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@Man. Hi. Measuring frequency in terms of $\omega$ (radians/second) or in terms of $f$ (cycles/second, Hz) is the same as measuring speed in miles/hour or kilometers/hour. People measure frequency in terms that are convenient for them. In algebra equations it's convenient to represent frequency in terms of $\omega$ because it's easier to write the single $\... 3 Frequency is mathematically defined as the number of cycles per second. So it is a more strict word mathematically. It is represented numerically by the unit called Hertz.$f=1/T$, where$T$represents the one-period length of a waveform. This makes frequency quantifiable. Pitch on the other hand, is a perceptual characteristic of a sound frequency, so it'... 3 Consider a wheel rotating counter-clockwise at one revolution per second. Its frequency of rotation is 1 Hz. If it rotates clockwise, its frequency of rotation is -1 Hz. It's as simple as that. 2 Negative frequencies exist both mathematically and logically and you could probably accomplish the logical demonstration yourself if you want but I'll try. The mathematical demonstration is much more straightforward. OK so the logical approach would be this. Consider the energy flow in a tank circuit in a problem you are analysing. When the energy flows from ... 2 There are two numbers that square to be$-1$. Pick either one of those two numbers and call that "$j$". Then the other one is "$-j$". Doesn't matter which one is picked. The difference between$+j$and$-j$is only an arbitrary choice. A convention. Now multiply that$+j$and$-j$by a single non-zero real number. Doesn't matter which sign but let's ... 1 Yes this is very common to have a dynamic loop bandwidth such that during acquisition the loop bandwidth is wider, and then once acquired to tighten it up for better noise performance. A typical loop will have an error signal determined which is presented to the input of the loop filter. The filtered version of this error signal can be thresholded and used ... 1 What does it mean exactly to "exist" vs "just theoretical"? Do we for some reason think that$cos(\omega t)$exists while$e^{j\omega t}\$ does not? Both are equally mathematical constructions that describe our physical world. We somehow conclude that the latter as a complex quantity does not exist but the former as a real quantity does, but I don't see a ...

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Frequency is a mathematical/physical concept while pitch is a perceptual concept that correlates with frequency. Edit: or in wikipedias words: « Frequency is an objective, scientific attribute that can be measured. Pitch is each person's subjective perception of a sound wave, which cannot be directly measured.» https://en.m.wikipedia.org/wiki/Pitch_(music)

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I'm not sure but there's something called the time-frequency resolution limit, basically the shorter your windowing interval the broader your spectrum is going to be. The frequency resolution in the low frequency area may be poor because of this. Things like wavlets attempt to resolve this problem but i dont know anything about them.

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