8 votes
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Difference between RMS and a moving RMS

The total (standard) RMS, continuous time: $$ x_{RMS}=\sqrt{\frac 1{T_0} \int_0^{T_0} x^2(\tau)d\tau} $$ And the moving RMS, continuous time: $$ x_{RMS}(t)=\sqrt{\frac 1{T} \int_{t-T}^t x^2(\tau)d\...
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  • 1,357
6 votes

Can every type of linear filter be modelled by a convolution?

No. It's only LTI (Linear and Time-Invariant) systems that can be modeled with convolution through a unique single impulse response. For example the systems $$ y(t) = g(t) x(t) $$ or $$ y[n] = \sum_{...
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  • 26.8k
5 votes

Pixel Wise Write into a Video File in MATLAB

I assume your matrix is 3D where the first 2 dimensions are Width and Height and the third is time (Gray Scale Video). If you can write your processing as a Filter you can use MATLAB's ...
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5 votes

Extracting Peak Frequencies Using FFT vs. Time Domain Peak Finding

You basically have a slowly changing Sine signal where the parameter which changes is its frequency. The right approach in my opinion would be to use Frequency Modulation processing of the signal. ...
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4 votes
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Sampling Theorem: T-Sampled Signal

I will solve it for T=1. You can solve the others on your own. First, note that my definition of sinc is: $$sinc(t)=\frac{\sin(\pi t)}{\pi t}$$ Definitions of sinc tend do differ, so check what your ...
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4 votes

Sampling Theorem: T-Sampled Signal

This is the same answer as I posted here: Sampling Theorem Sampling in the Time Domain created replications on the Fourier Domain. The distance between the replications center is according to the ...
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4 votes
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Confused on the difference between the frequency spectrum of an entire song, and the frequency spectrum of a point in time

As far as my logic goes, I wont ge able to tell any of musical features just of an amplitude value in the time domain. That's wrong. The amplitude-over-time actually is the way the song is played by ...
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4 votes
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How to filter out everything but a single frequency in the time domain?

Depending on the exact characteristics of the signal and implementation requirements (if any) I can think of a number of approaches to extract content at a "single" frequency. The most common: Apply ...
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4 votes
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Index of stationarity of a time domain signal

This a very complicated question, and I would say a still open topic. The concept of stationarity is manifold, from pure statistics to applied DSP (strict, strong, wide-sense, quasi-stationarity, ...
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4 votes

Finite and Infinite support in time and frequency domain

The sinc is just fine an example as a signal with infinite support: Support being defined as the smallest interval in which the function has non-zero values, it's trivial to see that $\text{sinc}(x)=...
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4 votes

Optimal $ n $ -th Order IIR /AR Approximation of a Moving Average Filter

(Update: I just realized that the first part of this covering CIC structures is basically what Hilmar has already answered-- I'll leave this up since it offers more graphics and details in case that ...
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4 votes

Optimal $ n $ -th Order IIR /AR Approximation of a Moving Average Filter

This is not a full answer. It explores some basic approximations. For a moving average as long as 600 samples it is informative to look at impulse responses of continuous-time filters as ...
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4 votes
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Optimal $ n $ -th Order IIR /AR Approximation of a Moving Average Filter

I can show you some low order IIR approximations to an FIR moving average filter. In the figure below you see $3$ (infinite) impulse responses that approximate a moving average of length $N=600$. The ...
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4 votes
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What is wrong with my residue partial expansion method? (Transfer Function into State-Space Modal/Diagonal Form)

The discrepancy between your derivation and matlab's computation results because of a convention mismatch you used during the partial fraction expansion: Given that the function to be expanded is $H(s)...
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4 votes
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Can a 1-dimensional signal be in a domain other than the time or frequency domain?

If you have a one dimensional signal $s(\cdot)$, it somehow belongs to a combination of two different domains: the sampling domain: where samples are considered or taken, or how the signal is ...
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4 votes
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Where to start with DSP?

so I am wondering where can I go to form an understanding of DSP from the ground up. There is a great list of resources in this answer What Resources Are Recommended for an Introduction to Signal ...
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4 votes
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Why aren't the integrator and the differentiator inverse systems?

The flaw is in the assumption that convolution is associative. This is only true if it is allowed to interchange the order of the corresponding integrals, which is not the case here because the ideal ...
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3 votes

Difference between RMS and a moving RMS

A complement to the previous answer, which is really good. With a moving-average, or moving-RMS, the output rate of the RMS calculation is the same as the input rate. With a block average or block ...
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  • 3,620
3 votes
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Time-Frequency Analysis of Big Data - Data Size Reduction: averaging the most appropriate method?

So, first of all, CSV seems to me the least suitable format imaginable for this amount of data. It needs to be parsed, is memory hungry, and wastes precision, and isn't linearly addressable (ie. to ...
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3 votes

Stationary signal: time-domain vs frequency domain

Your definitions are not correct. For a Strict Sense Stationary process (signal) the joint distribution of your process' value for all instants of time must be independent of time, in other words if ...
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  • 1,306
3 votes
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Effect of low pass filter on the time domain

You have a finite length sequence $x[n]$, $n=0,1,\ldots, N-1$, with the discrete Fourier transform (DFT) given by $$X[k]=\sum_{n=0}^{N-1}x[n]e^{-j2\pi nk/N}\tag{1}$$ and its inverse DFT (IDFT) given ...
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  • 80.4k
3 votes

Effect of low pass filter on the time domain

If you sample a pure sinewave for an integer number of periods, the samples will sum to zero (it will have equal "ups" and "downs"). If you zero an FFT bin, that's the same as subtracting a sinewave ...
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3 votes
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Impulse response (general form for linear systems as two-variables function $h(t,\tau)$) applied to Time-invariant systems

If the response to $x(t)$ is given by $$y(t)=\int_{-\infty}^{\infty}h(t,\tau)x(\tau)d\tau\tag{1}$$ then the response to $x(t-T)$ is $$\tilde{y}_T(t)=\int_{-\infty}^{\infty}h(t,\tau)x(\tau-T)d\tau=\...
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  • 80.4k
3 votes
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Time domain maximum from frequency domain data?

Suppose that Alice has a vector $\mathrm x \in \mathbb R^n$. She computes the DFT of $\mathrm x$ $$\mathrm y := \mathrm F \mathrm x \in \mathbb C^n$$ where $\mathrm F \in \mathbb C^{n \times n}$ ...
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3 votes

Linear Constant Coefficient Differential Equations: Zero-Input and Zero-State responses

The two approaches should return the same solution. They are just two different ways to get to the same place. In the ZSR/ZIR method, you are solving two different IVPs - they have the same ...
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  • 4,872
3 votes
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Finite and Infinite support in time and frequency domain

The coreof the question relies on how to define for the support of a function with $x$ in a domain $\mathcal{D}$. The most common notion in DSP is the closure of the set where $f$ does not vanish, i.e....
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3 votes

Optimal $ n $ -th Order IIR /AR Approximation of a Moving Average Filter

Depends a bit on your application. A moving average filter is a low pass filter and one with many lobes and pretty poor stop band rejection at that. Depending on what specific requirements you have, ...
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  • 32.8k
3 votes

Optimal $ n $ -th Order IIR /AR Approximation of a Moving Average Filter

i would think that if your system has no complex poles, only real poles, then you could make the impulse response to be monotonic. the impulse response would be the sum of decaying exponential ...
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3 votes

Can a 1-dimensional signal be in a domain other than the time or frequency domain?

Really, there's nothing special about time and frequency domain. The math doesn't care whether you're transforming amplitude over time, gravel over mountain height, or smell intensity over fridge ...
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