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    <p>After the following subroutine</p> <pre><code>vDSP_ctoz((DSPComplex *)realData, 2, complexData, 1,samplesOver2); </code></pre> <p>is executed, <code>complexData</code> has <code>samplesOver2</code> elements. But soon after that, you call</p> <pre><code>vDSP_zvabs(complexData, 1, spectrumData, 1, samples); </code></pre> <p>which expects <code>complexData</code> to have <code>samples</code> elements, i.e. twice as many. This cannot be.</p> <p>Also, how is <code>realData</code> laid out? I ask because <code>vDSP_ctoz</code> expects its first argument to be laid out in the form</p> <pre><code>real0, imag0, real1, imag1, ... real(n-1), imag(n-1). </code></pre> <p>If your data is indeed real, then <code>imag0, imag1, ... imag(n-1)</code> should all be 0. If it is not, then <code>vDSP_ctoz</code> may not be expecting that. (Unless you are packing the real data in some clever way, which would be two [sic] clever by half!)</p> <p>Finally, <code>vDSP_create_fftsetup( 16, 2);</code> should probably be changed to</p> <pre><code>vDSP_create_fftsetup(16, 0); </code></pre> <p>===================================================================</p> <p>My sample code appended in postscript:</p> <pre><code> 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 &lt; 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 &amp;splitComplex, // DSPSplitComplex *__vDSP_Z, 1, // vDSP_Stride __vDSP_strideZ, (numSamples / 2) // vDSP_Length __vDSP_size ); vDSP_fft_zrip( fftSetup, // FFTSetup __vDSP_setup, &amp;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( &amp;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 "&lt; 600" in the for-loop below with "&lt;= (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 &lt; 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); </code></pre>
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    1. COthe real data is real0,real1,real2. At this point the imaginary part is all 0. (the real data comes from audio) Should the real data ba real0,0,real1?
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    2. COvDSP_ctoz is not being used here to convert interleaved complex data to separated complex data; it is being used to change the layout of the real data in realData to the format required by vDSP_fft_zrip. (This layout is an unfortunate legacy artifact.) So the data in realData should be just real0, real1, real2,... After the call, complexData->realp contains real0, real2, real4,..., and complexData->imago contains real1, real3, real5,...
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