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.
759
questions
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.
$$
\mathcal F\left\{h\star g\...
5
votes
1answer
86 views
Circular Convolution as Cyclic Shift Operator
Given the following signal vectors:
$$ Ī³=[Ļ_0,0,Ļ_1,0,Ļ_2,0,ā¦,Ļ_{N-1},0]^T\in \mathbb{R}^{2N}, Ļ=[1,\frac{1}{2},0,ā¦,0,\frac{1}{2}]^T \in \mathbb{R}^{2N}$$
I want to show that the convolution of $Ī³$ ...
0
votes
1answer
23 views
Convolution output signal is very large, do I need to scale inputs or outputs?
I am writing some simple matlab code to refresh my convolution knowledge (it has been awhile) in regards to DSP.
I have an input signal x and a filter -
...
0
votes
2answers
19 views
Impulse response of forward difference cascaded with one sample delay
Below is the excerpt from Discrete Time Signal Processing by Alan Oppenheim.
I don't get how $(\delta[n+1] - \delta[n]) * \delta[n-1])$ becomes $\delta[n] - \delta[n-1]$. The convolution sum operator ...
0
votes
1answer
24 views
generator matrix coefficient in convolutional code
I cant determine a type of the following code:
G_1=1 // g_1=1
G_2=11 // g_2=x+1
Accorsing to description, it is convolutional code but I dont understand the ...
1
vote
0answers
53 views
How to estimate the system characteristic function given experimental input and output
I have experimental signals $y_i(t)$ for $i = 1,\ldots,n$ that correspond to different excitation inputs to a system $x_i(t)$ for $i = 1,\ldots,n$. The goal is to find the system characteristic ...
0
votes
0answers
34 views
Fourier transform and energy of a convolution
Hi guys i have to find the fourier transform of the convolution:
$$ 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 $f_2$. Iād 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,$$
where $\star$ denotes cross-correlation, $*$ denotes convolution and $S_0 \star S_0 = \delta$. Is it true in general ...
2
votes
4answers
145 views
Defining the convolution for finite-length signals
How can the linear convolution be defined rigorously for two discrete signals $x = [x(0), ā¦, x(N_x-1)]$ and $h = [h(0), ā¦, h(N_h-1)]$ of different finite lengths $N_x$ and $N_h$ respectively?
Let's ...
2
votes
1answer
55 views
Discrete Time Convolution Evaluation
I'm trying to solve a problem on convolution from Alan V.Oppenheim:
Find the convolution output $y[n]$ for the following signals:
$$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 $x[n]= e^{jnĻ/4}$
Hi I'm trying to solve the problem when studying for an upcoming test.
The given solution is
$1.2503 e^{jnĻ/4 -0.2991}$, and is found by computing $H(Ī©)$ and evaluating this at $Ī©=Ļ/4$.
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{0ā¤ m ā¤ 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. ...
