Questions tagged [interpolation]

Interpolation is a method of constructing new data points within the range of a discrete set of known data points.

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42 views

Stolt interpolation and ifft in range migration algorithm

I am using range migration algorithm for focusing stripmap synthetic aperture radar data. I have successfully tested my algorithm using the following steps after range compression (similar to this ...
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shannon interpolation in image processing

I tried to implement Shannon interpolation on a 2D array. First, implemented it on a 1D signal, just for sanity-check: ...
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115 views

Can compressed sensing be used instead of intepolation for missing values?

Consider a signal that is sparse in frequency, but it measured in the time domain, for example (in matlab): ...
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Interpolating the spectrum at L levels

I am new to signal processing but having some experience in implementing Fast-Multipole-Method (FMM - single level) and now looking forward to understand the interpolation of samples from fine $\...
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4answers
73 views

Sequence expansion by zeros and interpolation - does it insert additional frequencies?

I am struggling with understanding the consequences of oversampling on the frequency spectrum of the signal. If I understand correctly, with an oversampling rate of 8X we insert 7 new values for each ...
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How to allign audio signals after DTW?

Hello I am not a domain expert in signal processing but I need to align two audio signals. I have seen the following page https://librosa.github.io/librosa_gallery/auto_examples/plot_music_sync I ...
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Composition of interpolation and decimation matrices

I understand that interpolation is a linear transformation of a signal vector that combines interleaving the elements of the input vector with zeros followed by a filtering operation to remove any ...
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B-Spline for computing image warps

I have 2 images A and B, and a set of point correspondences S which indicate the position of the same point in the 2 images. The goal is to fit a grid on the image A and warp the grid such that the ...
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Polynomial Response

I was referring to the below paper from @robert bristow-johnson https://www.researchgate.net/publication/266675823_Performance_of_Low-...
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U-nets : how exaclty is upsampling performed

In U-nets I would like a more straight-forward/detailed explanation in how the upsampling part ("right part of the U") is performed. I read that it can be done by "transposed convolution layers" aka....
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Transposed convolutional layer

Can someone define the weights in a transposed conv2D kernel used to perform interpolation (NN or bilinear or whatever)? The idea is to get "convinced" that one can perform upsampling (interpolation) ...
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Sampling $x(t)=\cos(4\pi t)+\cos(2\pi t)$

Imagine that we sample the signal $x(t)=\cos(4\pi t)+\cos(2\pi t)$ with a certain sample frequency $f_s$ and we obtain $x[n]$. Now, by ideal interpolation, we get $y(t)$ from $x[n]$. How can we know ...
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How to improve interpolation for chroma upsampling (4:2:0 to 4:4:4)?

I am trying to perform the best possible interpolation in order to perform proper chroma upsampling from 4:2:0 YCbCr to 4:4:4 YCbCr. I have implemented the improved interpolation proposed at this ...
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Lagrange Vs Sinc interpolation

I was wondering what is the practical difference between Lagrange Interpolation using Farrow Structure and Sinc Interpolation? Both require pre-computation of time offset coefficients using a lookup ...
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control points and concentration of sampled points in a parametric curve

Can anybody explain to me what the following sentence means? "In cubic Hermite, as any parametric curve, the control points density reflect in the concentration of sampled points in more dense parts ...
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23 views

resample interpolation decimation filters algorithm

I'm creating a program in order to perform Resample, Interpolation and Decimation Frequency. ...
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45 views

Second (numerical) derivative as estimation of oscillation

I have a discrete signal (vector of numbers) coming from a measurement. This signal has been filtered so that the noise has been removed. Now I am looking for an analytical representation of the ...
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84 views

Why do we need to increase sampling frequency at the transmitter?

I've thinking about this for some time now and I was wondering why do we need to increase smapling rate in the transmitter? I will explain a bit more. From the point of view of a software-defined ...
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Deriving the Langrangian interpolation polynomials in Cook-Toom convolutions

I'm working through Blahut's 'Fast Algorithms for Signal Processing'. Trying to develop an intuition for the Cook-Toom algorithm for convolutions as used by Lavin and Gray in their Winograd paper for ...
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Drawbacks of upsampling using polynomial interpolation

I've come across an upsampler that uses polynomial interpolation and no filter. What are the drawbacks to this? I looks more efficient than filtering.
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Different images between MATLAB and ImageMagick

I'm using ImageMagick 7.0.8-64 Q16 for Windows and MATLAB R2019. I'm doing the same operation (resizing with bicubic interpolation method) in both programs. ImageMagick code: ...
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O-MOMS3 interpolating function?

I've been reading the following paper on a B-spline based interpolation technique: https://pdfs.semanticscholar.org/fd55/61d561fa2bf1124959cba0d4abfd5d81a784.pdf The paper derives the so-called O-...
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1answer
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Why zero padding the 2-d DFT interpolates images in spatial domain?

I was applying different image interpolation techniques and I came know to about interpolation in frequency domain. In this technique we first take 2d DFT of an image, pad it with zeros and take the ...
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Purely theoretical question about idelal filters and infinite oscillations

I am asking perhaps a naive question, but still, it would be nice to have this formally stated one time: in theory, if we could do it (of course, we cannot, but imagine we could), if we could ...
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Interpolation FIR filter Remez design criteria

I want to upsample an audio signal by a factor of 8. The technique I was going to use was to upsample by zero stuffing and then interopolate using a low pass anti-aliasing FIR filter designed using ...
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Why does my sinusoid look “AM” in shape?

My code is : Fs=200e6; Ts=1/Fs; NFFT=2^14; Runtime=(NFFT-1)*Ts; t=0:Ts:Runtime; f_in=90*1e6; y_in=sin(2*pi *f_in *t); plot(t,y_in) ylim([-1.5 1.5]) Then why does ...
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Linear interpolation formula

In the following lecture: http://www.ece.mcmaster.ca/~xwu/interp_1.pdf the model (formula) for solving the linear interpolation problem (1D) given at p.5 is: $f(x)= a_1x_1 + a_0x_0$ solve for $a1,...
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Sinc interpolation in spatial domain

I have tried to perform sinc interpolation (in 1D) with the following Matlab code: ...
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Estimation / Reconstruction of an Image from Its Missing Data 2D DFT

Given the 2D DFT of an image i.e. a NxM matrix of complex numbers, with some missing lines (or even partial lines), considering we have zeros in the missing positions. Any suggestions for an ...
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70 views

Why would FFT interpolation using zero-padding undershoot the true frequency of a single tone sinusoid?

Why would FFT interpolation by zero-padding or using the Chirp Z-Transform produce a maximum at a bin that corresponds to a frequency less than the input frequency of a single tone sinusoid? I am ...
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The annihilating filter-based low-rank Hankel matrix approach (ALOHA) for conpressed sensing

Can someone give an intuition about the annihilating filter-based low-rank Hankel matrix approach (ALOHA) for compressed sensing approaches ? It is for an MRI problem of k-space interpolation, i.e., "...
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80 views

Design of efficient digital interpolation filter

I came across this paper entitled "Design of Efficient Digital Interpolation Filters and Sigma-Delta Modulator for Audio DAC" where the author oversamples an input frequency, fsig = 1kHz with ratio L =...
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Multi-stage interpolation [closed]

So I've read here Multi-Stage digital FIR filter vs Single stage FIR filter. Which is better? if you want to interpolate by a great number, it's always better to do so in multi-stage interpolations so ...
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How to draw a smooth spectrum from a discrete array of measurements at selected frequencies?

I have a AS7265x triad spectroscopy sensor from SparkFun (link) which gives me measurements at 18 individual light wavelengths between 410nm and 940nm. The datasheet says that the FWHM of each sensor ...
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258 views

Resampling and removing high frequency noise?

I am currently working on a simple sampler that will allow me to load in a wav file and use my MIDI keyboard to play the loaded wav sample at the frequency according to the note played. Now I need ...
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Given local responses by a bank of equally spaced (log-)Gabor filters, how can we estimate the response of an intermediate-scale filter?

Consider a grayscale image convolved with a bank of 2D wavelet quadrature pairs – in my case, log-Gabor filters. I have eight filters. For simplicity, let's say they are all vertically oriented, and ...
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166 views

Optimal trade-off between oversampling and filter length

For some sampling-frequency-preserving operations on Nyquist–Shannon sampled signals, such as: a shift a.k.a. translation, and differentiation by applying a derivative filter a.k.a. gradient filter, ...
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29 views

Method to rescale signals to mean length

I have a set of signals of varying lengths. I have provided an example of the same below - Their lengths vary between 186 to 202, with a mean length of 197. I am looking to rescale them to the mean ...
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1answer
146 views

Side Lobes in the Magnitude Response of a Low Pass FIR Filter

I have the impulse response (from the filter coefficients) of an FIR filter obtained from MATLAB's "interp" function using the command: [y, b] = interp(x, 5); % where b contains the interpolation ...
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How can single low-resolution have multiple high-resolution versions?

I'm trying to prove the fact that the super-resolution problem is an ill-posed problem. Having a single low-resolution image, we can generate multiple high-resolution images. Which also known by ...
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1answer
290 views

Frequency Domain Interpolation: Convolution with Sinc Function

I am reading a paper, and I came across the following definition of sinc interpolation. Warning. I don't have a strong background in signal processing. Also, I have no clue what that bar on $\bar{F}$ ...
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Sparse to Dense Flow

I'm trying to upgrade a flow from sparse to dense and have been recommended this for my use-case https://uk.mathworks.com/matlabcentral/fileexchange/25634-smoothn . When I run the interpolation, ...
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153 views

Sinc interpolation of pure sine wave sampled just at Nyquist frequency

Following this question: Shannon-Nyquist theorem reconstruct 1Hz sine wave from 2 samples could you explain the algorithm to apply for sinc interpolation to avoid the "sawtooth" effect due to linear ...
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415 views

Absolute convergence of periodic sinc interpolation

An $N$-periodic complex discrete-time sequence $[x_0, \dots, x_{N-1}]$ can be resampled to an $M$-periodic sequence $[y_0, \dots, y_{M-1}]$ with $M>N$, using sinc interpolation: $$\begin{align}y_m ...
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283 views

Why does downsampling stretch a signals frequency response and upsampling shrink and create images of a signals frequency response?

I am learning some basic DSP and I have a pretty good intuition as to why sampling creates spectral images of the frequency response at intervals of the sampling frequency (convolution with pulse ...
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How to calculate splines of different order under MATLAB?

I am trying to compare spline interpolation of different order to show that Cubic is working better. Is there any toolbox or so to spline interpolate points between knots?
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Omega-K algorithm implementation for synthetic aperture radar

I have been trying to develop Omega-k algorithm for SAR image formation. I am using the equations from chapter 8 in digital processing of Synthetic Aperture Radar data by Cumming and Wong. The steps I ...
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How to get an interpolation weight from a mathematical definition

It was recently explained to me that a "Nearest neighbor" kernel for 1D interpolation can be implemented like this using NumPy ...
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1answer
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Estimate gap between two adjacent images

I have two images of a panoramic view but there is a small gap (<24 pixels) in the horizontal dimension between them. I would like to do interpolation/inpainting to fill the gap, but the exact size ...
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103 views

Interpolation and harmonics

A real valued causal sequence $x1[n]$ exists with length of the sequence being $N$. Valid indices of x conform to $0 \le n \le N-1 $ The DFT of x[n] is: $$ X1[k] = \sum_{n=0}^{N-1} x1[n].e^{-j.2.\...

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