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Fixed: autocorrelation → cross-correlation
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Edgar Bonet
Edgar Bonet
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Your Arduino is incapable of stereo sampling. Since it has only one ADC, it can only sample one channel at a time. This means you will have to alternatingly sample the left channel, then the right channel, then the left channel... Since the left and right samples are not taken at the same time, this will have an implication on how you interpret the results from the autocorrelationcross-correlation. Did you think about how you will handle this? Is this acceptable? Will you have to instead use external ADC chips in order to have real stereo sampling?

In 224 µs, the sound travels about 76 mm, which is thus the spatial resolution of your autocorrelationcross-correlation. How does this translate into angular resolution? Is this resolution satisfactory? Do you plan to use interpolation methods to try to improve it?

When you use analogRead(), the time between consecutive samples can depend on the code you run between the consecutive calls to analogRead(). It can also depend on how your code gets interrupted by, say, the timer interrupt, or the UART interrupt if you are sending data out. An inconsistent sampling rate is something you want to avoid when doing autocorrelationscross-correlations.

Mathematically, the autocorrelationcross-correlation is typically defined for an infinite series of samples. In your experiment, you will have to deal with finite arrays, and this makes a subtle difference. Did you think about how you will deal with the finiteness of the arrays? Are you going to zero-pad? Remove the average before zero-padding? Apply a windowing function?

Your Arduino is incapable of stereo sampling. Since it has only one ADC, it can only sample one channel at a time. This means you will have to alternatingly sample the left channel, then the right channel, then the left channel... Since the left and right samples are not taken at the same time, this will have an implication on how you interpret the results from the autocorrelation. Did you think about how you will handle this? Is this acceptable? Will you have to instead use external ADC chips in order to have real stereo sampling?

In 224 µs, the sound travels about 76 mm, which is thus the spatial resolution of your autocorrelation. How does this translate into angular resolution? Is this resolution satisfactory? Do you plan to use interpolation methods to try to improve it?

When you use analogRead(), the time between consecutive samples can depend on the code you run between the consecutive calls to analogRead(). It can also depend on how your code gets interrupted by, say, the timer interrupt, or the UART interrupt if you are sending data out. An inconsistent sampling rate is something you want to avoid when doing autocorrelations.

Mathematically, the autocorrelation is typically defined for an infinite series of samples. In your experiment, you will have to deal with finite arrays, and this makes a subtle difference. Did you think about how you will deal with the finiteness of the arrays? Are you going to zero-pad? Remove the average before zero-padding? Apply a windowing function?

Your Arduino is incapable of stereo sampling. Since it has only one ADC, it can only sample one channel at a time. This means you will have to alternatingly sample the left channel, then the right channel, then the left channel... Since the left and right samples are not taken at the same time, this will have an implication on how you interpret the results from the cross-correlation. Did you think about how you will handle this? Is this acceptable? Will you have to instead use external ADC chips in order to have real stereo sampling?

In 224 µs, the sound travels about 76 mm, which is thus the spatial resolution of your cross-correlation. How does this translate into angular resolution? Is this resolution satisfactory? Do you plan to use interpolation methods to try to improve it?

When you use analogRead(), the time between consecutive samples can depend on the code you run between the consecutive calls to analogRead(). It can also depend on how your code gets interrupted by, say, the timer interrupt, or the UART interrupt if you are sending data out. An inconsistent sampling rate is something you want to avoid when doing cross-correlations.

Mathematically, the cross-correlation is typically defined for infinite series of samples. In your experiment, you will have to deal with finite arrays, and this makes a subtle difference. Did you think about how you will deal with the finiteness of the arrays? Are you going to zero-pad? Remove the average before zero-padding? Apply a windowing function?

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Edgar Bonet
Edgar Bonet
  • 45.2k
  • 4
  • 42
  • 81

I am not going to directly answer the question, as I think it is ill-posed. Before posting a question here, you are supposed to have done your research, and come with very specific problems you cannot solve by your own. I may be mistaken, but it looks to me like you are at a very preliminary stage where you barely started to think about the project.

So, instead of trying to answer an overly broad question, I will try to provide some guidance by asking questions back to you. Below is a list of some problems and challenges you will have to consider for advancing your project. It may not be complete: it's just what I can think off the top of my head. This will hopefully help you tackle the right problems.

Non-stereo sampling

Your Arduino is incapable of stereo sampling. Since it has only one ADC, it can only sample one channel at a time. This means you will have to alternatingly sample the left channel, then the right channel, then the left channel... Since the left and right samples are not taken at the same time, this will have an implication on how you interpret the results from the autocorrelation. Did you think about how you will handle this? Is this acceptable? Will you have to instead use external ADC chips in order to have real stereo sampling?

Slow sampling rate

If you analogRead() in a tight loop, you are taking at most one sample every 112 µs. And since you are alternating between the channels, on each channel you get one sample every 224 µs. This is a sampling rate of 4.46 kHz, and a Nyquist frequency of 2.23 kHz. Is this fast enough for your application?

In 224 µs, the sound travels about 76 mm, which is thus the spatial resolution of your autocorrelation. How does this translate into angular resolution? Is this resolution satisfactory? Do you plan to use interpolation methods to try to improve it?

If the time resolution is not good enough, you can speed up the ADC by a factor 2 or 4 at the cost of lowered accuracy. You will have to dig on the MCU datasheet (or the Internet...) in order to learn how to do that.

Inconsistent sampling rate

When you use analogRead(), the time between consecutive samples can depend on the code you run between the consecutive calls to analogRead(). It can also depend on how your code gets interrupted by, say, the timer interrupt, or the UART interrupt if you are sending data out. An inconsistent sampling rate is something you want to avoid when doing autocorrelations.

You could try to mitigate this problem by running the acquisition with interrupts disabled. However, the only way to guarantee periodic sampling is by configuring the ADC to be triggered automatically, either by a timer or by itself (free running mode). Walking this path will require you to forego the comfort of the Arduino library (analogRead() is just so easy to use...), and carefully study the datasheet, which would be a very significant time investment.

Do you have the time and energy for this? If you end up learning all this low-level details on the configuration of the ADC, will this learning be relevant to the course for which this is a project?

Finite data arrays

Mathematically, the autocorrelation is typically defined for an infinite series of samples. In your experiment, you will have to deal with finite arrays, and this makes a subtle difference. Did you think about how you will deal with the finiteness of the arrays? Are you going to zero-pad? Remove the average before zero-padding? Apply a windowing function?

I hope it is clear by now that the “cross correlation part” is only one of the many issues you will have to face. I suggest you discuss all these questions with your supervisor. He might be able to advise you on how to tackle them, whether it's worth it, where you may cut corners...