Question

Important update: I already figured out the answers and put them in this simple open-source library: http://bartolsthoorn.github.com/NVDSP/ Check it out, it will probably save you quite some time if you’re having trouble with audio filters in IOS!

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I have created a (realtime) audio buffer (float *data) that holds a few sin(theta) waves with different frequencies.

The code below shows how I created my buffer, and I’ve tried to do a bandpass filter but it just turns the signals to noise/blips:

    // Multiple signal generator
__block float *phases = nil;
[audioManager setOutputBlock:^(float *data, UInt32 numFrames, UInt32 numChannels)
{
    float samplingRate = audioManager.samplingRate;
    NSUInteger activeSignalCount = [tones count];

    // Initialize phases
    if (phases == nil) {
        phases = new float[10];
        for(int z = 0; z <= 10; z++) {
            phases[z] = 0.0;
        }
    }

    // Multiple signals
    NSEnumerator * enumerator = [tones objectEnumerator];
    id frequency;
    UInt32 c = 0;
    while(frequency = [enumerator nextObject])
    {
        for (int i=0; i < numFrames; ++i)
        {
            for (int iChannel = 0; iChannel < numChannels; ++iChannel) 
            {
                float theta = phases[c] * M_PI * 2;
                if (c == 0) {
                    data[i*numChannels + iChannel] = sin(theta);
                } else {
                    data[i*numChannels + iChannel] = data[i*numChannels + iChannel] + sin(theta);
                }
            }
            phases[c] += 1.0 / (samplingRate / [frequency floatValue]);
            if (phases[c] > 1.0) phases[c] = -1;
        }
        c++;
    }

    // Normalize data with active signal count
    float signalMulti = 1.0 / (float(activeSignalCount) * (sqrt(2.0)));
    vDSP_vsmul(data, 1, &signalMulti, data, 1, numFrames*numChannels);


    // Apply master volume
    float volume = masterVolumeSlider.value;
    vDSP_vsmul(data, 1, &volume, data, 1, numFrames*numChannels);


    if (fxSwitch.isOn) {
        // H(s) = (s/Q) / (s^2 + s/Q + 1)
        // http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt
        // BW 2.0  Q 0.667
        // http://www.rane.com/note170.html
        //The order of the coefficients are, B1, B2, A1, A2, B0.
        float Fs = samplingRate;

        float omega = 2*M_PI*Fs; // w0 = 2*pi*f0/Fs

        float Q = 0.50f;
        float alpha = sin(omega)/(2*Q); // sin(w0)/(2*Q)

        // Through H
        for (int i=0; i < numFrames; ++i)
        {
            for (int iChannel = 0; iChannel < numChannels; ++iChannel) 
            {
                data[i*numChannels + iChannel] = (data[i*numChannels + iChannel]/Q) / (pow(data[i*numChannels + iChannel],2) + data[i*numChannels + iChannel]/Q + 1);
            }
        }

        float b0 = alpha;
        float b1 = 0;
        float b2 = -alpha;
        float a0 = 1 + alpha;
        float a1 = -2*cos(omega);
        float a2 = 1 - alpha;

        float *coefficients = (float *) calloc(5, sizeof(float));


        coefficients[0] = b1;
        coefficients[1] = b2;
        coefficients[2] = a1;
        coefficients[3] = a2;
        coefficients[3] = b0;

        vDSP_deq22(data, 2, coefficients, data, 2, numFrames);

        free(coefficients);
    }

    // Measure dB
    [self measureDB:data:numFrames:numChannels];
 }];

My aim is to make a 10-band EQ for this buffer, using vDSP_deq22, the syntax of the method is:
vDSP_deq22(<float *vDSP_A>, <vDSP_Stride vDSP_I>, <float *vDSP_B>, <float *vDSP_C>, <vDSP_Stride vDSP_K>, <vDSP_Length __vDSP_N>)
See: http://developer.apple.com/library/mac/#documentation/Accelerate/Reference/vDSPRef/Reference/reference.html#//apple_ref/doc/c_ref/vDSP_deq22

Arguments:

float *vDSP_A is the input data
float *vDSP_B are 5 filter coefficients
float *vDSP_C is the output data

I have to make 10 filters (10 times vDSP_deq22). Then I set the gain for every band and combine them back together. But what coefficients do I feed every filter? I know vDSP_deq22 is a 2nd order (butterworth) IIR filter, but how do I turn this into a bandpass?

Now I have three questions:

a) Do I have to de-interleave and interleave the audio buffer? I know setting stride to 2 just filters on channel but how I filter the other, stride 1 will process both channels as one.

b) Do I have to transform/process the buffer before it enters the vDSP_deq22 method? If so, do I also have to transform it back to normal?

c) What values of the coefficients should I set to the 10 vDSP_deq22s?

I’ve been trying for days now but I haven’t been able to figure this on out, please help me out!

Answer 1

Your omega value need to be normalised, i.e. expressed as a fraction of Fs – it looks like you left out the f0 when you calculated omega, which will make alpha wrong too:

    float omega = 2*M_PI*Fs; // w0 = 2*pi*f0/Fs

should probably be:

    float omega = 2*M_PI*f0/Fs; // w0 = 2*pi*f0/Fs

where f0 is the centre frequency in Hz.

For your 10 band equaliser you’ll need to pick 10 values of f0, spaced logarithmically, e.g. 25 Hz, 50 Hz, 100 Hz, 200 Hz, 400 Hz, 800 Hz, 1.6 kHz, 3.2 kHz, 6.4 kHz, 12.8 kHz.