调频综合算法

根据阅读的内容，我制定了一种用于FM声音合成的算法。我不确定我是否做对了。创建软件合成器乐器时，将使用函数来生成振荡器，并使用调制器来对该振荡器的频率进行模数化。我不知道FM合成是否仅适用于调制正弦波？

该算法采用仪器的波函数以及调制器的调制器指标和比率。对于每个音符，它都采用频率并存储载波和调制器振荡器的相位值。调制器始终使用正弦波。

这是伪代码中的算法：

function ProduceSample(instrument, notes_playing)
    for each note in notes_playing
        if note.isPlaying()
            # Calculate signal
            if instrument.FMIndex != 0 # Apply FM
                FMFrequency = note.frequency*instrument.FMRatio; # FM frequency is factor of note frequency.
                note.FMPhase = note.FMPhase + FMFrequency / kGraphSampleRate # Phase of modulator.
                frequencyDeviation = sin(note.FMPhase * PI)*instrument.FMIndex*FMFrequency # Frequency deviation. Max deviation is a factor of the FM frequency. Modulation is done by a sine wave. 
                note.phase = note.phase + (note.frequency + frequencyDeviation) / kGraphSampleRate # Adjust phase with deviation
                # Reset the phase value to prevent the float from overflowing
                if note.FMPhase >= 1
                    note.FMPhase = note.FMPhase - 1
                end if
            else # No FM applied
                note.phase = note.phase + note.frequency / kGraphSampleRate # Adjust phase without deviation
            end if
            # Calculate the next sample
            signal = signal + instrument.waveFunction(note.phase,instrument.waveParameter)*note.amplitude
            # Reset the phase value to prevent the float from overflowing
            if note.phase >= 1
                note.phase = note.phase - 1
            end if
        end if
    end loop
    return signal
end function 

因此，如果音符的频率为100Hz，则FMRatio设置为0.5，而FMIndex为0.1，则应该以50Hz的周期产生介于95Hz和105Hz之间的频率。这是正确的方法吗？我的测试表明，它听起来并不总是正确的，尤其是在调制锯齿波和方波时。可以像这样调制锯齿波和方波，还是仅用于正弦波？

这是C和CoreAudio的实现：

static OSStatus renderInput(void *inRefCon, AudioUnitRenderActionFlags *ioActionFlags, const AudioTimeStamp *inTimeStamp, UInt32 inBusNumber, UInt32 inNumberFrames, AudioBufferList *ioData){
    AudioSynthesiser * audioController = (AudioSynthesiser *)inRefCon;
    // Get a pointer to the dataBuffer of the AudioBufferList
    AudioSampleType * outA = (AudioSampleType *) ioData->mBuffers[0].mData;
    if(!audioController->playing){
        for (UInt32 i = 0; i < inNumberFrames; ++i){
            outA[i] = (SInt16)0;
        }
        return noErr;
    }
    Track * track = &audioController->tracks[inBusNumber];
    SynthInstrument * instrument = (SynthInstrument *)track;
    float frequency_deviation;
    float FMFrequency;
    // Loop through the callback buffer, generating samples
    for (UInt32 i = 0; i < inNumberFrames; ++i){
        float signal = 0;
        for (int x = 0; x < 10; x++) {
            Note * note = track->notes_playing[x];
            if(note){
                //Envelope code removed
                //Calculate signal
                if (instrument->FMIndex) { //Apply FM
                    FMFrequency = note->frequency*instrument->FMRatio; //FM frequency is factor of note frequency.
                    note->FMPhase += FMFrequency / kGraphSampleRate; //Phase of modulator.
                    frequency_deviation = sinf(note->FMPhase * M_PI)*instrument->FMIndex*FMFrequency; //Frequency deviation. Max deviation is a factor of the FM frequency. Modulation is done by a sine wave. 
                    note->phase += (note->frequency + frequency_deviation) / kGraphSampleRate; //Adjust phase with deviation
                    // Reset the phase value to prevent the float from overflowing
                    if (note->FMPhase >= 1){
                        note->FMPhase--;
                    }
                }else{
                    note->phase += note->frequency/ kGraphSampleRate; //Adjust phase without deviation
                }
                // Calculate the next sample
                signal += instrument->wave_function(note->phase,instrument->wave_parameter)*track->note_amplitude[x];
                // Reset the phase value to prevent the float from overflowing
                if (note->phase >= 1){
                    note->phase--;
                }
            } //Else nothing added
        }
        if(signal > 1.0){
            signal = 1;
        }else if(signal < -1.0){
            signal = -1.0;
        }
        audioController->wave[audioController->wave_last] = signal;
        if (audioController->wave_last == 499) {
            audioController->wave_last = 0;
        }else{
            audioController->wave_last++;
        }
        outA[i] = (SInt16)(signal * 32767.0f);
    }
    return noErr;
}

非常感谢您的回答。

您在这里所做的是相位调制。这就是Yamaha DX-7等“ FM”合成器的工作方式。通常，合成器振荡器是按音乐音阶而非线性Hz音阶进行调谐的。因此，直接调节音调会导致不必要的音调偏移，这就是为什么相位调制更合适的原因。您可以调制任何波形，但是更复杂的形状将更容易混叠。即使是调制过的罪过也可以混叠，因此也不被禁止。