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2

If you’re looking for modeling the amplifier itself, convolution will not provide a complete model for the internal processes. However, convolution is the basis for a number of cab modeling products. I have a line 6 helix that I use frequently. A dry guitar doesn’t sound great. A dry guitar through an amp model sounds bad. A dry guitar through an amp and ...


11

When talking about modeling, there are two things that usually get modeled: 1. the guitar amp, and 2. the speaker cabinet. Only the latter is modeled by an impulse response, which means that the cabinet is simply represented by an LTI system and implemented by convolution. This is of course an approximation but it works fairly well. You can find a lot of ...


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If you're an EE student, you will have encountered the term LTI System (or you certainly will soon enough!): A system that, no matter the absolute time, outputs, given the same input, the same output; if you scale the input by a factor, the output is scaled by the same factor. Linear, time-invariant, so to speak. LTI systems can be applied to time-domain ...


3

If you represent a second-order polynomial $s(x)$ with Lagrange polynomials $L_i(x)$ and interpolation points $\beta_i$, $i=0,1,2$, such that $$s(x)=s(\beta_0)L_0(x)+s(\beta_1)L_1(x)+s(\beta_2)L_2(x)\tag{1}$$ then for the equality in $(1)$ to be satisfied, the polynomials $L_i(x)$ must have zeros at $x=\beta_j$, $j\neq i$, and they must equal $1$ at $x=\...


0

It seems you are mixing discrete and continuous notations and it's unclear which it is for time and frequency. You use the term DTFT which would indicate both are discrete but you use the frequency index $\omega$ which would be continuous in the frequency domain. Your time domain equation doesn't make any sense, since your left side depends on $n$ which ...


1

Circular convolution can be done using FFTs, which is a O(NLogN) algorithm, instead of the more transparent O(N^2) linear convolution algorithms. So the application of circular convolution can be a lot faster for some uses. However, with a tiny amount of post processing, a sufficiently zero-padded circular convolution can produce the same result as a ...


0

When you want to perform a time-domain linear convolution using a transform (Fourier, trigonometric) domain multiplication technique, then the concept of circular convolution arise. Because the effect of transform-domain multiplication on the time-domain is a circular convolution. Therefore a linear convolution is actually implemented by an underneath ...


1

Technically, shifting the kernel above the still image, or shifting the image "below" the centered kernel are equivalent. This is because convolution of a kernel and an image is a commutative operation: $$\sum_{k_1=-\infty}^{\infty} \sum_{k_2=-\infty}^{\infty} h(k_1,k_2)x(n_1-k_1,n_2-k_2) = \sum_{k_1=-\infty}^{\infty} \sum_{k_2=-\infty}^{\infty} x(k_1,k_2)h(...


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