Jazzmaniac
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Comparison between Fourier transform, short-time Fourier transform and wavelets
18 votes

All three transforms are inner product transforms, meaning the output is the inner product of a family of basis functions with a signal. The parametrization and form of the basis functions determine ...

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Why is the Fourier transform of a Dirac comb a Dirac comb?
11 votes

Your intuition fails because you're starting with wrong assumptions. Heisenberg's uncertainty doesn't say what you think it says. As you already say in your question, it's an inequality. To be precise,...

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Are complex exponentials the only eigenfunctions of LTI systems?
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10 votes

All eigenfunctions of an LTI system can be described in terms of complex exponentials, and complex exponentials form a complete basis of the signal space. However, if you have a system that is ...

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Removing transients in highpass filtering with MATLAB
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9 votes

Your first order filter recursion for some real constants $a,b,c$ is $$ y[n] = a x[n] + b x[n-1] - c y[n-1] $$ with the two initial memory states $x[-1]$ and $y[-1]$ at $n=0$. Your "no transient" ...

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Is sinusoids the nature's default signals?
9 votes

Time invariance plays a huge role in nature. Most systems (including your ear/brain) don't have an absolute time reference but treat all points in time equally. That results in a preference for the ...

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Why can't DFT be used when samples are not equally spaced in time?
8 votes

You can actually use the DFT on non-unformly sampled data. It is still an orthogonal bijective map and has no inherent mathematical issues. However, interpreting the meaning of the resulting ...

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Tensor in signal processing
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7 votes

This has little to do with intuition. Tensors are rigorously defined mathematical objects, and in general simple arrays don't qualify as tensors. Specifically, signals are not tensors. In the ...

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Guess the frequency response of a filter with little information
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7 votes

If you know that the system is linear and time invariant, the easiest method (assuming that you have no noise added in the process) is to let the system act on an impulse function. The Fourier ...

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Does this Signal Smoothing algorithm have a name?
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6 votes

Not sure if this has a name, but it is a nonlinear low pass filter that uses different smoothing constants depending on the input signal deviation from the filtered output. Small deviations are ...

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Measure and simulate non-linear distortion
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6 votes

Nonlinear systems are very hard to classify and there's no unified theory like for linear systems. In general, you cannot measure/identify non-linear systems in finite time. There are some specific ...

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Does windowing affect Parseval's theorem?
5 votes

While the Fourier transform, discrete or continuous, can be regarded as unitary transform i.e a naturally norm preserving change between orthonormal bases in a normed complex vector space, the ...

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Discontinuity in the angle of a complex exponential signal
5 votes

That's not really a discontinuity. On a circle the two points $-\pi$ and $+\pi$ are identified: They are the same point. That is true for all $x$ and $x+n 2\pi$ for integer $n$. If you would like to ...

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What subclass of nonlinear systems can be represented by Volterra series?
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5 votes

The system must be time invariant and smooth in the functional derivative sense. That doesn't guarantee that the Volterra series converges (like with Taylor series, there are pathological counter ...

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strange phenomenon in spectrogram of Windowed Fourier Transform [edited]
5 votes

In discrete signal processing the frequency domain axis topology is surprisingly not a straight line, but a closed circle. Therefore the upper and lower edge of your image are really "identified", ...

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How is temporal pre masking possible?
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4 votes

Auditory processing has a latency of around 40ms from stimulation at the cochlea to awareness in the brain. Those 40ms appear in a number of auditory cognitive effects and mark the separation between ...

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$\lim \limits_{a \to 0} \frac{1}{a}[u(\frac{t}{a}+\frac{1}{2})-u(\frac{t}{a}-\frac{1}{2})]= \delta(t) $
4 votes

The graph of $F_a(t)$ is a rectangle with base length $a$ and height $a^{-1}$. The area of the rectangle is therefore equal to $a \cdot a^{-1}=1$. The Dirac delta distribution is often defined as a ...

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Useful natural "Hilbert-like" $n$-uples and $n$-fold "analytic signals
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4 votes

The generalisation of the concept of an analytic signal is not straight forward. I'm quite certain however that looking for such a generalisation with quarternions (or even octonions) will not turn ...

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Is there such a thing as band-limited non-linear distortion?
4 votes

A few approaches to alias-free nonlinear distortion (in increasing order of difficulty): Subband distortion: Use a low pass filter to extract the lower end of the signal. If you choose a cutoff ...

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Eigenvalues and Eigenvectors of a 3D Image Laplacian
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4 votes

This answer comes a little late, but I think that it's necessary to clear up some of the confusion about what the eigenstructure of a Laplacian is and how it is calculated. First of all, it's ...

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What is the rate of expansion of an image as it aproaches the human eye?
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4 votes

The magnification of an object at distance $g$ from a thin lens with focal length $f$ is given as $$\beta=\frac{f}{g-f}$$ which is generally negative for objects at distances greater than the focal ...

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"cascaded" cross-correlation
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4 votes

I'm afraid your statement isn't true. This can best be seen in a suitable choice of basis, one that simplifies the cross correlation. This basis if of course the shift invariant periodic Fourier basis ...

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How to quantify asymmetry of a signal?
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4 votes

Assuming you're looking for symmetry around $x=0$, you can decompose any function into a symmetric and an antisymmetric part: $$ f(x) = \frac{1}{2}\left(f(x)+f(-x)\right) + \frac{1}{2}\left( f(x) - f(...

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If an autocorrelation function of a process is a rectangular function, then is the process deterministic?
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4 votes

An autocorrelation function like that is not possible for ordinary signals. The autocorrelation function is the Fourier transform of the power spectral density, which is a strictly positive quantity. ...

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Nonlinear wavelets transform?
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4 votes

A transform being linear has very little to do with its ability to analyze linear or nonlinear systems. The wavelet transform $W[s(t)]$ of a signal $s(t)$ is linear because $$W[a s_1(t) + b s_2(t)]=a ...

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AutoExposure with nonlinear camera: Non linear proportional PID?
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4 votes

If you know the exact response of the camera, you can convert the brightness samples of each pixel to a linear intensity scale and perform the averaging there. That will make your whole problem ...

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Design a comb notch filter when sampling rate is not an integer multiplicative of the cutoff frequency
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4 votes

You can design that filter manually without problems. Matlab just uses a very simplistic approach to comb filtering with a delay line. In order to keeps things as simple as possible I would recommend ...

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For an LTI system, why does the Fourier transform of the impulse response give the frequency response?
4 votes

The key ingredient is that the base functions of the Fourier transform $\exp(i \omega t)$ are eigenfunctions of LTI systems. That means the LTI system can be represented as a diagonal linear operator ...

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How to compute impulse and frequency response of Flanger?
3 votes

Only linear time invariant systems are fully characterised by their impulse response. Modulation effects like a flanger break time invariance. While you can still create a momentary impulse response (...

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Force an unstable IIR filter to be stable by forcing a nonlinearity in the digital block diagram
3 votes

You won't be able to avoid the instability with a linear model. With your current discrete model, the filter will blow up at a certain resonance setting. Using a better filter topology or higher ...

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Example of an LTI system with complex impulse response
3 votes

Complex band pass filters are used to get a band and its quadrature in one efficiently computed step. The most simple such design is a single-pole resonant bandpass with the discrete transfer function ...

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