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@@ -329,9 +329,11 @@ includefoot=true,top=19mm,nohead,footskip=12mm,bottom=6mm]{geometry} \item Not sensitive to other quantities \end{enumerate} An example of a bad sensor for example is the PacoSensor 1000+ that measures temperature with a photo camera by checking the color of a stove top. Sure you can do that but its judging temperature through color, which is bad, we should measure as directly as possible. The PacoSensor 1000+ violates the last 2 points. It is not sensitive to the quantity being measured, and it is sensitive to other quantities.\\ -A sensor should have a simple response curve, if we graph temp with respect to the response of the sensor, we want something linear or like exponential or log. A weird curve makes it harder to interpret the temperature from the response. $r(t) = f(t) = at+b$. But we generally want linear. This should at least be guaranteed in the sensor's operating range also called the dynamic range.\\ + \subsection{What a sensor measures} + In an ideal world, a sensor should have a simple response curve, if we graph tempurature with respect to the response of the sensor, we want something linear or like exponential or log. The sensor's response curve shouldn't be some weird bumpy loopy line. A weird curve makes it harder to interpret the temperature from the response. $r(t) = f(t) = at+b$. But we generally want linear. This should at least be guaranteed in the sensor's operating range also called the dynamic range.\\ Remember, transduction is the conversion of a physical phenomenon to an electrical signal, called $s(t)$. If $f(t)$ is physical quantity, then $s(t) = f(t) + n(t)$ with $n(t)$ being noise (conversion is noisy). For a microphone, noise can include background noise, sensor distortion, electromagnetic interference, thermal noise, etc. You can account and remove some noise, but you cannot fully eliminate it.\\ We also have to do sampling, because $f(t)$ is continuous which computers handle that poorly. Sampling is taking a subset of a continuous curve, making discrete measurements at a uniform distribution. We then only consider those discrete points. Issues such as data loss, especially important if the continuous data changes quickly. This can be mitigated with a higher sampling rate. Also between the points we assume a straight line or constant data, which introduces distortion.\\ + \subsubsection{} Definition -- Fourier analysis is the deconstruction of a wave function into sine and cosine functions.\\ So we can apply Fourier analysis onto $s(t)$ to break it down into sine and cosine functions with different frequencies. The point of doing this is the find the highest frequency component that matters, (which sin/cos function contributes the most to the overall wave) because sampling has to be double the highest frequency. Otherwise you lose too much data. Human sound is around 20khz, so a microphone needs to sample at 40khz. 44.1khz is the CD sampling quality. Finding the most significant frequency also helps with filtering noise.\\ For us, we will look at Fourier analysis through the lens of discrete linear algebra. For this, ortho-normal basis are important.\\ |