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9

A "pure" signal, No. A less noisy signal? Possible? Yes but there are several complications that may make this impractical. You basically need to align the 2 recordings and then add them. You might gain 3dB in SNR. but The paths from the source to the 2 locations aren't the same, so they will differ to some extent, so the copies may not add ...


8

Is it possible to reconstruct the original pure signal? No, that is information-theoretical impossible. Also, that signal doesn't exist, probably, to begin with ;) However, you can definitely increase the the SNR simply by averaging; that becomes pretty obvious when you consider the signal of interest to be correlated within your recording, whereas your ...


6

Common Approaches for Commercial Denoisers Commercial denoisers are different than what you'd see on most papers. While on papers the results are mostly using objective metrics (PSNR / SSIM) and are evaluated vs. Additive White Gaussian Noise (AWGN) with high level of noise real world images are mostly with moderate level of noise with Mixed Poisson ...


6

There can't be. One man's signal is another man's noise. In fact, a communication system making the absolute most of a bandwidth would be spectrally white, just like white noise, and hence be indistinguishable from noise to anyone but the receiver for that specific system.


4

If you are simply interested in plotting the data then any data reduction technique would do,even if it appears to be crude. Effectively, the plotting function itself will not plot all the data, because the space assigned to the plot has a finite number of $N_x \times N_y$ pixels assigned to it. For example, if your plotting area was $1024 \times 768$, then ...


3

The first paper is more clear than the second. "Let $\mu$ represent the distribution of linear attenuation coefficient of an object and $[A \mu]_m$ represents their line integral. " The signal obtained from Computed Tomography (CT) depends on how much was the X-Ray beam attenuated as it travels through the human body (there are other modalities such as ...


3

A continuous-time white noise process $\{X(t)\colon -\infty < t < \infty\}$ is a hypothetical construct that we can treat (in the simplified versions that we use on dsp.SE) as a zero-mean wide-sense stationary process with autocorrelation function $K\delta(\tau)$ where $\delta(\cdot)$ is the Dirac delta. More strongly, all the random variables $X(t)$ ...


3

A) The quantization of the photocurrent is an actual physical phenomenon. I'll use $\Delta T$ in place of your $dT$. It is not a variable describing the actual physical process but rather the time step of your approximate model. Effectively you are filtering the continuous-time Poisson point process by a continuous-time "moving average" filter with a ...


3

This is an excellent series of questions, so I will have a go at part of it! I will start with an example from Verdeyen’s book (J. T. Verdeyen, Laser Electronics, Prentice-Hall, Inc., Englewood Cliffs, NJ, ©1981, Chapter 14). Assume $\lambda$ = 500 nm, quantum efficiency = 0.15, photomultiplier (PMT) gain = 1.68x$10^7$, transimpedance = 1 k$\Omega$ and RC= ...


3

To be honest, I don't think CNNs, RNNs and LSTM are useful for this kind of problem – a bandpass filter followed by a threshold would be. Now, that would have three parameters: Lower cutoff frequency Upper cutoff frequency threshold value and what is usually called "Machine Learning" is nothing but finding local minima over some (loss) function with real ...


3

As Stanley Pawlukiewicz said: even under ideal circumstance, you can gain 3 dB of SNR per doubling of recordings. I.e., to increase SNR by, say, 15 dB, you'd need to average $$ 2^{\frac{15}{3}} = 2^{5} = 32$$ recordings. That alone shows that the whole thing isn't really practical: it just doesn't do much unless you use a crazy-high number of recordings. “...


2

This is a really nice problem. Problem Formulation I will formulate it as following: Let $ x \in \mathbb{R}^{n} $ be a signal. Given $ y \in \mathbb{R}^{n} $ which is a noisy measurement of $ x $ such that $ y = x + v $ and $ z $ be a noisy measurement of the derivative of $ x $ such that $ z = F x + w $ where $ F $ is the finite differences operator. ...


2

You will find some pointers with the correct wording. There is a lot of statistical literature on monotone or monotonic regression (sometimes called isotonic regression). A more generic term is "shape-constrained estimation". For instance, a few references: Constrained statistical inference: inequality, order, and shape restrictions, 2005, Mervyn J. ...


2

According to this app note by Freescale: http://cache.freescale.com/files/sensors/doc/app_note/AN5087.pdf which came from this recent related question: How to interpret Allan Deviation plot for gyroscope? with a copied graphic below where they give the bias instability for each axis. What a specific manufacturer does on their datasheet, you would be best ...


2

The significance is a statistical measure of frequency error you would get if you averaged the frequency error over that duration of time, $\tau$, as compared to the average over a same duration of time, that much time prior. So it is a measure of the difference in error, and specifically the rms value of many of these measurements. This is useful for non-...


2

If you hope that $f[n]$ can be sparser in some linear representation $L$, then robust statistics can be used to estimate variance bounds on coefficients of $L(X[n])$. One common method is orthogonal wavelet denoising, where a common standard deviation estimate is: $$ \mathrm{median} \frac{|c_i|}{0.67449} $$ where $c_i$ denotes the highest scale subband. The ...


2

How did the professor state this? Did they say that the noise is iid? That means that the samples are independent, identically distributed. That means they are independent by definition (they are assumed to be so). White noise, while a little more vague, also makes the assumption of independence. Again, this means that the noise is assumed to be ...


2

When would it be beneficial to model the signal as an outcome of a stochastic process? When the process that generates the image/signal has a strong element of chance. This is not related to noise necessarily. Sometimes, a deterministic model for the behaviour of a quantity simply does not exist. For example, modern supermarkets have barcode readers that ...


2

yes, you are right. But there is misconception that figure of merit is the ratio of output to input SNR. It is actually the ratio of output SNR of a receiver to the output SNR of a baseband system (without modulation). Here, the output SNR of a baseband system is taken as a benchmark for judging noise performance of receiver. Hence, FoM = (...


2

Without knowing the context, here is what probably is meant: 3.75 refers to a more real-world sensor. The sensor described in 3.74 apparently is assumed to be perfect, ie whenever there is a negative/positive sensor data, the true signal does have the associated property. Ideal sensors, however, do not exist and 3.75 tells you, that your sensor does have ...


2

Working with your definitions: $$ v \left( \left( n + 1 \right) {T}_{s} \right) - v \left( n {T}_{s} \right) = \int_{0}^{ \left( n + 1 \right) {T}_{s} } g(u) du - \int_{0}^{ n {T}_{s} } g(u) du = \int_{ n {T}_{s} }^{ \left( n + 1 \right) {T}_{s} } g(u) du $$ So basically we have integration (Which is a Low Pass Filter) of White Noise over a Time Interval ...


2

The frequency domain conjugate multiplication (correlation) of the received signal with the reference signal followed by the power delay profile will provide you the overall signal to noise ratio. As explained in paper titled "SNR Estimation based on Sounding Reference Signal in LTE Uplink". There are various noise reduction algorithm exist. Which will ...


2

The key issue here is whether the signal and noise are uncorrelated. Assuming two real random variables x and y are both zero mean, the power of the combined signal is $E\{(x+y)^2\} = E\{x^2+2xy+y^2\} = E\{x^2\}+E\{y^2\}+2E\{xy\}$ If the two variables are uncorrelated, then $E\{(x+y)^2\}=E\{x^2\}+E\{y^2\}$ In other words, the power of the combined signal ...


2

Synthetic Method: If $\{\hat X(t)\}$ and $\{\hat Y(t)\}$ are zero-mean uncorrelated low-pass WSS processes with identical autocorrelation function $R(\tau)$ and identical power spectral density $S(f)$ enjoying the property that $S(f) = 0$ for $|f|>B$, then $$\hat{N}(t) = \hat X(t)\cos(2\pi f_ct) - \hat Y(t)\sin(2\pi f)ct$$ is a band-pass process whose ...


2

...And now for a differing opinion.... The OP's representation of bandpass white noise as $$n(t) = n_I \cos(2\pi f_ct) - n_Q \sin(2\pi f_ct)\tag{1}$$ is inadequate; because each sample path of this noise process is a pure sinusoid of fixed frequency $f_c$ Hz which is not noise-like at all. Why so? Well, a sample path is what one gets when all the random ...


2

There are two mistakes in your code/method. The first is the term $\sqrt{\Delta t}$ in your second formula; it should be replaced by $\Delta t$. The second is in the computation of the power spectrum from the estimated auto-correlation. What you do is square the result of the FFT Y to obtain mY, but that's not correct. First of all, Y is complex-valued, and ...


2

i would suggest you use randn() instead of rand(). The most straightforward way to produce band limited noise is to filter white noise. you could conceivably use a Gibbs sampler but that would be less efficient and require knowing how to set up the problem. Could you explain why you are making a distinction?


2

There are indeed many peak detection algorithms, and no clear consensus on which ones are "good" or "bad". But for what it's worth, your approach makes sense. Using median or other quantiles to detect sparse signals is common, e.g. the "median clipping" stage in Lasseck (2014), Large-scale identification of birds in audio recordings. In effect, you're ...


2

I'd do some small adjustments to your idea (You really nailed them). Assumptions The Signal Model - Signal + Additive White Gaussian Noise (AWGN) Probably we could generalize it more but this is beyond the scope of this question. The DFT of the signal contains Peaks with relatively small roll off This is important as we're almost saying the Signal is a ...


2

Assuming that the sensors share the same characteristics, have the same timing (acceleration signals are aligned), the model with $y_1= x + n_1$ and $y_2= x + n_2$, $n_1$ and $n_2$ being uncorrelated noises of the same power, averaging them is a way to reduce the noise. The theory that asymptotically, averaging $N$ sensors reduce the variance by a factor of $...


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