5

The developers of both are the same hence the similarity is indeed "By Design". The only difference is the addition of 2 constants in SSIM (C1 and C2). The UQI: The SSIM: As the writers write in the SSIM paper: Namely, UQI is a private case of SSIM for C1 = 0 and C2 = 0.


5

In ideal world you'd have the correct model and use it. In your case, the model isn't perfect. Yet the steps you're suggesting are based on a knowledge you have about the process - which you should incorporate into your process equation using your dynamic model matrix: The classic and correct way given F matrix is built correctly according to your knowledge....


3

Similar to the preferred answer above (Jason S.), and also derived from the formula taken from Knut (Vol.2, p 232), one can also derive a formula to replace a value, i.e. remove and add a value in one step. According to my tests, replace delivers better precision than the two-step remove/add version. The code below is in Java, mean and s get updated ("...


3

Preface First of all: Arduino might really not be the tool of choice here; with a 1MS/s max, and some something-in-between-8-and-16-effective-bits ADC, there's hard limits on what you can detect. I will explain the theory of how to do better estimation than just sample-wise, but I won't address these limits here. Furtherore, I assume you do real-valued ...


3

why does this power measurement (which is an instant function of time) It's NOT a instant function of time. For example instantaneous power of a sine wave is $$ p(t) = x(t)^2 = A \cdot cos^2(t) = \frac{A^2}{2}(1+cos(2t))$$ You have to apply some amount of time averaging to get rid of the $cos(2t)$ component and that's what all spectral analyzer do. : if I ...


2

Following my comment, I now have time to post it as an answer. If you expect that a large enough portion of the vectors belong to that line, you can use RANSAC. RANSAC works by selecting a small and random subset of the data and fit it to the desired model (say a line). The fitting can be achieved in any way you like, e.g. least-squares. Then, the data is ...


2

A variation on @geometrikal's answer would be to use the Goertzel Algorithm. $$ y[n] = x[n] + e^{+j\omega_0} y[n-1] $$ where $x[n]$ is your input signal, $\omega_0$ is the frequency you know, and $y[n]$ is the (complex-valued) estimate of the discrete Fourier coefficient.


2

In my experience in the defense industry, the quality assurance engineers are mostly just “box checkers” that have limited understanding of how all of the individual facets of the algorithms and systems work. We have design engineers, integration engineers, and then the QA engineers. I have never seen an integration engineer or QA engineer get involved in ...


2

Most technical terms, such as these two, do not get their definitions purely from their etymology, but rather from the context of application, by experience and by tradition of acceptance. And for this case, your understanding of separability as the allowence (or ability) of someone to distinguish between two closest time of arrivals seems a synonym to the ...


2

Not sure to understand what you are asking, Microwaves wavelengths range between 300 MHz (1 m) and 300 GHz (1 mm) which is indeed of the same order of magnitude as the probe. 1GHz corresponds to a wavelengths of about 30 cm and is also in the Microwave range. Are you saying that it is possible to measure a frequency of 1GHz with a probe while it is ...


2

I only know the vastly simplified form: all satellite nav systems work by the satellites telling you where they are and what time it is. In GPS terms, that time is the "pseudorange", and it's all you need (in theory) to locate yourself. With no satellites in view, you have no clue where or when you are. With one satellite in view, you can place yourself ...


2

Using an FFT to measure phase for just two tones results in a lot more processing that doing the following alternate approach that can be either streamed or processed in blocks. No windowing is needed: Apply the received signal as the input to two multipliers. Apply a normalized local copy of one tone as the second input to one of the multipliers and a ...


1

If your data $\mathbf{x}$ has variance $\text{var}(\mathbf{x})$ and you want to add Poisson noise to it with signal to noise ratio of $\text{SNR}$ dB, then you can just generate Poisson random numbers with appropriate variance. The variance of the noise $\mathbf{n}$ you need is $\text{var}(\mathbf{n})=\frac{\text{var}(\mathbf{x})}{10^{\text{SNR}/10}}$. So ...


1

Zero pad your FFT (append zeros) such that you get more samples of the Discrete Time Fourier Transform (DTFT). The DTFT would give you the sidelobes and roll-off that you want to see (specifically for your diagram you would zero pad an input that is all ones, or an input that is any constant value).


1

The standard (conventional) definition of DFT (1D or 2D) is not unitary. See for example the 1D standard (conventional) DFT pair as: $$ X[k] = \sum_{n=0}^{N-1} x[n] e^{-j \frac{2\pi}{N} n k } $$ and $$ x[n] = \frac{1}{N} \sum_{k=0}^{N-1} X[k] e^{j \frac{2\pi}{N} k n} $$ DFT is not unitary due to the fact that the forward and backward transforms are not ...


1

So I guess I should have looked around a little better. I've found that SINAD and THD+N are reciprocals. These references were useful: https://www.ap.com/technical-library/more-about-thdn-and-thd/ http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.476.1903&rep=rep1&type=pdf


1

So, when you remember how the step response, impulse response and frequency response are related, you'll notice that if you, instead of an actual impulse integral (i.e. a step) use something that is wider, then the frequency response simply gets windowed to lower frequencies. In other words, and to put it as an information-gathering problem: if the ...


1

My office is also struggling with this problem. We concluded that three skill sets required: signal processing, human centered computing (HCC), and computer science (CS). The algorithm development needs programming skills that are typically beyond the skill set of an electrical engineer who specializes in signal processing, so the job applicant deserves a ...


1

I agree with @user28715 answer. The best method is to apply a filter to your timeseries to get calibrated timeseries. Filter You did not specify which language you are using, but in Matlab I use the designfilt function. https://www.mathworks.com/help/signal/ref/designfilt.html d = designfilt('arbmagfir',...); a = 1; b = d.Coefficients; or you ...


1

Jitter should pretty much be zero-mean, otherwise it'd be a frequency offset. I've zoomed into your screenshot and it seems the horizontal distance between two points in the FFT plot is about 5 pixels, and your picture happens to be 1000 pixel wide – wild guess, this is an 256-point FFT. In that case, the frequency bin spacing is $\frac{f_{sample}}{256}=\...


1

You've got it – zero mean noise still has power. That power happens to be its variance. RMS of such signals thus happens to be the noise amplitude's standard deviation – and give a sensible number to assess link quality and error probabilities.


1

I would want to start from e.g. making a measure of "color" that's a single real value, rather than a triplet. Then I could perhaps want to make a function that calculates the "change in" color between pixels adjacent to each other. So a derivative of some kind Why would you need the color to be a single value for that? I'll do an analogy: To measure the ...


1

It's (fitted) parameters are mean = 35 units, std.dev. = 8 units and I read the values as 8 bit integers. The choice of parameters hint at a normal distribution. Is this the case? You might want to obtain a histogram and perhaps substitute mean and standard deviation with modal mean and range. This will also help with an estimation of entropy. I'm trying ...


1

To the extent you can assume your process is a white stationary ergodic process, the variance of the mean is the variance of the process divided by N where N is the number of samples. Assuming that you can estimate the variance from your sample using $$\sigma_x = \frac{1}{N-1}\sum_{i=1}^N(x_i-\mu_x)^2$$ NOTE: This is the unbiased estimator since the ...


1

You're right that when you're using this method to calculate the RMS value of a sinusoid, it's sensitive to getting an integer number of periods of that sinusoid in the observation window. I can see a couple ways to tweak your approach: Since it's important to get full periods into your estimate, you could add some tracking of the sinusoid's frequency and ...


1

If you know the frequency beforehand you can simply correlate the signal with a sine and cosine of that frequency and find the magnitude of the response. This is what the DFT is doing at that bin. Let $x[t]$ be your signal, and $f_c$ be the frequency you are interested in, and $f_s$ be your sample rate. Then let $$ a = \left<x,\cos(2\pi t f_c/f_s)\...


1

The usual way to do this is to form a calibration plate. One way to form a calibration plate is to place known-shaped "fiducials" in a known-sized array on the surface where you want to do the measurement. Then, knowing the measurements of the calibration plate, you can count pixels and do a map from pixels in each direction (possibly in each area of the ...


1

I think a digital low-pass filter, applied after sampling, should be a good solution. One benefit of digital filtering is that you can obtain very sharp transition regions, and large rejection of out-of-band signals. The cost is relatively high computational complexity, in the sense that your processing code will execute many arithmetic operations. Another ...


1

Like the 50 Hz mains hum and its harmonics, the easiest explanation for the 5 kHz harmonic interference is a nearby switching power supply, like a wall wart. Try disconnecting appliances from mains, turning off monitors, moving things around, and altering your grounding scheme or altering the capacitance of things by touching them to reduce interference.


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