Question

Not sure what I am doing wrong. The results I get from the Accelerate framework seem incorrect to me. Any help would be much appreciated!

Here are some graphs comparing AForge with vDPS

This is the vDSP Code I run

fftSetup = vDSP_create_fftsetup( 16, 2);

 // Convert the data into a DSPSplitComplex 
int samples = spectrumDataSize;
int samplesOver2 = samples/2;

DSPSplitComplex * complexData = new DSPSplitComplex;
float *realpart = (float *)calloc(samplesOver2, sizeof(float));
float *imagpart = (float *)calloc(samplesOver2, sizeof(float));
complexData->realp = realpart;
complexData->imagp = imagpart;    

vDSP_ctoz((DSPComplex *)realData, 2, complexData, 1,samplesOver2);

// Calculate the FFT
// ( I'm assuming here you've already called vDSP_create_fftsetup() )
vDSP_fft_zrip(fftSetup, complexData, 1, log2f(samples), FFT_FORWARD);

// Scale the data
//float scale = (float) FFT_SCALE; //scale is 32
vDSP_vsmul(complexData->realp, 1, &scale, complexData->realp, 1,samplesOver2);
vDSP_vsmul(complexData->imagp, 1, &scale, complexData->imagp, 1, samplesOver2);


vDSP_zvabs(complexData, 1, spectrumData, 1, samples);

free(complexData->realp);
free(complexData->imagp);
delete complexData;

// All done!
return spectrumData;

This is what I do in AForge

        foreach (float f in floatData)
            {
                if (i >= this.fft.Length)
                    break;
                this.fft[i++] = new Complex(f * fftSize, 0);
            }
            AForge.Math.FourierTransform.FFT(this.fft, FourierTransform.Direction.Forward);

Answer 1

After the following subroutine

vDSP_ctoz((DSPComplex *)realData, 2, complexData, 1,samplesOver2);

is executed, complexData has samplesOver2 elements. But soon after that, you call

vDSP_zvabs(complexData, 1, spectrumData, 1, samples);

which expects complexData to have samples elements, i.e. twice as many. This cannot be.

Also, how is realData laid out? I ask because vDSP_ctoz expects its first argument to be laid out in the form

real0, imag0, real1, imag1, ... real(n-1), imag(n-1).

If your data is indeed real, then imag0, imag1, ... imag(n-1) should all be 0. If it is not, then vDSP_ctoz may not be expecting that. (Unless you are packing the real data in some clever way, which would be two [sic] clever by half!)

Finally, vDSP_create_fftsetup( 16, 2); should probably be changed to

vDSP_create_fftsetup(16, 0);

===================================================================

My sample code appended in postscript:

  FFTSetup fftSetup = vDSP_create_fftsetup(
                                           16,         // vDSP_Length __vDSP_log2n,
                                           kFFTRadix2  // FFTRadix __vDSP_radix
                                           // CAUTION: kFFTRadix2 is an enum that is equal to 0
                                           //          kFFTRadix5 is an enum that is equal to 2
                                           // DO NOT USE 2 IF YOU MEAN kFFTRadix2
                                           );
  NSAssert(fftSetup != NULL, @"vDSP_create_fftsetup() failed to allocate storage");

  int numSamples = 65536;  // numSamples must be an integer power of 2; in this case 65536 = 2 ^ 16
  float realData[numSamples];

  // Prepare the real data with (ahem) fake data, in this case
  // the sum of 3 sinusoidal waves representing a C major chord.
  // The fake data is rigged to have a sampling frequency of 44100 Hz (as for a CD).
  // As always, the Nyquist frequency is just half the sampling frequency, i.e., 22050 Hz.
  for (int i = 0; i < numSamples; i++)
  {
    realData[i] = sin(2 * M_PI * 261.76300048828125 * i / 44100.0)  // C4 = 261.626 Hz
                + sin(2 * M_PI * 329.72717285156250 * i / 44100.0)  // E4 = 329.628 Hz
                + sin(2 * M_PI * 392.30804443359375 * i / 44100.0); // G4 = 391.995 Hz
  }

  float splitReal[numSamples / 2];
  float splitImag[numSamples / 2];

  DSPSplitComplex splitComplex;
  splitComplex.realp = splitReal;
  splitComplex.imagp = splitImag;

  vDSP_ctoz(
            (const DSPComplex *)realData,  // const DSPComplex __vDSP_C[],
            2,                             // vDSP_Stride __vDSP_strideC,  MUST BE A MULTIPLE OF 2
            &splitComplex,                 // DSPSplitComplex *__vDSP_Z,
            1,                             // vDSP_Stride __vDSP_strideZ,
            (numSamples / 2)               // vDSP_Length __vDSP_size
            );

  vDSP_fft_zrip(
                fftSetup,                               // FFTSetup __vDSP_setup,
                &splitComplex,                          // DSPSplitComplex *__vDSP_ioData,
                1,                                      // vDSP_Stride __vDSP_stride,
                (vDSP_Length)lround(log2(numSamples)),  // vDSP_Length __vDSP_log2n,
                // IMPORTANT: THE PRECEDING ARGUMENT MUST BE LOG_BASE_2 OF THE NUMBER OF floats IN splitComplex
                // FOR OUR EXAMPLE, THIS WOULD BE (numSamples / 2) + (numSamples / 2) = numSamples
                kFFTDirection_Forward                   // FFTDirection __vDSP_direction
                );

  printf("DC component = %f\n", splitComplex.realp[0]);
  printf("Nyquist component = %f\n\n", splitComplex.imagp[0]);

  // Next, we compute the Power Spectral Density (PSD) from the FFT.
  // (The PSD is just the magnitude-squared of the FFT.)
  // (We don't bother with scaling as we are only interested in relative values of the PSD.)
  float powerSpectralDensity[(numSamples / 2) + 1];  // the "+ 1" is to make room for the Nyquist component

  // We move the Nyquist component out of splitComplex.imagp[0] and place it
  // at the end of the array powerSpectralDensity, squaring it as we go:
  powerSpectralDensity[numSamples / 2] = splitComplex.imagp[0] * splitComplex.imagp[0];

  // We can now zero out splitComplex.imagp[0] since the imaginary part of the DC component is, in fact, zero:
  splitComplex.imagp[0] = 0.0;

  // Finally, we compute the squares of the magnitudes of the elements of the FFT:
  vDSP_zvmags(
              &splitComplex,         // DSPSplitComplex *__vDSP_A,
              1,                     // vDSP_Stride __vDSP_I,
              powerSpectralDensity,  // float *__vDSP_C,
              1,                     // vDSP_Stride __vDSP_K,
              (numSamples / 2)       // vDSP_Length __vDSP_N
              );

  // We print out a table of the PSD as a function of frequency
  // Replace the "< 600" in the for-loop below with "<= (numSamples / 2)" if you want
  // the entire spectrum up to and including the Nyquist frequency:
  printf("Frequency_in_Hz    Power_Spectral_Density\n");
  for (int i = 0; i < 600; i++)  
  {
    printf("%f,          %f\n", (i / (float)(numSamples / 2)) * 22050.0, powerSpectralDensity[i]);
    // Recall that the array index i = 0 corresponds to zero frequency
    // and that i = (numSamples / 2) corresponds to the Nyquist frequency of 22050 Hz.
    // Frequency values intermediate between these two limits are scaled proportionally (linearly).
  }

  // The output PSD should be zero everywhere except at the three frequencies
  // corresponding to the C major triad.  It should be something like this:

/***************************************************************************
 DC component = -0.000000
 Nyquist component = -0.000000

 Frequency_in_Hz    Power_Spectral_Density
 0.000000,          0.000000
 0.672913,          0.000000
 1.345825,          0.000000
 2.018738,          0.000000
 2.691650,          0.000000
 .
 .
 .
 260.417175,          0.000000
 261.090088,          0.000000
 261.763000,          4294967296.000000
 262.435913,          0.000000
 263.108826,          0.000000
 .
 .
 .
 328.381348,          0.000000
 329.054260,          0.000000
 329.727173,          4294967296.000000
 330.400085,          0.000000
 331.072998,          0.000000
 .
 .
 .
 390.962219,          0.000000
 391.635132,          0.000000
 392.308044,          4294966784.000000
 392.980957,          0.000000
 393.653870,          0.000000
 .
 .
 .
***************************************************************************/

  vDSP_destroy_fftsetup(fftSetup);