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This is the classical sampling theorem. When you sample a continuous signal $x(t)$, you are basically multiplying it by a sample train $s(t) = \sum_{-\infty}^{+\infty}\delta(t-kT_s)$, the value at consecutive $T_s$ being your samples. In frequency domain, it effect is to convolve $X(\omega)$ and $S(\omega)$ $$S(\omega) = \sum_{-\infty}^{+\infty}\delta(\...


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We can do it in 2 simple steps: You can actually estimate $\omega$ of your input signal easily by taking FFT of the measured n samples. I am suggesting this only because offline processing is an option, otherwise this would be pretty computationally costly. Once you have a close estimate of $\omega$, then you can use Weiner filtering to predict $x[n]$ from ...


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On a simpler note, if you take WLAN systems, the preamble has initial sequence called STF which is comprised of repetitions of known sequences. Let us say the length of basic sequence is $L$. If there are 4 repetitions (like 802.11n), total length of STF will be $5/4L$ including Cyclic Prefix. For now, we will ignore cyclic prefix part and let us consider ...


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The noise of interest would ultimately be over the bandwidth of your signal and specifically all filtering done prior to ultimately making a decision over which symbol was transmitted- which would typically be the bandwidth of your matched filter. So given a noise density in $dBm/Hz$ you can translate that to the total noise in the signal to noise ratio of ...


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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 ...


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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 ...


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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 ...


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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.


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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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With respect to a known given fixed point in time (and space if you assume a time-space coordinate system), a negative frequency sine wave is simply the negative of a sine wave or sine() function basis vector that starts with a phase of exactly zero at that same exact point in time. The fixed point in absolute time can also be defined to be periodic with ...


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Can someone please kindly explain this idea of representation of real sinusoidal signals in terms of positive and negative frequency components? Here is my view. As you can see in most books related to DSP, a complex exponential $e^{j\omega_0 t + \phi}$ is a fundamental signal representing a point on unit circle on complex plane at the angle $\omega_0 t ...


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You can have the channel of 200kHz split into orthogonal sub-carriers. But for this you need to meet certain requirements to eliminate ICI (Inter-Carrier Interference, Not ISI Inter Symbol Interference). If you lose orthogonality, the data in one sub-carrier will be affected by data in another sub-carrier (hence inter-carrier interference). In order to ...


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In addition to the distinction that frequency is an objective measure and pitch is a subjective one, it's also useful to note that the pitch of a note may not be directly related to any easy measure of frequency. Case in point: a bell, tuned to A440, will generally emit sound energy at roughly 880Hz, 1320Hz, 1760Hz, etc. -- in other words, for a pitch ...


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In simple terms your regular frequency is how many times in a second, the signal goes through the same cycle. This is not restricted to a sinusoid alone (because any real world signal can be represented by sum of sinusoids). When you say regular frequency is 60Hz, the signal cycles itself 60 times in a second. Each period is 1/60s. A sinewave is a ...


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'...


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It's a matter of the units used to measure frequency as events which happen per unit of time. For the regular frequency f, we ask: How any wavelengths pass a specific point per second?\ For the angular frequency $\omega$, we ask: How many radians are traversed per second? The easiest way to visualise the angular frequency is by understanding the ...


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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 $\...


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Many signals we observe are functions of time, i.e., their value changes with an independent time variable, which can be measured in seconds. Frequency is a measure of how fast a signal changes and thus measured in "per second" which is the same as Hertz: 1 Hz = 1/s. An oscillation is an excellent example: a harmonic wave can be described as $e^{\jmath 2\...


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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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