Fast Peak Autocorrelation

So, I was at geekcon. It was a blast.
The lunar lander
There were many interesting projects, and I didn’t get to play with them all. I did get to work a bit on the Lunar Lander from last year, and this year it was finished successfully. My part was the PC game which interfaced with the microcontroller controlling the lander. As you probably guessed, it was written in Python.

This year, as promised, I worked on the Automatic Improviser. I worked on it with Ira Cherkes.

While the final version worked, it didn’t work well enough, and there is still much work to be done. Still, we had excellent progress.
By the way, I know this subject has been tackled before, and I still wanted to try it myself, without reading too much literature about it.

One of the components of the system is a beat recognizer. My idea to discover the beat is simple: find the envelope (similar to removing AM modulation), and then find the low “frequency” of the envelope.
Instead of doing a Fast Fourier Transform for beat recognition, we were advised that autocorellation will do the trick better and faster. However, when trying to autocorellate using scipy.signal.correlate we discovered that autocorellation was too slow for real time beat recognition, and certainly wasteful.

To solve this issue, we decided to first do peak detection on the envelope, and then autocorellate the peaks. Since there shouldn’t be too many peaks, this has the potential of being really quick. However, there was no standard function to do autocorellation of peaks, so we implemented it ourselves. We were pretty rushed, so we worked fast. Here’s the code:

def autocorrelate_peaks(peaks):
    peaks_dict = dict(peaks)
    indexes = set(peaks_dict.keys())
    deltas = set()
    for i in indexes:
        for j in indexes:
            if j>i:
                continue
            deltas.add(i-j)
 
    result = {}
    for d in deltas:
        moved = set(i+d for i in indexes)
        to_mult = moved & indexes
        assert to_mult <= indexes
        s = sum(peaks_dict[i-d]*peaks_dict[i] for i in to_mult)
        result[d] = s
    return result

This function takes as input a list of tuples, each of the form (peak_index, peak_value), and returns a mapping between non-zero corellation offsets and their values.
Here’s is a sample run:

In [7]: autocorrelate_peaks([(2, 2), (5,1), (7,3)])
Out[7]: {0: 14, 2: 3, 3: 2, 5: 6}

After implementing this function, our recognition loop was back to real-time, and we didn’t have to bother with optimizing again.

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