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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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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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Convolution of Input signal and Impulse response

I can solve the output if the input is $$ x[n] = \delta[n+1] + \delta[n] + 2\delta[n-1] + \delta[n-2]$$ and the impulse response is $$ h[n]= 3\delta[n] − 2 \delta[n−1] − \delta[n−2] + \delta[n−3]$...
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Extracting positive frequencies of discrete-time signal

Convolution in the time domain is the same as multiplication in the frequency domain. My data is sampled at 200 Hz, which means that the Nyquist frequency is 100 Hz, and all frequency content is <=...
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Seam in between output segment in linear convolution and filter design

I am attempting to design a matching filter from long sequences. I want to do this in the time domain. I have 3 inputs. Let's called it p,s, and r. The matching filter is to be designed between p and ...
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Space-time trellis coding

Can someone explain to me how to calculate the branch metric of a Viterbi algorithm for a MIMO communications system? In an example, I came across they vaguely show the calculations and I have no ...
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56 views

FIR filter design and implementation meaning [closed]

What is the output of the convolution meaning which is used in the FIR filter? how can conclude the output of the FIR filter in the output according to the input $x[n]$?
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Convolution offset and factor in frequency domain

See this link. The following Convolution in Spatial domain code is written in C#. ...
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90 views

Count matches to kernel

So, I have this problem where I want to apply a kernel to an image and count the number of matches that happened. So for example, if I have the kernel: $$\begin{bmatrix} 1 & 2 & 1\\ 1 & ...
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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 ...
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2answers
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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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1answer
90 views

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 ...
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3answers
148 views

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] ...
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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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Convolution - change of variables

I am struggling trying to understand the 3rd line of the expression below. The second line can be simply visualized by letting the kernel size be 3 and $i=2$ for eg. Then $ y_2 = \sum_a x_{2+a-1}...
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extracting a room response [duplicate]

So I have a wav file containing a record of a sine sweep played on my pc and recorded by a mic. And I want to extract the room impulse of it, I've looked online but I couldn't find any clear answers. ...
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Circular Convolution, modulo N smaller than Length

I am having a small Problem here, which I can't figure out on my own. I am supposed to perform a circular convolution y[n] with three different modulo N values N =...
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1answer
77 views

Gaussian Equivalent of Convolving an Image 50 Times with a Box Filter

I have a image that I'm convolving 50 times with a box filter, and I like to replace this with a single gaussian filter. Because both box filter and gaussian filter are separable I can just study the ...
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3answers
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Difficulties while understanding Convolution [duplicate]

I have just started convolution sum. I am able to do Mathematical convolution sum. But I am unable to make a figure of it in my mind. So I tried to go through the graphical convolution. Below is the ...
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154 views

Convolution Sum [closed]

I understand convolution is linear combination of delayed impulses of decomposed signal. $$\int_{-\infty}^{+\infty} x(\tau)h(t-\tau)\mathrm{d}\tau = g(t)$$ I want to know about these decomposed ...
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969 views

Convolution and cross-correlation on 2D image (Example)

I have read that convolution and cross-correlation are the same thing, but convolution flips 180 degrees (images), or time reverses (sequences) the kernel, before performing the elementwise ...
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2answers
222 views

pdf of the sum of gaussian distributions using fft Ask [closed]

I am trying to derive the pdf of the sum of independent random variables. At first i would like to do this for a simple case: sum of gaussian random variables. I was surprised to see that i don't get ...
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204 views

Is there any relationship between the convolution and cross-correlation of two signals? [duplicate]

There are two square 2-D signals with the same size $m \times m$, if the result of convolution of those two signals is first picture, And the result of cross-correlation of those two signals is second ...
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How do I draw convolution? [duplicate]

I know what is form for convolution but when I try to draw that I never get good answer. I think I don’t understand that good. How someone explain me with picture convolution of u[n]-u[n-5] and u[n+3]-...
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Generating synthetic zero offset seismic data

Essentially, I am struggling with producing the depth model for this problem, which is a finite reflector dipping at an angle in the subsurface. I just started using matlab so I am not quite sure what ...
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2answers
119 views

Problem with convolution

For a flat fading channel (SISO system) we have: $y=h \star s+n$ But for a mimo system, we have: $y=Hx+n$ with $H \in \mathbb{C}^{N_r \times N_t}$ Why is there not the product of convolution for a ...
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Bandwidth of product of two signals

POINT 1: According to convolution theorem, if g1(t) has a bandwidth B1 and g2(t) has a bandwidth B2, then product g1(t)g2(t) has a bandwidth = B1 + B2. POINT 2: Now, consider an AM waveform s(t)=g(t)...
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Create colour-coding filter for Fourier transformations

I have to conduct a Fourier transform on a 2D-RGB-image, filter out low frequencies and then apply a colour-coding filter so that the remaining frequency peaks are represented by different colours. I ...
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1answer
236 views

1D convolution and deconvolution using FFT

The task: there is some original signal, and there is some response function. I need to convolve them using FFT and then do deconvolution to restore original signal. The task graphical illustration ( ...
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1answer
56 views

Finding the output of a system where the input is a sum of complex exponentials

So, I have to find $H\{ x(t)\})$ (which is an LTI system), where $$x(t) = \sum_{k=0}^{\infty} a_ke^{ \ jw_kt}$$ and where the impulse response of the system is given by: $$h(t) = \frac{\delta(t+\tau)-\...
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0answers
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Gaussian filter convolution giving unexpected results

I am trying to smooth a time series signal with a Gaussian filter and then differentiate the signal (this is for an application for edge detection). A nice property of convolution is: $$ \frac{d}{dx} \...
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37 views

Recursive systematic convolutional code with TCM

My question is: What are the outputs from the TCM encoder ?
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116 views

Using the flip-and-drag method to draw a convolution

So, we are asked to graphically convolve (using the flip-and-drag method) the following pair of signals: $$x_1(t) = \delta(t+1)-2\delta(t-1) \ \ \ \ \ \ \ \ \ \ \ \ \ x_2(t) = \begin{cases} -1-2t, &...
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2answers
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How to calculate time of arrival using room impulse response

I need to find the timestamp of arrival of a particular signal at a receiver location within a room. The known parameters are the room impulse response h for a ...
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42 views

Matrix used for a transposed convolution?

I was wondering what would be the matrix used for a transposed convolution? I understand that the matrix for Conv2d given the initialization below: ...
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83 views

Amplitude is affected by the sampling interval in convolution of input signal with impulse response?

I simulated convolution using an application, I then wanted to see if the output would match the derived mathematical output. The square wave below is being convoluted with itself, the impulse ...
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794 views

Proof of the convolution property of Fourier Series in continuous time

I am facing problem in understanding the proof of Convolution property of Fourier Series (FS) in continuous time CT; that is: $$\mathrm{FS} \big\{x_1(t)\star x_2(t)\big\}=T\sum_{n=-\infty}^{\infty}...
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1answer
42 views

Clarification on Discrete-time convolution and signal shifting

What are $y_1[n]=x_1[n]*h[n]$ and $y_2[n]=x_2[n]*h[n]$? $$x_1[n]=(0.1)^nu[n],\quad x_2[n]=(0.2)^n,\quad h[n]=(0.3)^nu[n]$$ I am confused about how to calculate $y_{1}[n]$. The formula for discrete ...
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Does Function to Function Multiplication and Convolution, Follow Laws of Convolution

Apologies this is long – I do not want to leave any ambiguity. I have a hopefully simple question, that does not seem to be covered by the DSP books I have in regards to theory of operation. I ...
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263 views

Zero Padding FFT: ifft(fft(x)) is unequal to x

I implemented an iterative radix-4 FFT and IFFT, and after performing these on zero padded, but further unchanged signal, the output differs. What am i getting wrong? Problem Description: A signal ...
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69 views

Multistage-Multirate-Filters, convolution of all impulse responses to estimate frequency response

I want to evaluate the frequency response of a cascade of filters. The Cascade is as follows: ->CIC_Deci(N1)->CIC_Deci(N2)->FIR->CIC_Inter(2*N2)-> As you see I have different decimation factors <...
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50 views

How to apply the convolution matrix of a filter of an image

When I am dealing with one dimensional signals I can apply a filter of that signal by multiplying the convolution matrix built with that filter times the signal itself. $x[n]$ column vector filter $...
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1answer
139 views

Fourier coefficients of product of two periodic signals

question: If $x(t)$ and $y(t)$ are two periodic signals(both with period T) with Fourier coefficients $c_{n}$ and $d_{n}$ respectively then, Fourier coefficient of $z(t)=x(t)\cdot y(t)$ is: (a) $\...
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42 views

Basic question about Block Diagrams and Scale factor

I am doing a project about controlling a thermoelectric module, and for doing so I must reverse the current direction. This is achieved changing the voltage polarity. So the output of the controller (...
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1answer
99 views

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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1answer
1k views

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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1answer
424 views

How to find inverse of convolution integral?

If $x^{-1}(t)$ and $ y^{-1}(t)$ denote the integrals of x(t) and y(t) defined by $x^{-1}(t)=\displaystyle\int_{-\infty}^{t} x(\lambda)d\lambda$ $y^{-1}(t)=\displaystyle\int_{-\infty}^{t}y(\lambda)d\...
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2answers
827 views

how to evaluate derivative of convolution integral?

If the signal $x(t)$ has ordinary first derivative $\dot x(t)$, then $\dfrac{d}{dt}\big(x(t)\star y(t)\big)$ is: (a) $\dot x(t)y(t)$ (b) $x(t)\dot y(t)$ (c) $\dot x(t)\star y(t)$ (d) $\...
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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 ...