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I couldn't quite follow your code (you calculate two different versions of the ACF?), but I believe the problem with the plot being shifted toward zero is that xcov calculates the cross covariance not correlation. Remember that cross covariance is subtracting the mean, so there should be a shift! You should be calling xcorr instead.
The following code ...
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There are a few things going on:
The complex representation of frequency is such that the real part corresponds to a cosine component and the imaginary part to a sine component. So a complex phase of 0 corresponds to a cosine wave, not a sine wave. This is why the computed phases are off by about 90 degrees from what you expect, according to the trig ...
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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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You are asking to understand this in the context of an implementation for signal processing, which requires an explanation based on programming. Ever the two worlds. Math has to work on paper and in reading minds, programmed implementations has to work in the world.
Because I read the 1988 Byte article, I searched just now and found [an article that ...
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Here's a definition of the energy of a signal from Wikipedia: https://en.wikipedia.org/wiki/Energy_(signal_processing)
For your specific signal, I recommend to draw the original signal and then the transformation. Finally, just calculate the squared magnitude and the area under it.
These are plots of the steps I mentioned (from Matlab):
As you can see in ...
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Scrambler is a randomizer with a purpose to encode transmitted data so that there will be no long sequences of only zeros or only ones in transmitted data. It is done to support proper timing recovery, when receiver waits for bit transitions to synchronize. Scrambling is usually done for channels with self-synchronized line codes, e.g. ISDN u-interface and ...
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"Target" is a military term; historically, that's why it's the word used for "identifiable thing from a radar system".
So, I wouldn't use "target detection" outside of radar systems, whereas the word "object detection" is generally used in image processing (for anything that isn't a person). I might be a bit alone with ...
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Not really an answer but some hints on how to proceed.
You need to debug this on step at a time. Start with shortening the inputs to the Focusrite and disconnect the Linux computer entirely. If you still see noise, disconnect the power supply from you laptop and run battery only. If it's still noisy, either the Focusrite or the USB interface are bad (i.e. ...
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I'll give this a shot.
The Fourier Transform of a Gaussian is also a Gaussian. The standard deviations in each domain are related as $\sigma_t \cdot \sigma_F = \frac{1}{2\pi}$ The time standard deviation, $\sigma_t$ has units of time and the frequency domain standard deviation $\sigma_F$ has units of Hz.
We can define the "bandwidth" of a gaussion ...
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The fact that it's modulated with a sinusoid doesn't change the FWHM bandwidth of your pulse – the $e^{jx}$ function has $\left\lvert e^{jx}\right\rvert\equiv 1$ at every point. That doesn't change the amplitude, so the FWHM of a sinusoid-modulated gaussian is just the same as of the unmodulated gaussian.
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Is that to be expected when doing FFT analysis of any signal?
No. Either your calculation or the implementation of your analysis is off.
Secondly, I thought that the fundamental frequencies in my signal should have the highest amplitudes from all other peaks.
Why did you think that? There are many signals where the fundamental is lower than the harmonics ...
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The physical siginificance of the Fourier transform for nonperiodic (finite energy) signals is not something clear from any point of view.
The limiting case of a Fourier transform of a periodic signal, as the period goes to infinity, consists of line components (dirac impulses at a countable set of discrete frequencies) which becomes more and more crowded, ...
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Perhaps standard deviation is what you want. Standard deviation
$$\sigma= \sqrt{\frac{1}{n}\sum_{k=1}^n (x_k-x_{ave})^2}$$
(where $x_{ave}$ is the average of your sequence) quantifies the fluctuations of your sequence above and below the sequence's average value. The square of the standard deviation, $\sigma^2$, is the variance of your sequence which is a ...
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You seem to be computing phase near the beginning of your window, where there can be a circular discontinuity. There are (at least) 2 ways to solve this issue.
One is to use a window and FFT or DFT length that are exact integer multiples of the period of any sinusoidal inputs.
The second way is to measure phase from the middle of your data window, by doing ...
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