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In music theory, an octave is an interval in frequency, from a frequency $f$ to frequency $2f$. For example "an octave higher" means "twice the frequency". Expressed as wavelength inversely proportional to frequency, $\lambda \propto \frac{1}{f}$, an octave would be the interval from a $\lambda$ to $\frac{1}{2}\lambda$. In the SIFT paper'...


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There is no reason why your piezo shouldn't be able to produce a bipolar output, if you use proper biasing and/or preamp. See for example https://www.homemade-circuits.com/diy-contact-mic-circuit/ Working with the magnitude only is probably a non-starter. $y = |x|$ is a highly non-linear operation and will dramatically change your spectrum. For example a ...


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Analyzing signals per segments, with proper windowing, is a way to cope with non-stationary in audio samples. With full-size analysis, features can get mixed. Segment-splitting is thus at play in many algorithms (mp3, shazam). The length of window is often a matter of trade-offs, between data information and computing advantages: signal sampling (window ...


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A feature is a number that describes one aspect of a signal. Signals can be very complex, and the simplest analysis tools (like a time plot, a spectrum, or an energy measurement) don't tell you everything; in fact, for specific types of analyses, they almost don't tell you anything useful. So, features are designed to describe very specific aspects of a ...


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I don't understand whether these processes are also invariant to object-alterations! They are not. How would the extracted fft-features look, if I alter the object (scratches, marks, dents etc.)? Would I still be able to match them properly? Yes. But within certain limits. The Fourier-Mellin transform is based on the Discrete Fourier Transform (DFT) whose ...


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The Karhunen–Loeve Transform is the equivalent of PCA analysis for continuous signals, you could seek more informations on this type of Feature extraction. 1/The idea is to compute the covariance matrix on known signals (i don't know, maybe the ECG of a person suffering from a particular heart disease). $C = (x-\bar{x})(x-\bar{x})^T$ where X is your ...


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