Perform autocorrelation with vDSP_conv from Apple Accelerate Framework - iphone

Question

I need to perform the autocorrelation of an array (vector) but I am having trouble finding the correct way to do so. I believe that I need the method "vDSP_conv" from the Accelerate Framework, but I can't follow how to successfully set it up. The thing throwing me off the most is the need for 2 inputs. Perhaps I have the wrong function, but I couldn't find one that operated on a single vector.
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vDSP_conv
Performs either correlation or convolution on two vectors; single
precision.
void vDSP_conv ( const float __vDSP_signal[], vDSP_Stride
__vDSP_signalStride, const float __vDSP_filter[], vDSP_Stride __vDSP_strideFilter, float __vDSP_result[], vDSP_Stride __vDSP_strideResult, vDSP_Length __vDSP_lenResult, vDSP_Length __vDSP_lenFilter );
Parameters
__vDSP_signal
Input vector A. The length of this vector must be at least __vDSP_lenResult + __vDSP_lenFilter - 1.
__vDSP_signalStride
The stride through __vDSP_signal.
__vDSP_filter
Input vector B.
__vDSP_strideFilter
The stride through __vDSP_filter.
__vDSP_result
Output vector C.
__vDSP_strideResult
The stride through __vDSP_result.
__vDSP_lenResult
The length of __vDSP_result.
__vDSP_lenFilter
The length of __vDSP_filter.
For an example, just assume you have an array of float x = [1.0, 2.0, 3.0, 4.0, 5.0]. How would I take the autocorrelation of that?
The output should be something similar to float y = [5.0, 14.0, 26.0, 40.0, 55.0, 40.0, 26.0, 14.0, 5.0] //generated using Matlab's xcorr(x) function

Answer 1

performing autocorrelation simply means you take the cross-correlation of one vector with itself. There is nothing fancy about it.
so in your case, do:
vDSP_conv(x, 1, x, 1, result, 1, 2*len_X-1, len_X);
check a sample code for more details: (which does a convolution)
http://disanji.net/iOS_Doc/#documentation/Performance/Conceptual/vDSP_Programming_Guide/SampleCode/SampleCode.html
EDIT: This borders on ridiculous, but you need to offset the x value by a specific number of zeros, which is just crazy.
the following is a working code, just set filter to the value of x you desire, and it will put the rest in the correct position:
float *signal, *filter, *result;
int32_t signalStride, filterStride, resultStride;
uint32_t lenSignal, filterLength, resultLength;
uint32_t i;
filterLength = 5;
resultLength = filterLength*2 -1;
lenSignal = ((filterLength + 3) & 0xFFFFFFFC) + resultLength;
signalStride = filterStride = resultStride = 1;
printf("\nConvolution ( resultLength = %d, "
"filterLength = %d )\n\n", resultLength, filterLength);
/* Allocate memory for the input operands and check its availability. */
signal = (float *) malloc(lenSignal * sizeof(float));
filter = (float *) malloc(filterLength * sizeof(float));
result = (float *) malloc(resultLength * sizeof(float));
for (i = 0; i < filterLength; i++)
filter[i] = (float)(i+1);
for (i = 0; i < resultLength; i++)
if (i >=resultLength- filterLength)
signal[i] = filter[i - filterLength+1];
/* Correlation. */
vDSP_conv(signal, signalStride, filter, filterStride,
result, resultStride, resultLength, filterLength);
printf("signal: ");
for (i = 0; i < lenSignal; i++)
printf("%2.1f ", signal[i]);
printf("\n filter: ");
for (i = 0; i < filterLength; i++)
printf("%2.1f ", filter[i]);
printf("\n result: ");
for (i = 0; i < resultLength; i++)
printf("%2.1f ", result[i]);
/* Free allocated memory. */
free(signal);
free(filter);
free(result);