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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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Recursive systematic convolutional code with TCM

My question is: What are the outputs from the TCM encoder ?
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1answer
167 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
105 views

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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1answer
1k 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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44 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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63 views

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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57 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
239 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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124 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
2k 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
484 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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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 ...
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3answers
952 views

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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1answer
69 views

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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1answer
179 views

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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1answer
33 views

Convolution including $\delta(t-5)$

I know the two properties of convolution that are related to my question $\quad x(t)*\delta(t)=x(t) $ $\quad x(t)*\delta(t-t_0)=x(t-t_0)$ But my question is, how can I use those two to calculate $$ ...
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1answer
97 views

why did convolution coding achieve BER less than Reed-Solomon?

I tried convolutional coding and Reed-Solomon (RS) (block coding technique) for wireless channel where the input data is bitstream. Convolutional coding achieved lower BER comparing with RS. If the ...
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2answers
216 views

Convolution and Modulation Theorem with Octave Example

As far as I know, convolution theorem stated that $$ x[n] * y[n] = X(e^{j \omega}) Y(e^{j \omega}) $$ $$ X(e^{j \omega}) * Y(e^{j \omega}) = x[n] y[n] $$ I tried a simple experiment using GNU Octave ...
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168 views

Convolution of BPSK signal in frequency domain implementation

Here is the simplified version of code which implement convolution of BPSK-signal in frequency domain: ...
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2answers
298 views

Convolution effects width of the signal?

Let's say there are two signal with different frequency: \begin{align} X_1(\omega) &= 0\quad\text{for}\quad \lvert \omega\rvert > 1000\pi\\ X_2(\omega) &= 0\quad\text{for}\quad\lvert \omega\...
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1answer
159 views

How to convolve an arbitrary signal with a causal decaying exponential?

I need to simplify the following convolution $$x(t)\star [e^{-2t} u(t)]$$ where $u(t)$ is the unit step function. I'm very confused with this. Using the definition of convolution of continuous-time ...
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2answers
624 views

Convolution in spatial domain is multiplication in frequency domain

I have to prove convolution in spatial domain = multiplication in frequency domain using two matrices. $$ x(m, n) = \begin{bmatrix} 1 && 2 \\ 3 && 4 \end{bmatrix} $$ $$ h(m, n) = \...
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1answer
514 views

Linear convolution of discrete signals with defined lengths

What is the maximum count of non-zero elements, that can a linear convolution of discrete signals of "lengths" 5 and 7 have? When I label the length of signal $x[n]$ as $M$, and the length of signal $...
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1answer
213 views

Autocorrelation function

For what signal applies, that its autocorrelation function at point $0$ is zero, i.e. $R_f(0) = 0\ ?$ I know that autocorrelation is (RootMeanSquare)^2 and for $R_f(0)$ this equals: $$ R_f(0) = \frac{...
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1answer
63 views

Create an input so that poles show up as outputs?

Let's say we have a rational, causal, stable LTI system with transfer function $$H(z) = \frac{A(z)}{B(z)}$$ If $H(z)$ has $N$ poles, we can in theory have only 1 of those poles, $p_i$, show up at the ...
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1answer
289 views

Convolution between two unequal length vectors

Considering an example, where the model is \begin{align} x[n] = \mathbf{h}^\mathsf{T}\mathbf{u}[n] + w[n]. \label{Eq1} \end{align} $\mathbf{h} = [h_0,h_1,\ldots,h_{M-1}]^\mathsf{T}$ of length $M$ ...
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0answers
32 views

Where does convolution fit into tracking fluorescent photons using MC models?

I have been reading this old paper by Steven Jacques, a titan in the world of using Monte-Carlo methods for photon propagation and distributions. https://www.osapublishing.org/ao/abstract.cfm?uri=ao-...
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1answer
147 views

How to calculate multiplication of two discrete series

Short version: How to multiply two discrete sequences? Long version: Convolution of two discrete sequences is weighted sum. For instance, convolution of two sequences: ...
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2answers
106 views

why exponential term neglected in equation?

where does that exponential term gone, is this because it is a constant term or it has to do something with stablity?
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1answer
33 views

Question on LSI system

Why second option (1) is not correct ?
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1answer
72 views

Are convolution and multiplexing synonymous?

Other than preferences to use one or the other words in different domains, do they refer to essentially the same process? And likewise for the opposite operations, demultiplexing and deconvolution?
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1answer
151 views

Intervals of convolution product

Given are two Signals $x_1[n]$ and $x_2[n]$. $x_1[n]$ is in Intervall $[0,2]$ different than null and $x_2[n]$ is in Intervall $[0,3]$. The convolution product is Null outside intervals: $[0,6]$ and $[...
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1answer
174 views

Phantom harmonics when using cosine windows why do they appear and how to avoid them?

Given an L order cosine window, it is possible to show that the width of the main lobe is given by: $$\omega_w = \frac{2 \pi L}{(2N+1)}$$ Where $L$ is the order of the window, $N$ is the maximum ...
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1answer
121 views

Impulse response time period in circular convolution

While considering an input to be periodic of Period N, can the impulse response not be periodic of period greater than N ? If it can be, how can one compute it’s convolution?
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1answer
366 views

Question on convolution

I am stuck at question number 2.8 This is how I have gone about solving it: I have calculated $y(t)$ by convolving $x(t)$ with $h(t)$ using the fact that $x(t)$ convolved with an impulse at $t=t_0$ ...
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3answers
215 views

How to correct phase of Diagonal Volterra kernels obtained with exponential sweep sine?

I'm trying to model a non-linear system using non-linear convolution with Novak's (2010) synchronized exponential sine weep (SESS) that models them with a Generalized Hammerstein (Volterra diagonal). ...
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1answer
417 views

Why correlation is not associative in the context of image processing?

I can see most of the places it says "convolution is associative, while correlation, in general, is not". Denote $*$ convolution operator, let's say you have an image $f$, which you need to convolve ...
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1answer
104 views

Underdetermined deconvolution of windowed output

Consider a discrete 'blurred' output $h[t]$ given by the convolution of filter $f[t]$ and signal $g[t]$. This question considers recovering $g[t]$ from a window (subset) of $h[t]$. This causes the ...
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1answer
466 views

Identifying origin in convolution table

I am taking the convolution of $x(n)=\left\{2,1,-1,-2,3 \right\}$ with $n=0$ at the third position with $h(n)=\left\{1,2,0,3 \right\}$ with $n=0$ at the second position. The answer is $y(n)=\left\{2,5,...
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3answers
992 views

Convolution of even functions is even

Prove that the convolution of two even functions is an even function. I have my own proof which I have included as an answer, but it assumes a linear time-invariant system. I want to know if there is ...
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2answers
800 views

Circular convolution of length L of sequences of length greater than L

I'm trying to understand how may I obtain the circular convolution of length L when the sequences I'm trying to convolve are of length greater than L. For instance this Matlab code using sequences ...
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1answer
352 views

2D convolution in Matlab - artefacts

I`m trying to do a 2D fast convolution in Matlab of large matrices. If I use FFT version based on convolution theorem ( https://en.wikipedia.org/wiki/Convolution_theorem ), there are some artefacts in ...
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1answer
345 views

Convolution of $\sin(\omega t)$ and $\cos(\omega t)$?

If $x(t)=\sin(\frac{\pi t}{4})$ and $y(t)=\cos(\frac{\pi t}{4})$ then i need to find the Convolution $$z(t)=x(t) \circledast y(t)$$ So convolution will be $$\begin{align} z(t) &=\int_{-\infty}^{...
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0answers
117 views

Imfilter, FFT-bsed convolution speed

I want to convolve two large matrices and it is working fast - as long as one of those matrixes contains only separate points (point sources). If I replace the points by eg. Gaussians (line "HERE" ...
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3answers
1k views

Volterra Kernel Convolution Method

Here I understand that the first term is a simple convolution of the input signal with first volterra kernel that I have acquired through farina sweep method, my question is if the second term is the ...
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1answer
490 views

Find the nyquist sampling rate?

I have a signal $x(t)$ for which I want to find the Nyquist frequency : $$ x(t) = \frac{\sin{\pi t/2}}{\pi t/2} \ast \sum^\infty_{n=-\infty}\delta(t-10n)$$ I am trying to solve this in the time ...
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1answer
564 views

Circular vs Linear Convolution

When deriving DFT from DTFT,we sample the frequency domain with uniformly spaced samples,hence adding periodicity to time domain. But DFT requires a limited support: we take only 1 period. Does that ...
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1answer
825 views

Convolution in frequency domain, what is the output bandwidth

If two signals do convolution in frequency domain, would the output width/BW be related to the width/BW input signals? Would it be addition or any other?
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1answer
497 views

Downsampling and convolution

(Code snippet with example below). In MATLAB, assume I have a long signal vector y (length N) that I wish to convolve with a ...