Questions tagged [deconvolution]

in mathematics, the inverse operation of convolution signals. In general, the purpose of deconvolution is to find solutions of the convolution equation defined as: f * g = x. Where h is the recorded signal, and f is a signal that you want to recover, and we know that the first signal is obtained by convolution of the second with some known signal g. If the signal g is unknown, it has to be estimated (eg. statistical estimation).

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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 "...
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51 views

Removing Gaussian Noise from a Signal to Get Minimum Value

I have a signal that has a minimum value that I'm trying to read. The issue I'm having is that the signal is spread out by gaussian noise. I have the signal at a lot of timesteps (and expect the ...
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Recover an OFDM signal affected by AWGN

I have an OFDM signal affected by AWGN, if I know the power of the gaussian noise, can I recover the OFDM signal? Can I perform deconvolution to recover the original signal? thanks
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41 views

Obtaining an IR from a sine sweep without the dry sweep

I have a test vinyl record that includes an exponential sine sweep as one of the tracks. I have a recording of the sweep through my turntable/mixer, and now I want to calculate the system IR. The ...
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39 views

Receiver function, frecuency domain deconvolution not giving logic results

I'm working on some code for receiver function method in seismology. For anyone one not into the topic, it's just a deconvolution of two time series (seismograms). This can be done in the time domain ...
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139 views

Deconvolving a 1d Signal Using a Lookup Table of Kernels

assuming I measure a signal that has different PSFs per position in time. for example: ...
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How to water level deconvolve a noisy signal if i have a zeros and poles file?

Thanks for your time and help! I am working with Apollo project passive seismic experiment (PSE) data, and I have a large set of seismic records (on digital counts) and the corresponding file of poles ...
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38 views

Convolution that outputs a unit impulse

Im thinking whether any convolutional operation can output a unit impulse, an example to further explain: where a convolution between system $h[n]$ and unknown system $g[n]$ would output $\delta[n]$. ...
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scipy.signal.deconvolve not working, Blind deconvolution in python

I am trying to deconvolve my original signal with a given wavelet (Ricker wavelet). But scipy.signal.deconvolve is not giving any output to the signal. Impulse signal can be generated by below code. ...
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Whats the Correct Approach to Estimate the PSF of a Moving Detector

In lab, I did a bunch of scans using a radiation source and a detector. My source emits a gaussian beam (whose dimensions I know), and my detector is a uniform 7mmx7mm square. These are stationary and ...
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Zero forcing vs matched filtering vs LMMSE

In what scenarios would you choose each of Zero forcing, LMMSE and matched filtering receivers: Possible points to consider are: Receiver SINR, High Interference levels, Low interference levels, ...
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Division in the Fourier Domain (Deconvolution) - How to Handle Lengths of the Signals

In order to avoid circular convolution $y(t)$ of two functions say $u(t)$ and $v(t)$ in Fourier transforms, the data length must be at least (length $u(t)$)+length($v(t)$)$-$1. If we are interested in ...
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Best approach for discarding the ends of convolution in FT

In a recent discussion Linear vs. Circular Convolution on avoiding circular convolution by FFT, it was shown that the FFT length for convolution purposes set should be = (data set 1)+ (data set 2) -1. ...
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Linear and Circular Convolution in Fourier Domain (DFT)

Suppose we have two vectors A and B of length 100 and 80 obtained as a function of time. If we wish to perform convolution of the two vectors in the Fourier domain, we need to multiply the Fourier ...
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161 views

Estimating the Signal by Deconvolution with a Prior on the Filter Coefficients and the Signal Samples

Assume I have signal $y[n]$ which is a result of convolution between channel $h[n]$ and signal $x[n]$. which means: $$y[n] = h[n] \ast x[n]$$ where $\ast$ is the convolution operation The signal $...
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Deconvolution of an Image Acquired by a Square Uniform Detector

So, I acquired some images by scanning a radiation source with a square detector like in the following gif. Where the dashed grid represents reality, the 3x3 square my detector, and the 4x4 my ...
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Noise amplification with inverse filtering

I'm trying to gain a better (mathematical) understanding of why inverse filtering is almost never the solution for correcting an image. From what I understand, we start with a discrete signal $s[n]$ ...
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Transfer function and deconvolution

Forewords This question is about methodology references and numerical application. I am posting on Signal Processing because I think this question belong to this place. I am new to the stack, feel ...
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1answer
503 views

Complex output after inverse FFT of a real signal

I have a real one dimensional signal s (light absorbance in a flow cell), which has significant noise and some periodic noise after performing a deconvolution of $S$ from $S_o$. Basically fft($S$) was ...
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840 views

Can every type of linear filter be modelled by a convolution?

I have an input time series going through a filter that creates another time series as output. If I assume in first approximation that my filter is linear, does it necessarily mean that I can model ...
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120 views

FIR Filter Deconvolution [closed]

Suppose we have a system whose impulse response h has length K and fed with an input x that has length N. Then it is known that the output y has length M = K + N -1. This shows us the convolution ...
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Could kernel density map be recovered with known kernel function?

I'm confused whether a KDE map could be recovered with known kernel function. The KDE map (with no noise) generated with fast fourier trasnformation (FFT) could be recovered on very high accuracy (<...
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What Is the Correct Way to Apply Richarson Lucy Deconvolution to Luminance Data?

My question concerns the Richardson–Lucy deconvolution algorithm, which is described in Richardson's original paper. I am interested in applying it in the context of a raw image converter for digital ...
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The Gradient of Least Squares of 2D Image Convolution

Given the objective function: $$ \frac{1}{2} {\left\| h \ast x - y \right\|}_{2}^{2} $$ Where $ h $ is the 2D convolution kernel and $ x $ is the 2D convolution image and $ y $ is a given 2D image. ...
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Reconstructed output mismatch for LTI system

I have a system with measured input (u) and output (y). I assume that this is an linear time-invariant (LTI) system and I want ...
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181 views

How to express STFT and ISTFT as a 1d convolution and 1d deconvolution in tensorflow/keras

I'm trying to implement this paper in tensorflow and keras. At the end of section 3 it says. ...
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155 views

What Is the Relation Between Deblurring and Deconvolution in Computer Vision and Image Processing?

The deblurring problem can be modelled as follows $$ f = \phi u + \epsilon, \; \epsilon \sim N(0, \sigma) $$ where $\phi$ is a filter (e.g. a low-pass filter) and $\epsilon$ is a Gaussian noise. In ...
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Deconvolution of two FIRs

Basic questions: What's the "correct" way to deconvolve two causal FIRs in the frequency domain (i.e. using the FFT), neither of which may be minimum phase but both may be considered to have stable ...
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Scipy Deconvolve help

I was playing with the deconvolve method in scipy and I can't seem to get it working properly (I am still really new to DSP/deconvolution). I convolved a gaussian with a fwhm of 2.0e-9 with a ...
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Deconvolution of Synthetic 1D Signals - How To?

I convolved a square wave with a Gaussian wave using linear convolution. Can I get the original square wave back by deconvolving my output with the Gaussian function? I took the FFT of both signals, ...
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1answer
99 views

Blind Deconvolution

I have a signal X which is a sinusoid with asymmetrical clipping on the positive half of the waveform. The clipping characteristic is “soft”. I don’t know ahead of time either the clipping threshold ...
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759 views

The tail of scipy deconvolve

I have a dataset for the function $g(t) = \int_{0}^{\infty}f(t-\tau)h(\tau)d\tau$ I would like to deconvolve. My assumptions are The signal $f(t) = 0$ before the start of observation, that is for $t &...
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Deconvolution of 2 vectors (1 know + 1 unknown)

I am currently trying to deconvolute 2 vectors (a & b) from 1 (c). Actually, I have access to the recorded data of (a) & (c) but not (b). All are signal vs time with signal totally random. I ...
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745 views

Deconvolution of a 1D Signal with Known Kernel (Square Wave)

I have a signal measured from a radiation detector in a narrow beam of radiation. The peaks I get are quasi-gaussian in shape, see attached picture. The signal is not a function of time, rather a ...
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3answers
920 views

Deconvolution Using Complex Division in The Frequency Domain

Consider these two signals: a = [1 1 0 0 0 0 0 0] b = [1 0 1 0 0 0 0 0] their convolution is c = a * b = [1 1 1 1 0 0 0 0] ...
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328 views

Wiener deconvolution in cpp giving back the same image

I was trying to deblur a noisy image using wiener deconvolution. I found this code which added noise to an image and removed it as well. Modifying this code only i tried to implement the exact formula ...
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scipy.signal.deconvolve returns an array of NaNs [closed]

I am trying to implement a deconvolution-based event detection algorithm in python, but scipy.signal.deconvolve doesn't seem to work in my case. Here is a basic example: ...
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Finding the Best Gaussian Smoothing Kernel to Minimize the Discrepancy Between Two Images

Suppose we have two grayscale images, $A$ and $B$. $A$ and $B$ very strongly resemble each other, such that the mean of the absolute difference $\lvert A - B\rvert$ is fairly small. Suppose further ...
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Is it possible to “equalise” a signal by deconvolving the impulse response of the room in which it is to be played?

I am using a test sweep with a flat power spectrum and linear group delay (Optimized Aoshima's Time Stretched Pulse) to measure a room's frequency response. Having obtained the impulse response of the ...
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Help with deconvolving photon reads distributed across neighboring pixels

I'm building a radiation detector that collects photons in CCD pixels and we can relate the energy of the photon from the intensity of the pixel. To test the detector, I took the following spectrum of ...
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1answer
623 views

1D convolution and deconvolution using FFT

The task: there is some original signal, and there is some response function. I need to convolve them using FFT and then do deconvolution to restore original signal. The task graphical illustration ( ...
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142 views

Problems with IFFT not being symmetrical

I have two signals, a measurement and a reference which I have performed an FFT on. They have both been windowed with a Hanning window, and now I would like to deconvolve these to get the impulse ...
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159 views

Finding the Width of a Point Spread Function (PSF)

I have a binary image that has been convolved with the following PSF: $$\mathrm{PSF}(x,y)=\cosh^{-2}\left(\frac{\sqrt{x^2+y^2}}{w}\right)$$ where $w$ is unknown. The image binary image generally ...
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4answers
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Estimate Filter Coefficients from the Result of Linear Convolution with a Known Signal

If I have samples of input say x(1:500) and it passes through FIR filter with 9 taps and some unknown coefficients. The output y(1:508) is also known. The aim is to estimate the filter response in ...
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286 views

Invertibility of Room Impulse Response: Reproducing Research Paper

I have been trying to reproduce this paper¹. Few things which are unclear to me. The paper talks about finding whether a given Room Impulse Response(RIR) is invertible or not based on Nyquist plot. ...
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522 views

How to Use the DFT (FFT) to Solve a Least Squares Regularization Problem (Inverse Problem)?

Let $X$ and $K$ be an image and a Point Spread Function (PSF), respectively. The blur image $B$ is obtained as follows $$B = X * K$$ I want to solve the following general regularization problem $$...
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176 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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2answers
226 views

Deconvolving known impulse response from a sampled noisy signal

I am interested in measuring a signal with significant energy content up to 1-2 kHz. However, I am only able to sample the signal after it has passed through a first-order lowpass filter of known ...
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135 views

Question related to Deconvolution and Fourier Transform

Currently I am completely new to Signal Processing and I am about to kick off a project related to the system identification. The general idea is given a pair of sent and received signals, I have to ...
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1answer
1k views

How to properly match bit growth of a FIR filter with a reference value

I am trying to implement a chain of CIC/FIR filters on an ZYNQ FPGA. Using the Xilinx FIR compiler works fine so far but I am unable to properly get all the math. At the moment I have 2 chains of ...