math.PI;
                }*/

                baos.write(getBytesFromDoubles(abBufferDouble, samplesRead), 0, samplesRead * 2);
            }
        } catch (InterruptedException e) {
        }

        tdl.stop();
        tdl.close();

        writeWavFile(baos.toByteArray(), baos.size() / 2, "output.wav");
    }

    public static void main(String[] args) {
        AudioFormat audioFormat = new AudioFormat(AudioFormat.Encoding.PCM_SIGNED, SAMPLERATE, 16, 1, 2, SAMPLERATE, false);
        DataLine.Info info = new DataLine.Info(TargetDataLine.class, audioFormat, BUFFERSIZE);

        TargetDataLine targetDataLine = null;
        try {
            targetDataLine = (TargetDataLine) AudioSystem.getLine(info);
            targetDataLine.open(audioFormat, BUFFERSIZE);
            System.out.println("Buffer size: " + targetDataLine.getBufferSize());
        } catch (LineUnavailableException e1) {
            e1.printStackTrace();
        }

        // creating the recorder thread from this class' instance
        SSBHartley ssbHartley = new SSBHartley(targetDataLine);
        Thread ssbHartleyThread = new Thread(ssbHartley);

        // we use this to read line from the standard input
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        ssbHartleyThread.setPriority(Thread.MAX_PRIORITY);
        ssbHartleyThread.start();

        System.out.println("Recording... press ENTER to stop recording!");
        try {
            br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }

        ssbHartleyThread.interrupt();

        try {
            // waiting for the recorder thread to stop
            ssbHartleyThread.join();
        } catch (InterruptedException e) {
            e.printStackTrace();
        }
        System.out.println("Recording stopped.");
    }

}

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