# 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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### Impulse response when input to a system is differentiated, and its applicability to find response to general inputs

I will first give a short explanation of what I am asking, and then give a more comprehensive context. If we have a LTI dynamic system acted upon by inputs $y(t)$ and producing outputs $x(t)$, , we ...
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### Convolution of discrete time signal

I'm given a discrete time signal which is as follows: $$x[n] = \alpha^n u[n],\\$$ $$h[n] = u[n],\\$$ Why is unit function neglected in the following step: $$y[n] = \sum_{k=0}^{n} \alpha^{k}\\$$
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### Derivation of the Optimal Matched Filter - Convolution vs. Correlation

On the Wikipedia page for Matched Filters here, there is a matrix algebra derivation for an optimal matched filter. Now, considering the output of an LTI system is found using the convolution operator,...
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### What is about the circular convolution in OFDM

In an OFDM system, serial-to-parallel conversion for data is done, then the DFT is performed and then adding the cyclic prefix (CP). My question is related to that step of adding a CP. As I know, ...
0answers
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### How can I improve the Canny edge detection code?

I have converted this Matlab code for Canny edge detection into C# given that the Matlab version gives out a good output. The output from Matlab code is as follows: And my C# version's outputs are ...
1answer
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### How I can perform SIMO channel convolution in MATLAB

In OFDM system, I need to transmit a signal $x$ in SIMO channel $H$ of single Tx antenna and $4$ Rx antennas. The initial equation for that convolution is $r = Hx + n$ where $n$ is the noise. As ...
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### Matrix cross correlation in python

I'm currently performing matrix cross correlation in python using : C = scipy.signal.correlate2d(A,A) where A is a 2D matrix, typically a picture. As you can ...
2answers
152 views

### What is the relation between kernel functions, kernels used in convolution and null spaces of a matrix?

I have recently started learning about machine learning and have come across kernels and null spaces. I understand that null space is the set of all vectors that satisfy the equation A.v = 0 (Where A ...
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### Correlation peformed by convolution

Background: The question here is related to images in particular and not signal/waveforms. I have been reading a lot of answers about the difference between convolution and correlation but I am stuck ...
3answers
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### Deconvolution Using Complex Division in The Frequency Domain

Consider these two signals: a = [1 1 0 0 0 0 0 0] b = [1 0 1 0 0 0 0 0] their convolution is c = a * b = [1 1 1 1 0 0 0 0] ...
1answer
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### Numerical error while implementing a periodic pulse signal

I'm trying to illustrate the principle of constructing a periodic signal using an elementary pattern. This is the code I use (python 2.7 + numpy + scipy.signal) : ...
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### Applying BCJR equalization for LDPC encoded information

I want to apply BCJR decoder for LDPC encoded information. How can I change the BCJR originally for convolutional codes for this purpose?
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### Cyclic convolution between two matrices in matlab

How can I perform cyclic (periodic) convolution between two matrices in Matlab? And also, what would be the normalization term?
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### Calculating output of a system given impulse response and input

I'm trying to calculate the output given an impulse response $h(t)=e^{-t}u(t)$ and input $x(t)=\cos(2\pi t)$. I know I need to use the convolution but given that cosine is periodic, I don't see how ...
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### Applying the inverse FFT to even out a room's sound - What is the more efficient algorithm?

I have a way (the standard way) to correct for my room's acoustics, but I'm wondering if there's a more efficient algorithm, something that doesn't involve going to the frequency domain maybe? I ...
3answers
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### Solving for impulse response h[n] given input-output pairs

This is a homework problem that I've worked on and I want to confirm some of my reasoning. I'm given two sets of input-output pairs of a particular system, $S$, that we know is linear time-invariant ...
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### convolution of two signals with different step responses [closed]

for the given signal h(n), is it 1 for n=0:149 or the n's of each is a different thing?
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### Convolution of delta function in discrete time with parameter

If I have a delta function of the following type $$n\delta(5n-20) * 3^{5n}u[n]$$ How can I calculate this convolution? I have thought of the property $$\delta[n-n_0] *x[n] = x[n-n_0]$$ Then if ...
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