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
0answers
28 views

Reconstructing signal from frames

Edit: Please treat code here as python-esque pseudo-code; it would syntactically fall closest to MATLAB or Python+numpy+scipy users. If I have a signal in frames, and I want to put it back together - ...
1
vote
2answers
80 views

Convolution of two sets

In my systems and signals course I had been asked a question about finding the convolution of two sets. I was given: \begin{align} x[n] &= \{3,2,1\}\\ h[n] &= \{1,-2,3\}\\ \text{Find}\quad ...
0
votes
1answer
38 views

What is the correct length for obtaining a true linear convolution from DFT?

In the linear convolution of two equal length sequences M and N, the length of the output is length(A)+length(B)-1, and if we apply the DFT property of converting convolution into multiplication, the ...
0
votes
0answers
29 views

Possibilities in Audio Convolution Math

New Python user here! I am a musician working on a program to streamline a process of using convolution math on a folder of .wav samples. The idea is that each audio sample will be multiplied with ...
0
votes
1answer
19 views

multiplication of a function with a Fourier-transformed equals to Fourier-transformed with a function

I already showed b item using the fact that it is $h\left(0\right)=\int \:f\left(t\right)g\left(0-t\right)dt$ I struggle a lot of hours trying to find the trick in item C. Can anyone help please ?
2
votes
2answers
73 views

Inverse system of sinc?

I'm doing some self-study for an important exam I'll have in late March and came across the following question: So, using the convolution properties, if I want to find an identity system so that the ...
1
vote
1answer
43 views

Concrete use of convolution algebraic properties [closed]

There are 3 main properties of convolution in every image processing lecture notes I read : Commutativity: $f\star h = h\star f$ Associativity: $f\star (h_1\star h_2) = (f\star h_1)\star h_2$ ...
1
vote
1answer
57 views

Mathematical expression of Multicarrier frequency equalizer

I have a signal $X$ with length of $N$, multiplied with any unitary matrix, i.e the transpose of DCT matrix as: $x = D' X$ where $D'$ is the transpose of the of DCT matrix. Then let's add $CP$ guard ...
0
votes
2answers
49 views

Normalization factor in the convolution theorem

Maybe it's a trivial question, but I couldn't find any explanation for this. According to the convolution theorem, in the continues case we add normalization factor, i.e. $$ \mathcal F\left\{h\star g\...
5
votes
1answer
86 views

Circular Convolution as Cyclic Shift Operator

Given the following signal vectors: $$ γ=[ψ_0,0,ψ_1,0,ψ_2,0,…,ψ_{N-1},0]^T\in \mathbb{R}^{2N}, ϕ=[1,\frac{1}{2},0,…,0,\frac{1}{2}]^T \in \mathbb{R}^{2N}$$ I want to show that the convolution of $γ$ ...
0
votes
1answer
23 views

Convolution output signal is very large, do I need to scale inputs or outputs?

I am writing some simple matlab code to refresh my convolution knowledge (it has been awhile) in regards to DSP. I have an input signal x and a filter - ...
0
votes
2answers
19 views

Impulse response of forward difference cascaded with one sample delay

Below is the excerpt from Discrete Time Signal Processing by Alan Oppenheim. I don't get how $(\delta[n+1] - \delta[n]) * \delta[n-1])$ becomes $\delta[n] - \delta[n-1]$. The convolution sum operator ...
0
votes
1answer
24 views

generator matrix coefficient in convolutional code

I cant determine a type of the following code: G_1=1 // g_1=1 G_2=11 // g_2=x+1 Accorsing to description, it is convolutional code but I dont understand the ...
1
vote
0answers
53 views

How to estimate the system characteristic function given experimental input and output

I have experimental signals $y_i(t)$ for $i = 1,\ldots,n$ that correspond to different excitation inputs to a system $x_i(t)$ for $i = 1,\ldots,n$. The goal is to find the system characteristic ...
0
votes
0answers
34 views

Fourier transform and energy of a convolution

Hi guys i have to find the fourier transform of the convolution: $$ sinc(t/2T)*\sum\limits_{n-\infty}^{+\infty} (-1)^{n}\delta(t - nT) $$ i was thinking of express the summatory as : $$\sum\limits_{n-\...
0
votes
0answers
15 views

How to figure out the polynom of Convolutional encoder

I have Convolutional encoder with K=7, r=1/2 that steam of bits get enter to it from right to left (7 registers and steam of input is entering the convolutional encoder from left to right .. ) the ...
0
votes
0answers
14 views

How to compute inner product of Wavelet transform convoluted with signal

I have two datasets $X_1$ and $X_2$ in a sparse wavelet basis, and I have two filters $f_1$ and $f_2$. I’d like to compute the inner product of the convolutions $$\langle X_1 \star f_1, X_2 \star f_2\...
0
votes
2answers
56 views

$f \star (g \,* \,h) = (f \star g) * h$?

In this paper that I'm reading, I see this equation: $$S_0 \star (S_0 * N) = N,$$ where $\star$ denotes cross-correlation, $*$ denotes convolution and $S_0 \star S_0 = \delta$. Is it true in general ...
2
votes
4answers
145 views

Defining the convolution for finite-length signals

How can the linear convolution be defined rigorously for two discrete signals $x = [x(0), …, x(N_x-1)]$ and $h = [h(0), …, h(N_h-1)]$ of different finite lengths $N_x$ and $N_h$ respectively? Let's ...
2
votes
1answer
55 views

Discrete Time Convolution Evaluation

I'm trying to solve a problem on convolution from Alan V.Oppenheim: Find the convolution output $y[n]$ for the following signals: $$x[n]= u[n]\quad\text{and}\quad h[n]=a^{n}u[-n-1], \ a>1 $$ I ...
1
vote
1answer
41 views

Discrete-time Convolution Convergence Issue

I'm trying to solve a problem on convolution from Alan V.Oppenheim: Find the convolution output $y[n]$ for the following signals: $$x[n]= u[n]\quad\text{and}\quad h[n]=a^{-n}u[-n-1], \ a>1 $$ I ...
0
votes
0answers
50 views

Low-pass filters not producing smooth output

I'm relatively new to this material, so apologies in advance if I'm missing something obvious. I'm trying to smooth some very noisy signals. What I observe is that if I apply an ewma, even with a ...
0
votes
1answer
50 views

Smoothing power spectrum by convolution with boxcar function

I am trying to smoothing a signal's power spectrum by convolving the spectrum with a boxcar function in frequency domain. However, the result is obviously not what I expected: original two frequency ...
2
votes
1answer
92 views

Hilbert transform in the frequency domain

As I know, the Hilbert transform $$ H(x(t))=\frac{1}{\pi t}\star x(t) $$ in time domain is equal to $$ -j \operatorname{sgn}(f) \cdot X(f) $$ in frequency domain. so I tried simple example using ...
4
votes
3answers
804 views

Can FFT convolution be faster than direct convolution for signals of large sizes?

Let's say I have a 1D signal of size $N$ and am trying to filter it with a 10-tap FIR filter mask. When $N$ is large, the number of multiply-accumulates would approximately equal $$2 \times 10 \times ...
1
vote
0answers
49 views

The impulse response of a LTI discrete system is $h[n]=\big(\frac{1}{3}\big)^n u[n]$. Find the response of this system to the input $x[n]= e^{jnπ/4}$

Hi I'm trying to solve the problem when studying for an upcoming test. The given solution is $1.2503 e^{jnπ/4 -0.2991}$, and is found by computing $H(Ω)$ and evaluating this at $Ω=π/4$. when I try ...
0
votes
1answer
109 views

Finding the convolution $a^n u[n]$ with $b^n u[n]$

Hi I'm trying to solve the problem when studying for an upcoming test. The given solution is $$y[n]= \frac{1}{b-a}(b^{n+1}-a^{n+1}) \quad \text{for } n\ge0 \ .$$ However, I'm not sure how to reach ...
0
votes
0answers
65 views

Linear convolution in the DFT domain

Let's say I have 2 sequences a and b in the time domain. Both are length N. A and B are the DFT of a and b. If I do a circular convolution of A and B in freq domain (A o B), then the IDFT of the ...
0
votes
0answers
20 views

Calculation of eigendecomposition of a signal in its Fourier domain?

I want to find the eigendecomposition of a 3-dimensional discretely sampled signal $X$, where each sample $X_{i,j,k}$ is treated as a vector $\langle i, j, k\rangle$ (with the origin at the middle of ...
0
votes
2answers
87 views

Unclear time-to-frequency integration step

From here; $\hat f=\mathcal{F}(f)$, bar = complex conjugate: Time-shift property: $x(t-b) \Leftrightarrow e^{-j\omega b}{\bf X} (\omega)$, so why is it $+$ (red)? What at all is happening? Looks like ...
1
vote
0answers
124 views

Alternative convolution theorem?

Instead of padding $x_1[n]$ and $x_2[n]$ then taking $$ \text{iDFT}(\text{DFT}(x_1[n])\cdot\text{DFT}(x_2[n])), \tag{1} $$ assuming we know $x_1(t)$ and $x_2(t)$, and their FT's, what if we do $$ \...
2
votes
1answer
143 views

2D Frequency Domain Convolution Using FFT (Convolution Theorem)

In the time domain I have an image matrix ($256x256$) and a gaussian blur kernel ($5x5$). I've used FFT within Matlab to convert both the image and kernel to the frequency domain as zero padded $...
2
votes
1answer
82 views

linear convolution toeplitz matrix vs circular convolution toeplitz matrix

I have an issue in understanding the difference between building the Toeplitz matrix when the convolution is linear and when it's circular. As I know that Toeplitz matrix $H$ can be built as following ...
2
votes
1answer
178 views

PyWavelets CWT: normalization? Vs Scipy?

Related. The equation being implemented normalizes by sqrt(1 / scale): $$ C_{a, b} = \frac{1}{\sqrt{a}} \sum_k s(k)\left( \int_{-\infty}^{k+1} \overline{\psi \left(\...
0
votes
1answer
27 views

PyWavelets CWT: resampling vs recomputing wavelet

Related. The implementation pre-integrates a wavelet once, and resamples it at each scale, finally differencing to implement ...
0
votes
1answer
24 views

Multiple short-range impulse responses aggregated to simulate a long-distance impulse response

I'm a biologist and I was thinking of ways that impulse responses could be used to simulate how an animal sounds over various distances in different types of forests. Ultimately, if a tool was ...
1
vote
1answer
116 views

PyWavelets CWT implementation

I seek to understand PyWavelets' implementation of the Continuous Wavelet Transform, and how it compares to the more 'basic' version I've coded and provided here. In particular: How is integrated ...
0
votes
1answer
67 views

Convolutions with changes to the argument

I think I understand what happens when I shift the argument, but I'm not sure what should happen when the signal is compressed or expanded. In particular I'm trying to figure out what happens when the ...
2
votes
0answers
28 views

Showing that filtering a signal with bandwidth B with a brickwall filter of bandwidth W>B has no effect in time domain

The time-domain representation of $G(f) H(f)$, where $H(f)$ is an ideal brickwall filter of bandwidth $1/(2T)$ is: $$ \int g(\tau) \operatorname{sinc}\left(\frac{t-\tau}{T}\right) d\tau $$ I want to ...
-3
votes
2answers
152 views

Can digital filters actually separate signals?

I've come to realize what appears to be a hard limit in convolution theorem: to avoid time-domain aliasing, we must pad the signal/filter, but the padding distorts the spectrum. Consider a ...
0
votes
0answers
14 views

Amplitude Matching for Exponential Swept Sine

I am working in the area of aerospace vibration testing and we use swept sine tests on structures and measure the response using the accelerometers. I tried implementing the technique "...
0
votes
0answers
100 views

Why does time-domain convolution correspond to frequency-domain multiplication? (visual)

I seek a visual explanation of this. I've already seen the maths, and can derive the proofs - they amount to nill for an intuitive understanding. Any amount of math is welcome, as long as serving to ...
2
votes
1answer
33 views

Channel equalization affect on input signal

I have the following problem. Am trying to understand how the channel block affects the input signal s(n). I know that x(n), the input signal to the filter is basically: \begin{equation} x\left(n\...
0
votes
1answer
35 views

attenuation of the central difference differentiator

In the following snippet, I am differentiating a sine wave using the central difference equation, first through misc.derivative and then through convolution with the kernel [1/2, 0, -1/2] ...
2
votes
0answers
34 views

Determining the right order of time-domain low pass filter for desired cutoff frequency

I've been stuck on a problem regarding complex demodulation of a signal for a while and wondered if anyone could help. Suppose I have a signal $X(t)$ such that \begin{align} X(t) &= A(t)\cos(\...
1
vote
1answer
102 views

Fourier Transforms, Convolution, Cross-correlation: what is their physical unit exactly?

Let us assume we are talking about real, deterministic, electrical signals $x(t)$ and $y(t)$ (magnitude in Volts). There are different kind of Fourier Transforms. I made a table to summarize: NB: By ...
0
votes
0answers
125 views

Convolution of rectangular function with sinc function

I'm trying to create a rectangular function, defined between -0.5 to 0.5 I'm then convoluting it with a sinc function (using numpy.sinc) and plotting the convoluted ...
0
votes
1answer
46 views

Computing Autocorrelation via FFT

I have seen several methods to calculate Autocorrelations using FFTs, and am confused about why they differ. Zero-Pad it to double its original length.Take the FFT. Then replace all the coefficients ...
0
votes
0answers
32 views

Perform 2D convolution on a 2D unit step function

I am stuck with the following 2D convolution: Consider the sequence $f$ defined by the following: $f[m,n] = \begin{cases} 1 & \text{0≤ m ≤ n} \\\ 0 & \text{otherwise}\\ \end{...
2
votes
1answer
59 views

Exponential Swept Sine Distortion

I was able to get passable results on fundamental measurements using and exponential swept sine. Now I am trying to get distortion information from the same measurement but am puzzled by the results. ...

1
2 3 4 5
16