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.

Filter by
Sorted by
Tagged with
0 votes
0 answers
74 views

Prove the following [closed]

If $$x_1[n]=A$$ where $A$ is a constant, $$x_2[n]=u[n]$$ and $$x_3[n]= \left \{ \begin{array}{l} 1, \mbox{for n=0}\\-1, \mbox{for n=1}\\ 0, \mbox{otherwise} \end{array}\right.$$ Prove that $$x_3[n]\...
Bitsaa's user avatar
  • 21
1 vote
1 answer
84 views

Continuous-time convolution of signals with negative amplitudes

While preparing for a mid-term exam, I encountered negative amplitudes for the first time while convolving two signals. I've already solved the problem, but my result and results from others conflict ...
kesetovic's user avatar
2 votes
2 answers
99 views

Use DFT (`fft()`) to Replicate 2D Convolution (`conv()`)

In MATLAB, I tried to convert the fft2-based multiplication using conv2. ...
Ka Mirul's user avatar
0 votes
1 answer
39 views

Implementing point-wise multiplication as a convolution

As the title says, I'm looking for a way to implement the point-wise multiplication of 2 signals somehow as a convolution. Here's why: In my system, I have an input signal $x[n]$ which has been ...
Sammy Apsel's user avatar
2 votes
1 answer
60 views

What is the rationale behind the "same" mode of discrete convolution?

Having read up on discrete convolution and how it is implemented, I've started to think about which "mode" is applicable to which situation. For two signals ...
Doddy's user avatar
  • 123
0 votes
1 answer
59 views

Filtering in time domain vs filtering in frequency domain

The signal is an impulse repsonse. I am filtering the signal using a windowed sinc filter in both frequency and time domain. I am interested in knowing the differences between the two methods and ...
Tanmayee Pathre's user avatar
0 votes
1 answer
33 views

Truncating the output of a digital filter. Which part to discard?

Suppose I have a signal $\mathbf{x}\in \mathbb{C}^{N}$ and a digital filter with impulse response $\mathbf{h}\in\mathbb{C}^L$, where $L<N$. If we pass the signal through the filter, the output will ...
Math_Novice's user avatar
1 vote
0 answers
48 views

Determine Noise Level by Convolving N Signals

I using a microphone to determine (air) leakage characteristics. The signals need to be filtered to reduce the noise level and i thought of using the Spectral Subtraction Technique. Since im having 4 ...
Tom's user avatar
  • 77
2 votes
1 answer
161 views

Fourier transform of $|x_\mathrm{a}(t)|^2$

Let $x_\mathrm{a}(t)$ be the analytic signal for real signal $x(t)$. I want to find an expression for $\mathscr{F}\{|x_\mathrm{a}(t)|^2\}(f)$ in terms of $x(t)$. The analytic signal can be written as $...
S.H.W's user avatar
  • 726
1 vote
1 answer
60 views

Does block-based FIR filtering necessarily imply using the DFT?

Assume I want to filter a stream of data with a rather small FIR filter (in the order of 16 to 64 coefficients). In any case I have to split the input stream into chunks (blocks) of data. Searching ...
Junius's user avatar
  • 113
4 votes
2 answers
147 views

Infinite Sum of Future Signal Values of an LTI System

Let $x[n]$ be the input and $y[n]$ be the output of an LTI system. That is, $y[n]=\displaystyle\sum_{k=-\infty}^{\infty} h[n-k]\space x[k]$ where $h[\cdot]$ is the impulse response function. We are ...
singular's user avatar
2 votes
1 answer
45 views

Signal Processing of Long Term Behavior in Stochastic Systems

I am quite new to techniques of signal processing. I have a fairly generic problem and wish to find information about topics and/or techniques that may help me address this problem. Let $x(t)$ and $y(...
singular's user avatar
2 votes
1 answer
171 views

What is the Fourier Transform of $\operatorname{sgn}(t) \cdot \operatorname{sgn}(t)$?

I am wondering what the Fourier Transform of $\operatorname{sgn}(t) \cdot \operatorname{sgn}(t)$ will be, where $\operatorname{sgn}(t)$ indicates the signum function. It would seem obvious that this ...
Finn Heijink's user avatar
2 votes
1 answer
38 views

2d convolution: What is the difference between convolution using blocked Toeplitz matrix and convolution layers?

For a given matrices $A$ of size $4\times 4$ and $B$ of size $3\times 3$ then I construct a blocked Toeplitz matrix and perform the convolution. The resulting output is of size $6 \times 6$. I have no ...
jomegaA's user avatar
  • 655
1 vote
1 answer
89 views

Why are convolutions between those functions equivalent (signal processing for theoretical neuroscience)?

I'm reading a book on theoretical neuroscience [1], in which the following definitions are given: $\rho(t)=\sum_{i=1}^n \delta(t-t_i)$ where $\delta$ is Dirac's delta and the $t_i$ are timestamps at ...
Ash's user avatar
  • 111
0 votes
1 answer
52 views

Convolution output signal transient correction

I'm just starting out in signal analysis and I've come across this effect. When I use convolution of a sinusoid with any other, either triangular pulse, rectangular pulse or decreasing exponential (...
diegobrsrk's user avatar
1 vote
1 answer
135 views

Proving that the autocorrelation of a signal is the convolution with its time-reversed complex conjugate

I need to prove the property $$f(x)⊕f(x)=f(x)⊗f^*(-x)$$ That is the autocorrelation of a function is the convolution with its time-reversed complex conjugate. I have constructed most of the proof but ...
requiemman's user avatar
2 votes
1 answer
183 views

Impulse Response for an Input-Output Pair

Given an input-output pair of a LTI system \begin{gather*} x[ n] \ =\ 2\delta [ n+2] -\delta [ n+1] +\delta [ n-1]\\ y[ n] \ =\ 4 \delta [ n+2] +\ 4\delta [ n+1] -\delta [ n-1] \end{gather*} My ...
Anmoldeep's user avatar
0 votes
0 answers
72 views

Equipment to test my theory on time varying systems

How can I make a linearly time varying system to test my theory? Can I ask for a PID microcontroller available from my university such that $K$ is gradually increased from 0 to $c$
Volpina's user avatar
  • 295
1 vote
0 answers
37 views

Fusing convolutions

I am attempting to combine two consecutive 2D convolutions into a single 2D convolution. Ideally, a convolution operation is a linear transformation, so it should be possible to merge two linear ...
Federico Fontana's user avatar
1 vote
0 answers
50 views

PyWavelets CWT : error when differentiating after convolution?

I'm trying to understand the implementation of CWT in PYWT. This topic has already helped me quite a lot but there is still a thing that is unclear to me : why is the result differentiated only after ...
Tanguy Jonv's user avatar
0 votes
1 answer
57 views

How would the correlation coefficient between 2 images change if we rotated 1 image?

Suppose we have a image which is represented by a matrix $ \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \\ \end{bmatrix} $ and we want to find its correlation with ...
Cerise's user avatar
  • 143
0 votes
0 answers
90 views

Having problems with convolution in Fourier space

First attempt: I tried convolution in Fourier space. step: transform grayscale image ==> (real1,imag1) step: transform kernel (a simple box filter) ==> (real2, imag2) step: multiply (complex) ==...
Gianni's user avatar
  • 11
1 vote
2 answers
107 views

Why will the output be imprinted with delay effect or echo after convolving two direct dry signals' FFT values (convolution filtering)

I am recently working on the reproduction of the filtering effect of target play back devices, like phone, or speakers, etc using convolution techniques in MATLAB. I firstly created a function called &...
CPK's user avatar
  • 11
1 vote
1 answer
78 views

Correlation gives contradictory results

I am trying to find the correlation between the signals $u(t)$ and $\sin(t)[u(t)-u(t-2)]$ The correlation function $C(t) = \int^{\infty}_{-\infty} u(\tau+t)\sin(t)(u(t)-u(t-2))d\tau$ This is my ...
Cerise's user avatar
  • 143
0 votes
1 answer
67 views

How to handle undefined functions in a convolution?

When convolving with undefined functions, do we just treat them like variables? (eg. How do I handle $u \left( k \right)$ and $u \left( n - k \right)$ since they are just step functions with no ...
Axel's user avatar
  • 3
1 vote
0 answers
54 views

Incorrect Power Calculation in MATLAB Convolution

I have been working on a MATLAB code to perform convolution and calculate the power of the resulting signal. However, I have encountered an issue with the power calculation in my code. I am convolving ...
Marcus's user avatar
  • 11
1 vote
2 answers
173 views

Why does convolution give the output of a passing a signal through a filter?

I have a rudimentary understanding of Convolution, the Convolution Theorem and why the output z(t) of an LTI system can be found using the convolution of input signal x(t) and the impulse response h(t)...
SNIreaPER's user avatar
1 vote
1 answer
973 views

Why is the convolution of two sine waves a sinc function?

Problem/Question After taking the convolution of two discrete sine waves of the same frequency and length the result appears to be a sinc function but I was expecting to get a sine wave since this ...
Usman Mutawakil's user avatar
1 vote
0 answers
51 views

Doubt on linear and circular convolution derivation

[I'm very new to this website and to DSP in general as well! :)] Hello everyone! I have a question on the derivation of the circular convolution. As far as I understand, we can define a circular ...
edoverg's user avatar
  • 11
0 votes
2 answers
72 views

Is flipping a vector x the same as x[-n]?

I was intending to use the following convolution property in my Matlab code. $$y[-n]=x[-n]*h[n]=x[n]*h[-n]$$ However, I am noticing that the results seems not the expected ones, for example let have <...
ndarkness's user avatar
  • 113
0 votes
0 answers
16 views

Inequality involving zero-crossings of Difference of Gaussian and Laplacian of Gaussian

I am stuck on the following problem: Let $f$ be a smooth real function with a single inflection point and let $\sigma_1>\sigma_2>0$ be two real numbers. We denote $G_1$ and $G_2$ the associated ...
NancyBoy's user avatar
  • 121
1 vote
1 answer
53 views

Does convolution of delayed sequences produces a delayed output?

Say, I have $x[n]$ and $y[n]$ be periodic sequences of period $N$. Let us define $z[n] =x[n] \ast y[n]$ where $\ast$ denote the circular convolution operation. What is $x[n+\delta] \ast y[n+\delta]?...
wanderer's user avatar
  • 151
2 votes
1 answer
55 views

Why the difference of a vectorized VS non-vectorized FIR convolution differ?

I have an FIR filter that is a low pass at 11025Hz for 44100Hz, 461 taps. The reference implementation, i.e. naive convolution, works as expected. Now I've written a vectorized implementation to take ...
aybe's user avatar
  • 284
3 votes
1 answer
240 views

Convolution and Fourier transform for 1D signals

My problem is the following, I have 3 curves/signals (1D) , the measure, the signal and the resolution of my detector: $\mathcal{M},\mathcal{S},\mathcal{R}$, knowing that : \begin{equation}\label{eq:...
Michael's user avatar
  • 75
0 votes
1 answer
42 views

How to speed up convolution for symmetrical property of a half-band FIR filter?

I've discovered that such convolution can be further sped because of symmetric coefficients but I'm not able to get it right. The filter is a low pass filter at 11025Hz for 44100Hz, with 461 taps. The ...
aybe's user avatar
  • 284
1 vote
1 answer
77 views

Multiplying a finite signal with a unity window

I have a simple question to ask: Suppose $x[n]$ is finite and has a support for $|n|<L$ Let's denote its DTFT by $\operatorname{DTFT}\big\{x[n]\big\}(e^{j\omega})=X(\omega)$ Let's consider a unity ...
Sammy Apsel's user avatar
0 votes
1 answer
235 views

Convolution of step function with exponentials

I have a problem in signals and systems to solve which is basically math So suppose we have two functions x(t) = H(t) which is the Heaviside unit step function as input and an impulse response $$h(t)=...
useeeeer132's user avatar
2 votes
1 answer
140 views

Proof for the energy correction factor of DFT

I am looking for a mathematical proof for the energy correction factor in conteext of windowed discrete fourier transform. In Spectrum and spectral density estimation by the Discrete Fourier transform ...
mocquin's user avatar
  • 151
0 votes
0 answers
37 views

Confusion about convolution [duplicate]

I'm facing confusion about the definition of the convolution between two discrete periodic signals. Basically, the definition of convolution between s and ...
Franck Might's user avatar
2 votes
1 answer
85 views

Convolution error when using DFT for non-periodic functions

I need help understanding why FFT-based computation of convolution on a finite domain, between two non-periodic functions often gets it wrong. Specific questions: (1) why does FFT-based computation ...
pyatsysh's user avatar
0 votes
1 answer
41 views

Comparing methods of blind source separation

I am currently working on blind source separation using sparse hypotheses and convolutive mixtures. For my project, I have compared three different methods and calculated the Signal-to-Distortion ...
BLOBA fitz's user avatar
2 votes
1 answer
69 views

How can Haar basis be written as the impulse response of an LTI system?

Haar wavelets are defined as: $$\phi_{0,0}(t) = \begin{cases} 1, & \text{ for } 0<t< 1/2\\ -1, & \text{ for } 1/2<t<1 \\ 0, & \text{ ...
user avatar
1 vote
1 answer
140 views

3D convolution product with Fourier transforms, FFTW and MPI in C

My question is not really from the field of signal processing but I think you are the most suited for answering my question. I am willing to compute the gravitational potential which can be written as ...
YouShallNotPass's user avatar
1 vote
1 answer
53 views

Effect of BIBO-Instability on the frequency response of a ideal LPF

I recently came across this post stating that the continuous ideal LPF is BIBO-unstable since the impulse response is not absolutely integrable, and this post stating some examples. I have been trying ...
Finn Heijink's user avatar
2 votes
2 answers
106 views

Is downsampling LTI for bandlimited inputs?

This question stems from the discussion we had on a previous question of mine. The point of contention is whether the downsampling operator is time invariant or not. Which gives us a new condition to ...
Ahsan Yousaf's user avatar
  • 1,204
1 vote
1 answer
70 views

Is it possible to consider circular convolution in case of appending the guard interval as a suffix instead of a prefix

In OFDM system, the cyclic prefix is added into the head of time-domain signal to enable the circular convolution with the channel, and then perform one-tap frequency-domain equalization at the ...
Sajjad's user avatar
  • 165
0 votes
1 answer
54 views

Discrete convolution of a causal signal with a delayed unit step

I am computing the discrete convolution of a signal $x[n] = a^nu[n]$ with a delayed unit step, say $h[n] = u[n-5]$. If I place both directly into the discrete convolution formula I end up with: $\frac{...
Marco Marinho's user avatar
2 votes
2 answers
69 views

What is the reason my DFT of a convolution of signals with disjoint spectrums is not zero everywhere?

Assuming the convolution in the time domain produces a signal which spectrum is the product of individual spectrums, when the two convoluted signals are sinusoids with different frequencies, the DFT ...
mins's user avatar
  • 443
2 votes
1 answer
185 views

Can time aliasing cause peaks?

For the following I use the terms “time domain signal” and “frequency domain signal” as a Fourier Transform pair. The question is for generalized cases of continuous-time signals that once sampled in ...
Dan Boschen's user avatar
  • 48.9k

1
2 3 4 5
21