Jazzmaniac
• Member for 9 years, 1 month
• Last seen this week

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 ...

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,...

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 ...

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" ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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", ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

Assuming you're looking for symmetry around $x=0$, you can decompose any function into a symmetric and an antisymmetric part: $$f(x) = \frac{1}{2}\left(f(x)+f(-x)\right) + \frac{1}{2}\left( f(x) - f(... View answer Accepted answer 4 votes An autocorrelation function like that is not possible for ordinary signals. The autocorrelation function is the Fourier transform of the power spectral density, which is a strictly positive quantity. ... View answer Accepted answer 4 votes A transform being linear has very little to do with its ability to analyze linear or nonlinear systems. The wavelet transform W[s(t)] of a signal s(t) is linear because$$W[a s_1(t) + b s_2(t)]=a ...

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 ...

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 ...

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 ...

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 (...