This is a part of the DIY Synthesizer series of posts where each post is roughly built upon the knowledge of the previous posts. If you are lost, check the earlier posts!

The delay effect is a pretty simple effect that adds echo to a sound.

Two parameters at minimum are usually exposed on delay effects: delay time and feedback.

Delay time is how long the echo is, and feedback controls how much the sound feeds back into itself – or how loud the echo is.

Implementing delay is actually super simple. You figure out how many samples you need to hold “delay time” amount of sound (using the sample rate of the sound), and then just keep a circular buffer of previous sound samples. The feedback value controls how much the sound feeds back into the delay buffer.

Here is some pseudo code for how it might be implemented:

//The size of the delay buffer is controlled by the time parameter 
// make sure the delay buffer is initialized with silence
delayBuffer[delaySamples] = 0;

// start the circular delay buffer index at 0
delayIndex = 0;

// process each input sample
for (i = 0; i = delaySamples)
    delayIndex = 0;
}

Delay is an effect in it’s own right, but it’s also the basis for many other effect types as well. Flange, phaser, and chorus for instance rely on a delay buffer to be able to do their work.

Some common variations on the delay effect include having different delay parameters for the left and right channel in a stereo sound, or modifying the output sound before it goes into the delay buffer to make it so that the echo sounds a bit different than the original. For instance you could put a lowpass or highpass filter on the echo, or even flange it!

Play around with it and get creative. You might make some interesting and unique sounding sounds (:

Audio Samples

These files were processed with the sample code in this post.

Sample Code

The sample code below reads in.wav, applies a delay of 333ms with -12db feedback and writes it as out.wav.

Usual caveat: the wave reading code isn’t bullet proof (sorry). Seems to work best with 16 bit mono wave files. You can use libsndfile if you want more reliable and more diverse sound loading options!

#define _CRT_SECURE_NO_WARNINGS
   
#include 
#include 
#include 
#include 
#include 
#include 
   
#define _USE_MATH_DEFINES
#include 
   
//=====================================================================================
// SNumeric - uses phantom types to enforce type safety
//=====================================================================================
template 
struct SNumeric
{
public:
    explicit SNumeric(const T &value) : m_value(value) { }
    SNumeric() : m_value() { }
    inline T& Value() { return m_value; }
    inline const T& Value() const { return m_value; }
   
    typedef SNumeric TType;
    typedef T TInnerType;
   
    // Math Operations
    TType operator+ (const TType &b) const
    {
        return TType(this->Value() + b.Value());
    }
   
    TType operator- (const TType &b) const
    {
        return TType(this->Value() - b.Value());
    }
   
    TType operator* (const TType &b) const
    {
        return TType(this->Value() * b.Value());
    }
   
    TType operator/ (const TType &b) const
    {
        return TType(this->Value() / b.Value());
    }
   
    TType& operator+= (const TType &b)
    {
        Value() += b.Value();
        return *this;
    }
   
    TType& operator-= (const TType &b)
    {
        Value() -= b.Value();
        return *this;
    }
   
    TType& operator*= (const TType &b)
    {
        Value() *= b.Value();
        return *this;
    }
   
    TType& operator/= (const TType &b)
    {
        Value() /= b.Value();
        return *this;
    }
   
    TType& operator++ ()
    {
        Value()++;
        return *this;
    }
   
    TType& operator-- ()
    {
        Value()--;
        return *this;
    }
   
    // Extended Math Operations
    template 
    T Divide(const TType &b)
    {
        return ((T)this->Value()) / ((T)b.Value());
    }
   
    // Logic Operations
    bool operatorValue() < b.Value();
    }
    bool operatorValue()  (const TType &b) const {
        return this->Value() > b.Value();
    }
    bool operator>= (const TType &b) const {
        return this->Value() >= b.Value();
    }
    bool operator== (const TType &b) const {
        return this->Value() == b.Value();
    }
    bool operator!= (const TType &b) const {
        return this->Value() != b.Value();
    }
   
private:
    T m_value;
};
   
//=====================================================================================
// Typedefs
//=====================================================================================
   
typedef uint8_t uint8;
typedef uint16_t uint16;
typedef uint32_t uint32;
typedef int16_t int16;
typedef int32_t int32;
   
// type safe types!
typedef SNumeric      TFrequency;
typedef SNumeric        TTimeMs;
typedef SNumeric       TSamples;
typedef SNumeric   TFractionalSamples;
typedef SNumeric       TDecibels;
typedef SNumeric      TAmplitude;
typedef SNumeric          TPhase;
   
//=====================================================================================
// Constants
//=====================================================================================
   
static const float c_pi = (float)M_PI;
static const float c_twoPi = c_pi * 2.0f;
   
//=====================================================================================
// Structs
//=====================================================================================
   
struct SSoundSettings
{
    TSamples        m_sampleRate;
    TTimeMs         m_lengthMs;
    TSamples        m_currentSample;
};

//=====================================================================================
// CDelay -> the delay buffer object
//=====================================================================================

class CDelay
{
public:
    CDelay(TSamples delayTime, TAmplitude feedback)
        : m_feedBack(feedback)
        , m_sampleIndex(0)
    {
        m_samples.resize(delayTime.Value());
        std::fill(m_samples.begin(), m_samples.end(), TAmplitude(0.0f));
    }

    TAmplitude ProcessSample(TAmplitude sample)
    {
        TAmplitude ret = sample + m_samples[m_sampleIndex];
        m_samples[m_sampleIndex] = ret * m_feedBack;
        m_sampleIndex++;
        if (m_sampleIndex >= m_samples.size())
            m_sampleIndex = 0;
        return ret;
    }

private:
    TAmplitude              m_feedBack;
    std::vector m_samples;
    size_t                  m_sampleIndex;
};

//=====================================================================================
// Conversion Functions
//=====================================================================================
inline TDecibels AmplitudeToDB(TAmplitude volume)
{
    return TDecibels(log10(volume.Value()));
}
   
inline TAmplitude DBToAmplitude(TDecibels dB)
{
    return TAmplitude(pow(10.0f, dB.Value() / 20.0f));
}
   
TSamples SecondsToSamples(const SSoundSettings &s, float seconds)
{
    return TSamples((int)(seconds * (float)s.m_sampleRate.Value()));
}
   
TSamples MilliSecondsToSamples(const SSoundSettings &s, float milliseconds)
{
    return SecondsToSamples(s, milliseconds / 1000.0f);
}
   
TTimeMs SecondsToMilliseconds(float seconds)
{
    return TTimeMs((uint32)(seconds * 1000.0f));
}
   
TFrequency Frequency(float octave, float note)
{
    /* frequency = 440×(2^(n/12))
    Notes:
    0  = A
    1  = A#
    2  = B
    3  = C
    4  = C#
    5  = D
    6  = D#
    7  = E
    8  = F
    9  = F#
    10 = G
    11 = G# */
    return TFrequency((float)(440 * pow(2.0, ((double)((octave - 4) * 12 + note)) / 12.0)));
}
   
template 
T AmplitudeToAudioSample(const TAmplitude& in)
{
    const T c_min = std::numeric_limits::min();
    const T c_max = std::numeric_limits::max();
    const float c_minFloat = (float)c_min;
    const float c_maxFloat = (float)c_max;
   
    float ret = in.Value() * c_maxFloat;
   
    if (ret  c_maxFloat)
        return c_max;
   
    return (T)ret;
}
 
TAmplitude GetLerpedAudioSample(const std::vector& samples, TFractionalSamples& index)
{
    // get the index of each sample and the fractional blend amount
    uint32 a = (uint32)floor(index.Value());
    uint32 b = a + 1;
    float fract = index.Value() - floor(index.Value());
 
    // get our two amplitudes
    float ampA = 0.0f;
    if (a >= 0 && a = 0 && b < samples.size())
        ampB = samples[b].Value();
 
    // return the lerped result
    return TAmplitude(fract * ampB + (1.0f - fract) * ampA);
}
 
void NormalizeSamples(std::vector& samples, TAmplitude maxAmplitude)
{
    // nothing to do if no samples
    if (samples.size() == 0)
        return;
 
    // 1) find the largest absolute value in the samples.
    TAmplitude largestAbsVal = TAmplitude(abs(samples.front().Value()));
    std::for_each(samples.begin() + 1, samples.end(), [&largestAbsVal](const TAmplitude &a)
        {
            TAmplitude absVal = TAmplitude(abs(a.Value()));
            if (absVal > largestAbsVal)
                largestAbsVal = absVal;
        }
    );
 
    // 2) adjust largestAbsVal so that when we divide all samples, none will be bigger than maxAmplitude
    // if the value we are going to divide by is <= 0, bail out
    largestAbsVal /= maxAmplitude;
    if (largestAbsVal = TAmplitude(1.0f))
            {
                int ijkl = 0;
            }
        }
    );
}
 
void ResampleData(std::vector& samples, int srcSampleRate, int destSampleRate)
{
    //if the requested sample rate is the sample rate it already is, bail out and do nothing
    if (srcSampleRate == destSampleRate)
        return;
 
    //calculate the ratio of the old sample rate to the new
    float fResampleRatio = (float)destSampleRate / (float)srcSampleRate;
     
    //calculate how many samples the new data will have and allocate the new sample data
    int nNewDataNumSamples = (int)((float)samples.size() * fResampleRatio);
 
    std::vector newSamples;
    newSamples.resize(nNewDataNumSamples);
 
    //get each lerped output sample.  There are higher quality ways to resample
    for(int nIndex = 0; nIndex < nNewDataNumSamples; ++nIndex)
        newSamples[nIndex] = GetLerpedAudioSample(samples, TFractionalSamples((float)nIndex / fResampleRatio));
     
    //free the old data and set the new data
    std::swap(samples, newSamples);
}
 
void ChangeNumChannels(std::vector& samples, int nSrcChannels, int nDestChannels)
{
    //if the number of channels requested is the number of channels already there, or either number of channels is not mono or stereo, return
    if(nSrcChannels == nDestChannels ||
       nSrcChannels  2 ||
       nDestChannels  2)
    {
        return;
    }
 
    //if converting from mono to stereo, duplicate the mono channel to make stereo
    if(nDestChannels == 2)
    {
        std::vector newSamples;
        newSamples.resize(samples.size() * 2);
        for (size_t index = 0; index < samples.size(); ++index)
        {
            newSamples[index * 2] = samples[index];
            newSamples[index * 2 + 1] = samples[index];
        }
 
        std::swap(samples, newSamples);
    }
    //else converting from stereo to mono, mix the stereo channels together to make mono
    else
    {
        std::vector newSamples;
        newSamples.resize(samples.size() / 2);
        for (size_t index = 0; index < samples.size() / 2; ++index)
            newSamples[index] = samples[index * 2] + samples[index * 2 + 1];
 
        std::swap(samples, newSamples);
    }
}
 
float PCMToFloat(unsigned char *pPCMData, int nNumBytes)
{
    switch(nNumBytes)
    {
        case 1:
        {
            uint8 data = pPCMData[0];
            return (float)data / 255.0f;
        }
        case 2:
        {
            int16 data = pPCMData[1] << 8 | pPCMData[0];
            return ((float)data) / ((float)0x00007fff);
        }
        case 3:
        {
            int32 data = pPCMData[2] << 16 | pPCMData[1] << 8 | pPCMData[0];
            return ((float)data) / ((float)0x007fffff);
        }
        case 4:
        {
            int32 data = pPCMData[3] << 24 | pPCMData[2] << 16 | pPCMData[1] << 8 | pPCMData[0];
            return ((float)data) / ((float)0x7fffffff);
        }
        default:
        {
            return 0.0f;
        }
    }
}
   
//=====================================================================================
// Wave File Writing Code
//=====================================================================================
struct SMinimalWaveFileHeader
{
    //the main chunk
    unsigned char m_szChunkID[4];      //0
    uint32        m_nChunkSize;        //4
    unsigned char m_szFormat[4];       //8
   
    //sub chunk 1 "fmt "
    unsigned char m_szSubChunk1ID[4];  //12
    uint32        m_nSubChunk1Size;    //16
    uint16        m_nAudioFormat;      //18
    uint16        m_nNumChannels;      //20
    uint32        m_nSampleRate;       //24
    uint32        m_nByteRate;         //28
    uint16        m_nBlockAlign;       //30
    uint16        m_nBitsPerSample;    //32
   
    //sub chunk 2 "data"
    unsigned char m_szSubChunk2ID[4];  //36
    uint32        m_nSubChunk2Size;    //40
   
    //then comes the data!
};
   
//this writes a wave file
template 
bool WriteWaveFile(const char *fileName, const std::vector &samples, const SSoundSettings &sound)
{
    //open the file if we can
    FILE *file = fopen(fileName, "w+b");
    if (!file)
        return false;
   
    //calculate bits per sample and the data size
    const int32 bitsPerSample = sizeof(T) * 8;
    const int dataSize = samples.size() * sizeof(T);
   
    SMinimalWaveFileHeader waveHeader;
   
    //fill out the main chunk
    memcpy(waveHeader.m_szChunkID, "RIFF", 4);
    waveHeader.m_nChunkSize = dataSize + 36;
    memcpy(waveHeader.m_szFormat, "WAVE", 4);
   
    //fill out sub chunk 1 "fmt "
    memcpy(waveHeader.m_szSubChunk1ID, "fmt ", 4);
    waveHeader.m_nSubChunk1Size = 16;
    waveHeader.m_nAudioFormat = 1;
    waveHeader.m_nNumChannels = 1;
    waveHeader.m_nSampleRate = sound.m_sampleRate.Value();
    waveHeader.m_nByteRate = sound.m_sampleRate.Value() * 1 * bitsPerSample / 8;
    waveHeader.m_nBlockAlign = 1 * bitsPerSample / 8;
    waveHeader.m_nBitsPerSample = bitsPerSample;
   
    //fill out sub chunk 2 "data"
    memcpy(waveHeader.m_szSubChunk2ID, "data", 4);
    waveHeader.m_nSubChunk2Size = dataSize;
   
    //write the header
    fwrite(&waveHeader, sizeof(SMinimalWaveFileHeader), 1, file);
   
    //write the wave data itself, converting it from float to the type specified
    std::vector outSamples;
    outSamples.resize(samples.size());
    for (size_t index = 0; index < samples.size(); ++index)
        outSamples[index] = AmplitudeToAudioSample(samples[index]);
    fwrite(&outSamples[0], dataSize, 1, file);
   
    //close the file and return success
    fclose(file);
    return true;
}
 
//loads a wave file in.  Converts from source format into the specified format
// TOTAL HONESTY: some wave files seem to have problems being loaded through this function and I don't have
// time to investigate why.  It seems to work best with 16 bit mono wave files.
// If you need more robust file loading, check out libsndfile at http://www.mega-nerd.com/libsndfile/
bool ReadWaveFile(const char *fileName, std::vector& samples, int32 sampleRate)
{
    //open the file if we can
    FILE *File = fopen(fileName,"rb");
    if(!File)
    {
        return false;
    }
 
    //read the main chunk ID and make sure it's "RIFF"
    char buffer[5];
    buffer[4] = 0;
    if(fread(buffer,4,1,File) != 1 || strcmp(buffer,"RIFF"))
    {
        fclose(File);
        return false;
    }
 
    //read the main chunk size
    uint32 nChunkSize;
    if(fread(&nChunkSize,4,1,File) != 1)
    {
        fclose(File);
        return false;
    }
 
    //read the format and make sure it's "WAVE"
    if(fread(buffer,4,1,File) != 1 || strcmp(buffer,"WAVE"))
    {
        fclose(File);
        return false;
    }
 
    long chunkPosFmt = -1;
    long chunkPosData = -1;
 
    while(chunkPosFmt == -1 || chunkPosData == -1)
    {
        //read a sub chunk id and a chunk size if we can
        if(fread(buffer,4,1,File) != 1 || fread(&nChunkSize,4,1,File) != 1)
        {
            fclose(File);
            return false;
        }
 
        //if we hit a fmt
        if(!strcmp(buffer,"fmt "))
        {
            chunkPosFmt = ftell(File) - 8;
        }
        //else if we hit a data
        else if(!strcmp(buffer,"data"))
        {
            chunkPosData = ftell(File) - 8;
        }
 
        //skip to the next chunk
        fseek(File,nChunkSize,SEEK_CUR);
    }
 
    //we'll use this handy struct to load in 
    SMinimalWaveFileHeader waveData;
 
    //load the fmt part if we can
    fseek(File,chunkPosFmt,SEEK_SET);
    if(fread(&waveData.m_szSubChunk1ID,24,1,File) != 1)
    {
        fclose(File);
        return false;
    }
 
    //load the data part if we can
    fseek(File,chunkPosData,SEEK_SET);
    if(fread(&waveData.m_szSubChunk2ID,8,1,File) != 1)
    {
        fclose(File);
        return false;
    }
 
    //verify a couple things about the file data
    if(waveData.m_nAudioFormat != 1 ||       //only pcm data
       waveData.m_nNumChannels  2 ||        //must not have more than 2
       waveData.m_nBitsPerSample > 32 ||     //32 bits per sample max
       waveData.m_nBitsPerSample % 8 != 0 || //must be a multiple of 8 bites
       waveData.m_nBlockAlign > 8)           //blocks must be 8 bytes or lower
    {
        fclose(File);
        return false;
    }
 
    //figure out how many samples and blocks there are total in the source data
    int nBytesPerBlock = waveData.m_nBlockAlign;
    int nNumBlocks = waveData.m_nSubChunk2Size / nBytesPerBlock;
    int nNumSourceSamples = nNumBlocks * waveData.m_nNumChannels;
 
    //allocate space for the source samples
    samples.resize(nNumSourceSamples);
 
    //maximum size of a block is 8 bytes.  4 bytes per samples, 2 channels
    unsigned char pBlockData[8];
    memset(pBlockData,0,8);
 
    //read in the source samples at whatever sample rate / number of channels it might be in
    int nBytesPerSample = nBytesPerBlock / waveData.m_nNumChannels;
    for(int nIndex = 0; nIndex = TPhase(1.0f))
        phase -= TPhase(1.0f);
    while (phase  0.5f ? 1.0f : -1.0f);
}
   
TAmplitude AdvanceOscilator_Triangle(TPhase &phase, TFrequency frequency, TSamples sampleRate)
{
    AdvancePhase(phase, frequency, sampleRate);
    if (phase > TPhase(0.5f))
        return TAmplitude((((1.0f - phase.Value()) * 2.0f) * 2.0f) - 1.0f);
    else
        return TAmplitude(((phase.Value() * 2.0f) * 2.0f) - 1.0f);
}
   
TAmplitude AdvanceOscilator_Saw_BandLimited(TPhase &phase, TFrequency frequency, TSamples sampleRate)
{
    AdvancePhase(phase, frequency, sampleRate);
   
    // sum the harmonics
    TAmplitude ret(0.0f);
    for (int harmonicIndex = 1; harmonicIndex <= 4; ++harmonicIndex)
    {
        TPhase harmonicPhase = phase * TPhase((float)harmonicIndex);
        ret += TAmplitude(sin(harmonicPhase.Value()*c_twoPi) / (float)harmonicIndex);
    }
   
    //adjust the volume
    ret *= TAmplitude(2.0f / c_pi);
       
    return ret;
}
   
TAmplitude AdvanceOscilator_Square_BandLimited(TPhase &phase, TFrequency frequency, TSamples sampleRate)
{
    AdvancePhase(phase, frequency, sampleRate);
   
    // sum the harmonics
    TAmplitude ret(0.0f);
    for (int harmonicIndex = 1; harmonicIndex <= 4; ++harmonicIndex)
    {
        float harmonicFactor = (float)harmonicIndex * 2.0f - 1.0f;
        TPhase harmonicPhase = phase * TPhase(harmonicFactor);
        ret += TAmplitude(sin(harmonicPhase.Value()*c_twoPi) / harmonicFactor);
    }
   
    //adjust the volume
    ret *= TAmplitude(4.0f / c_pi);
   
    return ret;
}
   
TAmplitude AdvanceOscilator_Triangle_BandLimited(TPhase &phase, TFrequency frequency, TSamples sampleRate)
{
    AdvancePhase(phase, frequency, sampleRate);
   
    // sum the harmonics
    TAmplitude ret(0.0f);
    TAmplitude signFlip(1.0f);
    for (int harmonicIndex = 1; harmonicIndex <= 4; ++harmonicIndex)
    {
        float harmonicFactor = (float)harmonicIndex * 2.0f - 1.0f;
        TPhase harmonicPhase = phase * TPhase(harmonicFactor);
        ret += TAmplitude(sin(harmonicPhase.Value()*c_twoPi) / (harmonicFactor*harmonicFactor)) * signFlip;
        signFlip *= TAmplitude(-1.0f);
    }
   
    //adjust the volume
    ret *= TAmplitude(8.0f / (c_pi*c_pi));
   
    return ret;
}
 
//=====================================================================================
// Main
//=====================================================================================
int main(int argc, char **argv)
{
    //our desired sound parameters
    SSoundSettings sound;
    sound.m_sampleRate = TSamples(44100);
    sound.m_lengthMs = SecondsToMilliseconds(4.0f);

    // create a delay effect object with the specified parameters
    const TSamples c_delayTime = MilliSecondsToSamples(sound, 333.0f);
    const TAmplitude c_delayFeedback = DBToAmplitude(TDecibels(-12.0f));
    CDelay delay(c_delayTime, c_delayFeedback);
  
    // load the wave file if we can
    std::vector inputData;
    if (!ReadWaveFile("in.wav", inputData, sound.m_sampleRate.Value()))
    {
        printf("could not load wave file!");
        return 0;
    }
 
    // allocate space for the output file
    std::vector samples;
    samples.resize(inputData.size());

    //apply the delay effect to the file
    const TSamples c_envelopeSize = MilliSecondsToSamples(sound, 50.0f);
    for (TSamples index = TSamples(0), numSamples(samples.size()); index < numSamples; ++index)
    {
        // calculate envelope at front and end of sound.
        TAmplitude envelope(1.0f);
        if (index  (numSamples - c_envelopeSize))
            envelope = TAmplitude(1.0f) - TAmplitude((float)(index - (numSamples - c_envelopeSize)).Value() / (float)c_envelopeSize.Value());

        // put our input through the delay buffer
        TAmplitude outSample = delay.ProcessSample(inputData[index.Value()]);
 
        // mix the sample with the offset sample and apply the envelope for the front and back of the sound
        samples[index.Value()] = outSample * envelope;
    }
   
    // normalize the amplitude of the samples to make sure they are as loud as possible without clipping
    // give 3db of headroom
    NormalizeSamples(samples, DBToAmplitude(TDecibels(-3.0f)));
 
    // save as a wave file
    WriteWaveFile("out.wav", samples, sound);
 
    return 0;
}

Links

Wikipedia: Delay Effect

Next post will be about multitap reverb, which is similar to delay, but a little bit different.