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LOW SIGNAL NOISE RATIO FFT

Try using an input of a very pure sine wave at an exact multiple of 23.4375 Hz. A sinusoid that is integer periodic in the FFT length will show a maximum magnitude FFT result for a maximum (for the data type) amplitude input. Otherwise the energy of a non-saturating input will likely get spread into multiple FFT result bins, resulting in a lower peak magnitude. 1. A turn signal, in California?

A! Not a good idea to NOT signal going into your own driveway if you live near a heavly transited road

2. Calculating a periodic signal (way of solving this)?

HINT: Let be \$f(t)=Pi(t/2)Pi(t)\$. So we have \$\$ x(t)=sum_n=-infty^infty f(t-4n) \$\$ Can you see that \$x(t)\$ is periodic with period \$T=4\$? 3. UART signal distortion with AVR

Your problem is likely in using the wrong baudrate: 112500 is most likely a mistake, the standard rate in that range is 115200 (a search of the manufacturer's website for this number finds many hits, but none for 112500). You could also not be producing the programmed baud rate on one end or the other due to divider granularity; sometimes changing the oversampling of the UART can help. EDIT: Specifically, a value of 8 (divisor of 9) will get you 111111 baud from 8MHz if you set the "double speed" mode bit. Secondarily, you have a problem such as lack of a common ground between the boards, or have not grounded the scope to them, thus resulting in the distorted waveform. It's not clear yet if that is what the receiver sees, or if it's merely a measurement mistake in applying the scope.Additionally, have you verified that the un-named external board also runs without a serial level translator? Most modular inter-board serial communications is at RS232 levels and logically inverted from the logic-level signals, though there are exceptions.

4. What is the best way to detect repetition in xyz data for purposes of splitting data?

It sounds like you have a set of known patterns and want to find places in your signal where these patterns occur. A typical way of doing this is using the cross correlation. In this approach, you would compute the cross correlation of your pattern with the signal. You can think of this as repeatedly shifting the pattern by some lag to align it with a different portion of the signal, then taking the dot product of the pattern and the local portion of the signal. This gives a measure of the similarity between the pattern and the local signal at each lag. When the signal matches the pattern, this will manifest as a peak in the cross correlation. Different variants of the cross correlation exist. For example, some versions locally scale and/or normalize the signals. This can be useful if you want your comparison to be shift/scale invariant (e. g. you want the shape of the signal to be the same, but do not care about the actual magnitude; in the case of detecting accelerometer patterns, this might correspond to performing the same motion but more or less vigorously).The cross correlation will naturally fluctate, reflecting varying degrees of similarity between the pattern and signal. So, the question is how to distinguish peaks that represent a 'true match' from those that reflect partial similarity. You will have to define this based on the variant of cross correlation you use. For example, if the pattern exactly matches the signal at some offset, the magnitude of the unnormalized cross correlation will equal the squared \$l_2\$ norm of the pattern (i.e. the dot product of the pattern with itself). Some normalized versions of the cross correlation will have maximum amplitude 1. Another thing you would need to define is some tolerance, to account for noise in the signal (you probably do not want to require an exact match).Another possibility is that you want to use some other measure of similarity (e. g. the euclidean distance). In this case, you could use peaks in the cross correlation to identify candidate matches, then check them using whatever distance metric/similarity function you like.One of main the reasons to use cross correlation is that it's very computationally efficient. For large signals, you can gain even more speed by computing it in the Fourier domain, using FFTs. Many packages/libraries are available to do this.The cross correlation approach (and FFT acceleration) will also work for higher dimensional signals (e.g. images)

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