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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Calculating FIR filter coefficients with the windowing method and Convolution algorithm

Please advice how to calculate FIR filter coefficients with the windowing method using the Rectangular Window function and convolution method? What utility or FIR design application can perform this ...
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33 views

Fast convolution with very high order FIR

I am investigating the overlap-add and overlap-save methods for processing an audio signal with a FIR. The FIR is a measured impulse response of a reverberant space and may be of order greater than ...
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55 views

Increasing the number of points in the frequency spectrum

I have an image with few pixels in length and height. For this image I calculated the two dimensional Fourier transformation. What I got for the frequency spectrum in one direction was a very ...
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2answers
74 views

Perform Convolution in Frequency Domain Using FFTW?

I'm trying to convolve two signals $x(n)$ and $h(n)$ in C by using the FFTW library's functions to perform a Fourier transform on each, multiply the appropriate complex components together, and take ...
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22 views

FIR difference equation vs convolution summation

I'm sorry if my question is too simple, but I am self-studying FIR because we have to report it in our class. I am using the book of Proakis and Manolakis as reference. Under 7.2 Structures for FIR ...
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1answer
232 views

What does it mean to deconvolve the impulse response

I am learning DPS and I came across the problem of deconvolution and removing the impulse response from a signal? This still does little sense to me. My understanding of the impulse response is to ...
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3answers
143 views

Get a N-FFT with two N/2-FFT already computed

After somme researchs on the web, I don't find the answer of my problem (or I don't understand it) and I hope this post will succeed. I'm working on a real-time FFT convolution algorithm (C++) which ...
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0answers
38 views

Difficulties with derivative of convolutions in Fourier domain

I am trying to solve a minimization problem in the DFT domain. I have a formula where both dot products and convolutions are involved. Capital letters are the DFT of 2d images, the overline denotes ...
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1answer
30 views

Frequency Domain Filtering with big kernel size

I use FFT to do filtering in frequency domain, but when I use big kernel I got shift on border, I think it's due to nature of cyclical convolution and I need to do more zero padding. But how to ...
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2answers
87 views

Simple FFT convolution with impulse response wav file doesn't give the right results

I have been trying to find a solution to my FFT convolution problem but everything that I have found while searching hasn't been helping me. I have a working forward and backward FFT function, that I ...
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1answer
68 views

Basic question: Why is the output of a system the convolution between the impulse response and the input?

I forgot a very simple fact and I am now struggling to find reference that proves this basic property? How would you prove that for a single in single out system, the system output is the impulse ...
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60 views

Ideal BandPass Filter

Let suppose x(t)=$\sum\limits_{k=-∞}^∞ R(t-kT)$ $R(t) = \begin{cases}1 &[0,2T] \\ 0 & \text{otherwise} \end{cases}$ x(t) is the input to an ideal bandpass filter with $\text{BandWidth} = ...
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44 views

Confused with convolutions in scipy

I tried to write my own circular convolution function in python using the fact that for two signals $f$ and $g$ we have $$ \widehat{(f * g)} = f \cdot g $$ So I tried this ...
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42 views

Fast/efficient way to compute Laplacian edge enhancement filter

I would like to implement a somewhat smarter Laplacian edge enhancement convolution. Right now it is implemented as (generic 3x3 convolution): ...
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1answer
42 views

Filtering Passband Signals using Complex Baseband Filtering

So I'm given a pass band filter with specific transfer function $H_p(f)$, I want to implement this via baseband processing. I already know how to take the input signal $u(t)$ and process it such that ...
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1answer
49 views

Is there a convolution mistake in my method?

I have the input signal $x(t)$ And impulse response $h(t)=20 e^{-1000t} u(t)$ in which u(t) is the unit step function. When I try a convolution, I thought the solutions would be something like: $ ...
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1answer
37 views

Problems filtering image with prewitt

I'm trying to filter an image vertically to get the edges, in MATLAB, but I get very different results from convultion and correlation. CODE: ...
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2answers
50 views

convolution of a real and complex signal

How do we define convolution of: $$x(t)= \mathrm{sinc}(W t)$$ and $$y(t)= -j\mathrm{sinc}(2W t)$$ Answer: In the frequency domain, both of them are rectangular functions and multiplication of them ...
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2answers
193 views

Understanding circular convolution

Let $a$ and $b$ $\in \mathbb C^N$ and $a[k] = a[k \mod N]$ (same with b). Then the circular convolution of $a$ and $b$ is defined by $$ (a * b)[n] = \sum_{p=0}^{N-1} a[p] b[n-p].$$ I have a problem ...
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54 views

applying convolution theorem swaps quadrants

For educational purposes I implemented the DFT and inverse DFT for images using OpenCV. Applying the DFT to an image and taking the inverse DFT of the spectrum yields the original image, so this ...
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40 views

Are convolution and deconvolution kernel the same?

I need to clarify this and rather confused by this. Lets say: $x = h * g$ $x$ - measured data $h$ - raw data $g$ - instrument response function (convolution kernel) So lets say I ...
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23 views

Analytical expression for convolution of two 2D DFTs

I am trying to do an image analysis problem on some images, and I want to calculate some things in the frequency domain which are giving me problems. Say I have an (discrete) image $I(x,y)$ of size ...
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2answers
58 views

convolution matrix for image scaling

Is there any way how to compute convolution matrix for Nearest Neighbor (bicubic, bilinear) image scaling (upscale/downscale)?
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144 views

Implementing overlap add method for convolution with a slice of the filter

In overlap add method for convolution a filter $x$ of length $M$ will get convolved with a signal $y$ of length $N$ where $M << N$, i.e., $z = x * y $. Here the signal $y$ is sliced into ...
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19 views

Equivalence of transfer functions based on identical input and output

We have two transfer functions which are functions of frequency. No matter the frequency value of the input, which is of the form $e^{jwn}$ or the value of n, the output will be identical. Are the two ...
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39 views

Convolution / Correlation correct implementation in java

I have a java programm which is manipulating an RGB picture which comes in a 3dimensional matrix. I tried to implement an apply Convolution and an apply Correlation function, which applies a kernel ...
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33 views

N-point circular convolution with n > length of sequence

If I want to take an n-point circular convolution and both of my sequences are less than n length, how do I do this? Do I cutoff the terms that don't fit? For example, say I want to perform 4-point ...
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1answer
74 views

Prove that time-reverse yields inverse filter for deconvolution?

In reading literature on the construction of impulse responses from sine sweeps (e.g. papers by Farina), I see it stated over & over that the way the impulse response is constructed from a ...
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1answer
113 views

How to show that y[n] = x[n] * h[n] turns into the Y(z) = X(z).H(z)?

I'm trying to show that $y[n]=x[n]*h[n]$ turns into $Y(z) = X(z)H(z)$ in Z-domain by first applying convolution then by taking the inverse Z-transform of the $Y(z)$, stating that it's the same ...
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48 views

Efficient algorithm for computing area under convolution?

Consider $N$ discrete signals $x_1(n), x_2(n), \ldots,x_N(n)$ each a bounded support of size $M$. To convolve them, we can zero-pad each of them, multiply their FFTs, and take the result's inverse ...
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2answers
36 views

How can you intutively figure what the impulse response will behave like?

I was trying to understand convolution from this book and came across this figure: Here, the input signal is a combination of a sine wave and a ramp. In fig a, the input signal is convolved with a ...
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38 views

Size obtained by applying Linear convolution

We know that applying a filter on an image is called correlation or convolution depending on the filter angle. In Gonzalez I have read that we can apply linear convolution on an image. Here I have a ...
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27 views

What is the difference between Time-Frequency Represenation and TF Decomposition

I'm asking as I'm looking at Wavelet transforms, and I see that it is possible to have a TF decomposition or a representation of the signal. Looking for example at the code here we can see that the ...
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1answer
95 views

2D deconvolution of recorded electron beam data

I'm currently working on a project that involves using an electron gun and it would be really nice to know the spot shape of the electrons coming out of the gun (the frequency of electrons at some x,y ...
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95 views

Difference between correlation/convolution and matrix multiplication

Can anyone please clarify the difference between correlation/convolution and matrix multiplication? As I thought either convolution or correlation is similar to matrix multiplication. I read this ...
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4answers
503 views

What is convolution of two sine waves (tones)?

Convolution of two sine waves (or tones as called in audio) is theoretically not defined as the integral is infinite. Taking finite duration windowed sine waves and doing there convolution ...
2
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1answer
57 views

Avoiding edge repeats in a FFT convolution

I am trying to use FFT as a fast way to convolve a image, however one of the downsides of this is that the "kernel" image will repeat when reaching the edges of the sample. Is there a way to avoid ...
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1answer
25 views

Different results for seperable filtering v/s direct filtering on 2-D image in MATLAB

I compared the difference between seperable and direct filtering for MATLAB's cameraman image. The difference is huge. I would like to understand the reason for this. Code below. ...
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43 views

Convolution of h(n) & x(n)

can anyone please help me with finding Convolution for following problem ..... 1) $h(n) = \delta[\sin(1 + |n|)]\quad \text{and}\quad x(n) = \sin(n^2)$ 2) $h(n) = \delta[\sin(2\pi n/N)] \quad ...
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2answers
120 views

Convolving Room Impulse Response with a Wav File (python)

I have written the following code which is supposed to put echo over an available sound file. Unfortunately the output is a very noisy result which I don't exactly understand. Can anybody help me with ...
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1answer
77 views

How to derive the answer to this convolution problem?

I came across this below question, (which was a homework assignment question for Signal Processing class, which my friend mailed me for help solving), mulled over it for an hour and had no idea how to ...
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1answer
99 views

understanding discrete-time convolution in LTI systems

I'm trying to understand the discrete-time convolution for LTIs and its graphical representation. standard explanations (like: this one) start with the idea of decomposing an input signal $x[t]$ into ...
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2answers
123 views

Difference between convolution and multiplication of freq. response and freq. spectrum

Suppose I have impulse response like [1/25,2/25,3/25,4/25,5/25,4/25,3/25,2/25,1/25]. I did convolution with 600 samples of test signal (it seems that I did some filtering). Then I calculated the ...
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20 views

Extraction of a decision boundary (LDA) after a systematic querying of the feature space and convolution with Sobel filter (examples in numpy)

I am doing some experiments with LDA (Linear Discriminant Analysis), in python. Now I am at the point in which I would like to display the separation planes in the 3-dimensional feature space. I ...
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1answer
80 views

Writing a Discrete Fourier Transform program

I would like to write a DFT program using FFT. This is actually used for very large matrix-vector multiplication (10^8 * 10^8), which is simplified to a vector-to-vector convolution, and further ...
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83 views

Convolution: 2D kernel to full matrix

We know that a convolution can be replaced by a multiplication with a toeplitz circulant matrix. Meaning, assume I have convolution kernel $h$ and matrix $I$ (of size $m \times m$ for example), then ...
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120 views

Convolving two complex signals - relationship between phase

Suppose two continuous complex domain signals are convolved, how is the magnitude and phase of the resultant signal related to the magnitudes and phase of the original signals?
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132 views

Confusion about result of FIR All-pass filter design

I try to design a FIR All-pass filter with random phase in the frequency domain. I am a bit confused by my result and am not sure if the reason is a programming error or a misconception about ...
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1answer
80 views

Discrete Fourier Transform and Opposite Convolution Theorem

I am reading the Wiki for DFT. There is a part for circular convolution theorem which sounds a bit odd saying: $$ \mathcal{F} \left \{ \mathbf{x\cdot y} \right \}_k \ \stackrel{\mathrm{def}}{=} ...
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63 views

Convolution theorem

As stated by the convolution theorem, a convolution in spatial domain is equivalent to a multiplication in the frequency domain.Nevertheless, when should the first be preferred over the latter?