# Tag Info

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Yes, you should use 0 for both. As the EKF assumes that noises have 0 mean, I would evaluate them there. If you look up the Wikipedia page, it also suggests the same. If you would use a single sample, then You would need a random number generator (if you use the algorithm on an embedded system, you might want to avoid this). Most importantly, this would ...

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You can create noise with the same frequency-domain characteristic as your example noise image simply by multiplying a white noise frequency spectrum by the magnitude of the frequency spectrum you are trying to emulate. White noise is expected to have equal power at all frequencies (though this will not be exactly the case), so the multiplication will "...

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That's a common technique in audio Audio modulation effects like Flanger, Phaser and specifically Chorus Pitch shifting, sample players, auto-tune, etc. In a sense "sample rate conversion" would qualify FM modulation synthesizers.

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What features from them do I need to know in order to determine a strategy to remove them ? Likely the most important feature you need to know about these noises is their spectral content. In other words, you need to know how the energy of each of noise is spread out across different frequencies. If you have a recording of the noise you want to remove, you ...

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So, first of all, a filter in signal processing is analogous to a filter that you'd use on liquids. A coffee filter passes through the stuff you want (liquid coffee), and holds back the stuff you don't want (coffee grounds). It does this because the coffee grounds are bigger than water molecules, and all those yummy flavor molecules (not to mention ...

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https://ww2.mathworks.cn/matlabcentral/answers/644668-why-is-the-relationship-between-es-n0-and-snr-different-for-complex-and-real-signals?s_tid=srchtitle In my opinion, no matter it's complex signal or real signal, the SNR equals to the input signal power, S, divided by the noise power, N. The difference is, for complex signal, S = Si + Sq, (Si = Sq, no ...

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When you double the sampling rate, SNR halves, because the total noise power, $N$, in the sampling bandwidth, doubles, but $E_s$ is still the symbol bandwidth, i.e. $F$, the baud rate bandwidth, so $E_s$ remains the same. However, $E_s/N_0$ remains the same, because $B$ doubles when the sampling rate doubles, giving the same $N_0$ as before. It turns out ...

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The autocorrelation of white Gaussian noise is a delta. When the noise is filtered or band-limited, as is the case here, the autocorrelation becomes a sinc. This has interesting consequences, for example in telecommunications, where the noise at the output of a matched filter is uncorrelated only at certain time delays -- fortunately, the time delays we're ...

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I think you'll need to specify where you're adding the noise in your model. Are you adding at the Tx output or in the Rx before or after the filter? In one of your comments you show that you're scaling the noise based on an apparent TX SNR spec. I assume that means you'll want to add the noise at the Tx output. In that case you'd use the tx signal ...

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Well, the naive approach would of course be using the complementary of your band-pass filter (letting through the allowed information) as band-stop filter, and use that to shape uncorrelated noise to be where the stop-band of the original filter is. Then, add both. If you don't want to do that, for example because you've read about dirty paper coding and ...

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You are correct that there is no transfer function, because the system is nonlinear Your suggested approach to finding the statistics of $x$ won't work, because the definition is circular. There are methods for finding the probability density function of a function of another random variable.

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The function filtfilt filters the signal twice (forward and backward) in order to eliminate phase distortions. As a side effect, your signal is not filtered by the transfer function corresponding to the numerator and denominator polynomial coefficients supplied to the routine, but by its squared magnitude. You should use an ordinary filter routine, such as ...

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If the noises signal are mutually uncorrelated the power of the sum is the sum of the powers. For three signals you get $$\sigma_{total} = \sqrt{\sigma_A^2+\sigma_B^2+\sigma_C^2}$$ Works any type of uncorrelated noise, Gaussian or not.

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The Local Oscillator is multiplied in the time domain with the received (or transmitted) signal and therefore the spectrums (phase noise spectrum and signal spectrum) will convolve in frequency. A significant driver of the phase noise mask in the receiver is blocking (jamming) resistance and ability to demodulate two closely spaced channels that have a large ...

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How about the noise PSD when upsampling is filled with duplicated samples. Check this post.

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Something like Bendat and Piersol's Random Data Analysis might be a good starting point. It's written more for physical scientists rather than people doing estimation and detection theory like the references in the comments (Gray, Kay, etc.). For specifically spectral analysis, Percival and Walden's Spectral analysis for physical applications was recently ...

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An easy way to demonstrate how dithering improves accuracy in quantized systems (which includes the approach the OP used to estimate frequency) is to consider this example of a system that is quantized to integers with "truth" being some fraction in between such as $1.4$. With no noise added, our result would always be $1$. If we added enough noise ...

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Sounds like you have a zero crossing algorithm, and depending on the relationship between sine frequency and sampling frequency, I can easily see systematic errors when estimating frequency from zero crossing rate. Adding noise would presumably act as a dither that introduce spurious perturbations about the true (desired) mean. If you estimate frequency from ...

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