声音合成:使用AS3在频率间进行插值

Question

我有点迷茫，希望有人能对此有所了解。出于好奇，我正在研制一个简单的软合成器/测序器。一些想法是从流行于家庭电脑黄金时代的.mod格式中提出来的。目前这只是一场模拟。从一个包含多达64个值的数组中读出注释，其中数组中的每个位置对应于第16个音符。到目前为止一切都很好，一切正常，旋律也很好。如果从一个音符过渡到另一个音符，问题就出现了。因为这是一个突然的变化，所以有一个明显的弹出/点击的声音。为了进行补偿，我尝试在不同的频率之间进行插值，并开始编写一个简单的例子来说明我的想法，并验证它是否有效。

import flash.display.Sprite;
import flash.events.Event;
import flash.display.Bitmap;
import flash.display.BitmapData;

public class Main extends Sprite
{
    private var sampleRate:int = 44100;
    private var oldFreq:Number = 349.1941058508811;
    private var newFreq:Number = 349.1941058508811;
    private var volume:Number = 15;
    private var position:int = 0;
    private var bmp:Bitmap = new Bitmap();
    private var bmpData:BitmapData = new BitmapData(400, 100, false, 0x000000);
    private var col:uint = 0xff0000;

    public function Main():void
    {
        if (stage)
            init();
        else
            addEventListener(Event.ADDED_TO_STAGE, init);
    }

    private function init(e:Event = null):void
    {
        removeEventListener(Event.ADDED_TO_STAGE, init);
        bmp.bitmapData = bmpData;
        addChild(bmp);

        for (var a:int = 0; a < 280; a++)
        {
            if (a == 140)
            {
                col = 0x00ff00;
                newFreq = 415.26411519488113;
            }
            if (a == 180)
            {
                col = 0x0000ff;
            }
            oldFreq = oldFreq * 0.9 + newFreq * 0.1;
            bmpData.setPixel(position, Math.sin((position) * Math.PI * 2 / sampleRate * oldFreq * 2) * volume + bmpData.height/2, col);
            position++;
        }
    }
}

这将产生以下输出：

​

​

蓝点代表正弦波349.1941058508811 hz，红色415.26411519488113 hz，绿色点插值。对我的眼睛来说，这看起来应该是可行的！但是，如果我将这种技术应用到我的项目中，结果就不一样了！实际上，如果我将输出呈现为一个wave文件，那么这两个频率之间的转换如下所示：

​

​

很明显这会让爆发力更糟。有什么可能是错的？以下是我的(简写)代码：

import flash.display.*;
import flash.events.Event;
import flash.events.*;
import flash.utils.ByteArray;
import flash.media.*;
import flash.utils.getTimer;

public class Main extends Sprite
{
    private var sampleRate:int = 44100;
    private var bufferSize:int = 8192;
    private var bpm:int = 125;
    private var numberOfRows:int = 64;
    private var currentRow:int = 0;
    private var quarterNoteLength:Number;
    private var sixteenthNoteLength:Number;
    private var numOctaves:int = 8;
    private var patterns:Array = new Array();
    private var currentPattern:int;
    private var songOrder:Array = new Array();
    private var notes:Array = new Array("c-", "c#", "d-", "d#", "e-", "f-", "f#", "g-", "g#", "a-", "a#", "b-");
    private var frequencies:Array = new Array();
    private var samplePosition:Number = 0;
    private var position:int = 0;
    private var channel1:Object = new Object();

    public function Main():void
    {
        if (stage)
            init();
        else
            addEventListener(Event.ADDED_TO_STAGE, init);
    }

    private function init(e:Event = null):void
    {
        removeEventListener(Event.ADDED_TO_STAGE, init);
        quarterNoteLength = sampleRate * 60 / bpm;
        sixteenthNoteLength = quarterNoteLength / 2 / 2;
        for (var a:int = 0; a < numOctaves; a++)
        {
            for (var b:int = 0; b < notes.length; b++)
            {
                frequencies.push(new Array(notes[b % notes.length] + a, 16.35 * Math.pow(2, frequencies.length / 12)));
            }
        }
        patterns.push(new Array("f-4", "", "", "", "g#4", "", "", "f-4", "", "f-4", "a#4", "", "f-4", "", "d#4", "", "f-4", "", "", "", "c-5", "", "", "f-4", "", "f-4", "c#5", "", "c-5", "", "g#4", "", "f-4", "", "c-5", "", "f-5", "", "f-4", "d#4", "", "d#4", "c-4", "", "g-4", "", "f-4", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", "", ""));
        songOrder = new Array(0, 0);
        currentRow = 0;
        currentPattern = 0;
        channel1.volume = .05;
        channel1.waveform = "sine";
        channel1.frequency = [0];
        channel1.oldFrequency = [0,0,0,0];
        channel1.noteTriggered = false;

        updateRow();
        var sound:Sound = new Sound();
        sound.addEventListener(SampleDataEvent.SAMPLE_DATA, onSampleData);
        sound.play();
    }

    private function updateRow():void
    {
        var tempNote:String = patterns[songOrder[currentPattern]][currentRow];
        if (tempNote != "")
        {
            channel1.frequency = new Array();
            if (tempNote.indexOf("|") == -1)
            {
                channel1.frequency.push(findFrequency(tempNote));
            }

            channel1.noteTriggered = true;
        }

    }

    private function onSampleData(event:SampleDataEvent):void
    {
        var sampleData:Number;
        for (var i:int = 0; i < bufferSize; i++)
        {
            if (++samplePosition == sixteenthNoteLength)
            {
                if (++currentRow == numberOfRows)
                {
                    currentRow = 0;
                    if (++currentPattern == songOrder.length)
                    {
                        currentPattern = 0;
                    }
                }
                updateRow();
                samplePosition = 0;
            }


            for (var a:int = 0; a < (channel1.frequency).length; a++ )
            {
                channel1.oldFrequency[a] = channel1.oldFrequency[a]*0.9+channel1.frequency[a]*0.1;          
            }

            if ((channel1.frequency).length == 1)
            {
                sampleData = generate(channel1.waveform, position, channel1.oldFrequency[0], channel1.volume);
            }
            else
            {
                sampleData = generate(channel1.waveform, position, channel1.oldFrequency[0], channel1.volume);
                sampleData += generate(channel1.waveform, position, channel1.oldFrequency[1], channel1.volume);
            }

            event.data.writeFloat(sampleData);
            event.data.writeFloat(sampleData);

            position++;
        }
    }

    private function generate(waveForm:String, pos:Number, frequency:Number, volume:Number):Number
    {
        var retVal:Number
        switch (waveForm)
        {
            case "square": 
                retVal = Math.sin((pos) * 2 * Math.PI / sampleRate * frequency) > 0 ? volume : -volume;
                break;
            case "sine": 
                retVal = Math.sin((pos) * Math.PI * 2 / sampleRate * frequency * 2) * volume;
                break;
            case "sawtooth": 
                retVal = (2 * (pos % (sampleRate / frequency)) / (sampleRate / frequency) - 1) * volume;
                break;
        }
        return retVal;
    }

    private function findFrequency(inpNote:String):Number
    {
        var retVal:Number;
        for (var a:int = 0; a < frequencies.length; a++)
        {
            if (frequencies[a][0] == inpNote)
            {
                retVal = frequencies[a][1];
                break;
            }
        }
        return retVal;
    }
}

谢谢！=)

Answer 1

当您切换频率时，pos值在generate中会失去不变性，也就是说，当以不同的频率运行时，Math.sin((pos) * Math.PI * 2 / sampleRate * frequency * 2)会给出非常不同的值。相反，您应该使用“相位”变量，该变量将从0运行到1，然后返回到0，然后像锯齿图一样再次向前，并将由(当前频率)*(1/抽样率)的值转发。因此，错误是将两个generate()结果添加到一个sampleData (由于干扰而不能这样做)，以及使用一个position作为时间值来计算相位而不是累计相位。检查一下这种方法，它应该能更好地工作：

private function generate(waveForm:String, var phase:Number, frequency:Number, volume:Number):Number {
    // "pos" changed to "phase". This also means that "generate" should be called once per sample
    var retVal:Number;
    switch (waveForm)
    {
        case "square": 
            retVal = Math.sin(phase * 2 * Math.PI) > 0 ? volume : -volume;
            break;
        case "sine": 
            retVal = Math.sin(phase * 2 * Math.PI ) * volume;
            break;
        case "sawtooth": 
            retVal = (2*Math.abs(2*phase-1)-1)* volume;
            break;
    }
    phase+=frequency/sampleRate;// calculate new phase
    if (phase>1.0) { phase-=1.0; } // normalize phase to 0..1
    return retVal;
}
private function onSampleData(event:SampleDataEvent):void {
    var sampleData:Number;
    for(var i:int=0;i<bufferSize;i++) {
        if (++samplePosition == sixteenthNoteLength)
        { // leaving this part as is, seems working
            if (++currentRow == numberOfRows)
            {
                currentRow = 0;
                if (++currentPattern == songOrder.length)
                {
                    currentPattern = 0;
                }
            }
            updateRow();
            samplePosition = 0;
        }
        sampleData=0;
        for (i=0;i</*channels.length*/1;i++) {  
            // TODO convert "channel1" to an array 
            // sampleData+=generate(channels[i].waveform, channels[i].phase, channels[i].frequency, channels[i].volume);
            sampleData+=generate(channel1.waveform, channel1.phase, channel1.frequency[0], channel1.volume);
        }
        event.data.writeFloat(sampleData);
        event.data.writeFloat(sampleData);
    }
}

实际上，您的通道应该转到一个单独的类，该类将所有参数(相位、freq、波形、卷)放在一起，然后，当您需要它们进行采样时，您只需调用channels[i].generateNextSample()并得到一个浮点，而不需要使用所有参数。另外，一个频道，一个频率，所以跳过那些"oldFrequency“的东西。

作为后续，Channel类的草图：

public class Channel {
    public const WAVE_SINE:int=0;
    public const WAVE_SQUARE:int=1;
    public const WAVE_SAWTOOTH:int=2;
    private var phase:Number=0;
    private var currentVolume:Number=0;
    public var volume:Number; // 0 to 1, should build a setter to normalize
    public var frequency:Number=0;
    public var waveform:int; // should also not allow changing this mid-play probably
    public function Channel(v:Number=0,wf:int=WAVE_SINE,f:Number=0) {
        this.volume=v;
        this.frequency=f;
        this.waveform=wf;
        phase=0;
        currentVolume=0;
    }
    public function generateNextSample():Number {...} // use the generate() code above to fill
    public function reset():void { currentVolume=0; phase=0; } // POW
    // rest to taste, enabled, active, whatever
}

一个使用实例：

var ch:Vector.<Channel>=new Vector.<Channel>();
ch.push(new Channel());
function onSampleData(e:SampleDataEvent):void {
    for (var j:int=0;j<8192;j++) {
        // here to input code that can alter channels' freqs, volumes etc
        var sd:Number=0;
        for (var i:int=ch.length-1; i>=0;i--) { sd+=ch[i].generateNextSample(); }
        e.data.writeFloat(sd);
        e.data.writeFloat(sd);
    }
}