# Questions tagged [convolution]

Convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions.

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### Flipping the impulse response in convolution

During convolution on a signal, why do we need to flip the impulse response during the process?
31k views

### Deconvolution of 1D Signals Blurred by a Gaussian Kernel

I have convolved a random signal with a a Gaussian and added noise (Poisson noise in this case) to generate a noisy signal. Now I would like to deconvolve this noisy signal to extract the original ...
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### What is the difference between convolution and cross-correlation?

I've found on multiple sites that convolution and cross-correlation are similar (including the tag wiki for convolution), but I didn't find anywhere how they differ. What is the difference between ...
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### What is the physical meaning of the convolution of two signals?

If we convolve 2 signals we get a third signal. What does this third signal represent in relation to the input signals?
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### How to circularly shift a signal by a fraction of a sample?

The shift theorem says: Multiplying $x_n$ by a linear phase $e^{\frac{2\pi i}{N}n m}$ for some integer m corresponds to a circular shift of the output $X_k$: $X_k$ is replaced by $X_{k-m}$, where ...
3k views

### 1D Deconvolution with Gaussian Kernel (MATLAB)

Suppose that I know the output and the transfer functions of a system and I would like to calculate the input function using deconvolution. To get a grasp of the idea I have created a simple ...
331 views

### Filtering $n \times n$ Images by Separable $m \times m$ Filters. Computation Time for Filtering Using FFT, 2D Convolution and Two 1D Convolutions

Consider filtering square $n\times n$ images by square, separable $m\times m$ filters. Give general equations for the computation time for the following approaches to this: Filtering using FFT 2-D ...
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### Difference between correlation and convolution on an image?

Could you please clearly explain what is the difference between correlation and convolution that is done by a filter on an image? I mean in terms of signal processing definition I know that ...
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### How are two signals multiplied? And how is it different from convolving two signals?

Suppose that I have two signals $x[n] = \left\{2,4,1\right\}$ and $p[n] = \left\{5,1,8\right\}$ and I want to multiply them. How do you do that? How different is it from convolving two signals? I ...
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### Sampling Theorem and Dirac Comb

I am reading "The Scientist and Engineer's Guide to Digital Signal Processing" and trying to understand Figure 3.5 below which is about the sampling theorem and aliasing. I do not understand the ...
253 views

### Applying Image Filtering (Circular Convolution) in Frequency Domain

To filter an image we can: Use a 3x3, 5x5, 7x7, etc. filter, that is convolve the image and the filter in the space domain. Use a FFT on both the image and the filter, multiply them together in the ...
366 views

### understanding discrete-time convolution in LTI systems

I'm trying to understand the discrete-time convolution for LTIs and its graphical representation. standard explanations (like: this one) start with the idea of decomposing an input signal $x[t]$ into ...
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### How to find the convolution kernel in frequency domain?

I have a two vectors of spatial data (each about 2000 elements in length). One is a convolved version of the other. I am trying to determine the kernel that would produce such a convolution. I know ...
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### Generate the Convolution Matrix of 2D Kernel for Convolution Shape of same

I want to find a convolution matrix for a certain 2D kernel $H$. For example, for image Img of size $m \times n$ , I want (in MATALB): ...
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### Simulating analog filter using convolution or converting with fft

My task is simple; I want to simulate analog low-pass filtering of an input signal, using Python. Note that the input signal is an array of values, not an analytical function. My first question is if ...
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### Estimating the Impulse Response of the Room Using Sweep Signal Microphone Recorded Signal (Input & Output of a Convolution)

I played this signal A (a 20Hz to 20000Hz sinusoidal sweep in 10 seconds) with a studio monitor speaker in a big church, and I recorded the result B with good microphones. The result is very reverb-...
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### Why use a gaussian low pass filter, when we can convolve with gaussian kernel

Sorry if this question is too simplistic, but I am new to image processing and after successfully writing two programs, a convolution program and a low pass filtering program, I noticed that for ...
258 views

### Is convolution distributive over multiplication?

Is there any formula or expansion for $$a(t)*[b(t) \cdot c(t)]$$ $$a(t) \cdot[b(t)*c(t)]$$ where $*$ denotes the convolution? By expansion I mean something like \$a(t)\cdot[b(t)+c(t)]=a(t)b(t)+a(t)...