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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 ...


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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 ...


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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.


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You can try tracking Phase-frequency of your $50 Hz$ signal using Costas Loop. Costas loop does not require the signal to be pre-processed in order to expose the desired frequency. I am not giving details of a Costas Loop because it can be found anywhere.It is pretty popular Carrier Recovery technique and a good starting point would be Wikipedia: CostasLoop ...


4

This could happen as discriminator gain is increased with a filter discriminator approach since in many of those approaches the gain would be maximum and linear for small signals only and then the slope of the discriminator slowly goes down coinciding with the results in your plot (such that you no longer get a perfect sine wave out for a sine wave in—- so ...


4

Does mixing brown noise and white noise create pink noise? No. Pink noise has a spectrum of that falls with 3dB/octave (or 10dB/decade). The spectrum of the sum of white and brown noise will be "brown" at low frequencies and "white" at high frequencies. The spectrum will have two slopes: below the transition frequency it will be -6dB/octave and above it, ...


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

Important Information : Sampling at $f_{s}$ will map $[-\frac {f_{s}}{2}, \frac {f_{s}}{2}]$ to digital frequency $\omega=[-\pi, \pi]$, and similarly sampling at $2f_{s}$ will map $[-f_{s}, f_{s}]$ to digital frequency $\omega=[-\pi, \pi]$. Also, we need to look only at digital frequency $\omega = [-\pi, \pi]$ as the digital spectrum is a $2\pi$-periodic ...


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. “...


3

I hope you do not mind, but I am going to change terminology a little bit. Since you mentioned simulations, suppose you are sampling the Gaussian white noise, at the input to the integrator, at a constant rate of $f_s$ samples per second. The point spacing, $Δt$, is $1/f_s$ seconds. Suppose $N$ independent consecutive samples are collected. Then the $N$ ...


3

I assume you are working with discrete-time, since continuous-time white noise has infinite power ($\sigma^2$). First, remember that the power of a stationary process is always equal to the autocorrelation at 0 ($P_x = R_x[0]$); and the variance is the autocovariance at 0 ($\sigma^2_x = \rm{Cov}_x[0]$). These 2 expressions are equal for processes with 0 ...


3

Dirac delta function has a continuous argument, but Kronecker delta function has a discrete argument. Your example is a discrete signal so Kronecker delta is used.


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Below is a function which I wrote long back, when I needed to generate AWGN time-domain samples given Noise PSD in dBm/Hz. AWGN_NOISE() : Generates Additive White Gaussian Noise of PSD power in dBm/Hz AWGN has Gaussian PDF with 0 mean and $\sigma^{2} = N_{o}/2$ $NoisePSD_{dBm/Hz} = 10.log_{10}(\frac{N_o}{2.BW})$, Why? Because, Output Noise Power(in dBm) :...


3

Given that the FFT over that many samples does not show any results, your challenge may be in the overall spectral purity of the 50 Hz tone you seek. The FFT bin at 50 Hz is a correlation to that bin frequency which is the optimum detection in terms of SNR of a 50 Hz signal in the presence of white noise. The issue is the equivalent noise bandwidth of that ...


3

Uncorrelatedness of WSS noise process is required to model the Noise as White Noise. And, Whiteness of noise is a desired property of noise process so that we can assume that the image spectrum is affected by the noise equally across the complete image spectrum. There is no frequency selective impact on the image. Explanation : You can understand it like ...


3

It is simply because each sample of $n(t)$ has a random magnitude and phase by definition given as $n(t) = |n(t)|e^{j\phi(t)}$. With real and imaginary components as follows: $$|n(t)|e^{j\phi(t)} =|n(t)|\cos(phi(t))+j|n(t)|\sin(phi(t)) $$ Real: $I(t) = |n(t)|\cos(\phi(t))$ Imag: $Q(t) = |n(t)|\sin(\phi(t))$ Since the phase and magnitude are independent ...


2

I would like to give another take on @DanielSank's answer. We first suppose that $v_{n} \sim \mathcal{CN}(0, \sigma^{2})$ and is i.i.d. Its Discrete Fourier Transform is then: $$ V_{k} = \frac{1}{N} \sum_{n=0}^{N-1} v_{n} e^{-j 2 \pi \frac{n}{N} k}$$. We want to calculate the distribution of $V_{k}$ To start, we note that since $v_{n}$ is white Gaussian ...


2

I cannot post comments, as I created this account only to add something to this answer and I must have 50 reputation, as I found this post very helpful as a memory refresher (currently writing my PhD thesis). I hope this is not considered necro-posting. I would like to add to Dan Boschen's answer that one must pay A LOT OF ATTENTION to units: It is true ...


2

You can use cv2.PSNR like this example: import cv2 img1 = cv2.imread('img1.bmp') img2 = cv2.imread('img2.bmp') psnr = cv2.PSNR(img1, img2)


2

turn to float first!!!!!!!! turn to float first!!!!!!!! turn to float first!!!!!!!! def compute_psnr(img1, img2): img1 = img1.astype(np.float64) / 255. img2 = img2.astype(np.float64) / 255. mse = np.mean((img1 - img2) ** 2) if mse == 0: return "Same Image" return 10 * math.log10(1. / mse)


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

...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

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

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

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 ...


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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 ...


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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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How to calculate the variance of the noise samples $n[j]$ in terms of $N_0$ and $B$, where $n[j]$=$n_f(jT_s)$ and $T_s$ is the sampling period? Do you know how to calculate the variance of the process $\{n_f(t) \colon -\infty < t < \infty\}$? No? Hint: it is the area under the power spectral density curve of $\{n_f(t)\colon -\infty < t < \...


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