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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Sinc interpolation formula for signal reconstruction in frequency domain from bipolar samples

As per the title, I was wondering if there was a $\operatorname{sinc}$ based interoplation formula for reconstructing a signal in the frequency domain which has been sampled with respect the bipolar ...
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457 views

How to subsample shift with sinc interpolation?

Does anybody know of a way to shift data by a fraction of a sample by using sinc interpolation? For example, shift an image to the right by 0.1 pixels. I'm struggling to find a formula or reference ...
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Phase noise estimation and compensation schemes

Brief background There is a known problem that high order modulation schemes suffers from phase noise of reference generator. It's very important issue for e.g. line-of-sight (LOS) modems exploiting ...
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621 views

Interpolating on the borders of differently-resolved images

I'm creating a three-dimensional model of the earth based on SRTM height data. The data set is pretty huge, so only a small fraction of the data is available at any given time. The height data is ...
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Symbol timing recovery: Polyphase vs piecewise linear interpolation

A symbol timing recovery scheme shown below has been successfully implemented in C++. Different TEDs (Mueller & Mueller, Early-Late, Maximum Likelihood, Gardner, Zero-Crossing, etc) are included ...
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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 ...
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38 views

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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173 views

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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Exploiting coefficients symmetry of a FIR interpolation filter in a polyphase implementation

I'm trying to figure out whether there is a way to exploit a symmetry of a FIR interpolation filter in a polyphase implementation. I know for a fact that we can exploit the symmetry in a normal FIR ...
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356 views

Software based synchronizing of multiple data streams/sensors with slightly differing sampling rates

Situation: I try to synchronize the data streams of multiple sensors (ADXL372) of the same type but with different data output rates. The data sheet states all sensors should have the same sampling ...
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685 views

How do I interpolate between bins on an FFT in python?

I have four frequency peaks, which I have after applying FFT. Now I want to know precise values of these frequency peaks. there are different interpolation methods. How can I use this method of ...
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141 views

Upsampling Methods for Computed-Tomography

I have two sets of data of given Field of view, one of them only covers a subset of the FOV of the other. I therefore want to upsample the one with the larger FOV to combine it with the other one. So ...
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47 views

Software implementation of Gardner Loop

My objective is to create a Gardner loop to remove the timing offset present in my signal. To achieve best timing SNR, I downsample my signal to 2 samples per symbol. It is depicted below: where blue ...
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Eliminating drift generated from double integration of acceleration signal using Envelope Method

I'm trying to remove the drift generated upon the double integration of a noisy acceleration signal. But this question discusses only removing the drift upon single integration to generate velocity ...
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1answer
34 views

Direct and Transpose Polyphase Multirate Processing

Polyphase implementations of upsampling/ interpolation and downsampling/ decimation, after having invoked the Noble identities, are presented as follows (taken from Proakis): (Three-Channel Polyphase ...
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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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54 views

Impact of Interpolation Types in Image Filtering (Laplacian Pyramids)

I am trying to construct Laplacian pyramids with different interpolation schemes such as bilinear, nearest neighbor, cubic and spline to observe the effect of interpolation types. I wrote a code in ...
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Design of a Butterworth lowpass filter in MATLAB

I'm using the Signal Processing Toolbox in MATLAB to design a Butterworth low-pass filter. I'm told that my filter has been giving some unexpected results. In particular, when the values from this ...
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103 views

Regressing/interpolating between quasi-periodic sinusoids

This is a cross-post (on recommendation) from CV. My problem is very simple. I currently intend on using Kriging (Gaussian process regression) to perform regression between the trajectories marked ...
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135 views

How to shift with spline interpolation?

I have a sampled pulse shape: $ h = [1, 0.5]$ and I do not know what is its real underlying continuous-time pulse. I want to compute the samples of $h(t-\Delta t)$. If I write the continuous pulse ...
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How to proceed with this convolution problem?

If $$\alpha_k = \sum_l a_l \ \ g((k-l)T-l\Delta T)$$ $$s_k = \sum_l \alpha_l \ \ q((k-l)T+k\Delta T)$$ where $a_l \in \pm1$ and $g(t) = \frac {\sin(\pi t/T)}{\pi t/T}$ and $q(t) = \frac {\sin(\pi t/(...
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Image super resolution algorithm in Matlab

I'm trying to implement a simple Image super resolution algorithm (DWT-Based Resolution Enhancement ) in the following paper http://www.ripublication.com/aeee/52_pp%20%20%20405-412.pdf I tried to ...
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MATLAB implementation Spline Fitting

Let $s(t)$ be a signal that can be approximated by a uniform spline function of order $K$ (say $K=2$): $$s(t)\approx\sum_{n\in \mathbb{Z}}c_n\beta_+^{(K)}(t-n) $$ Suppose that we know the ...
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Interpolation methods for radar and acoustic imaging and potential pitfalls

A) What are the most common methods used to remap data for current generation imaging radars and acoustic sensors? B) What are some of the pitfalls in these methods? For example, in the past, at ...
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145 views

Extend linear spline interpolation to cubic spline interpolation - how calculate derivative

I'm trying implement in Java cubic spline interpolation based on this document: http://www.geos.ed.ac.uk/~yliu23/docs/lect_spline.pdf At first they show how to do linear spline and it's pretty easy. ...
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interpolation of filter coefficients

i've read that it is possible to interpolate between two sets of filter coefficients (if they are close of course), but how to interpolate between two sets of coefficients which are of different ...
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493 views

Implementation of halfband pass filter

I need to interpolate a complex valued bandlimited periodic function using local interpolation. I can have the signal sampled at any frequency I want over at equispace intervals. I am aware that for ...
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25 views

Role of oversampling within resampling / pitch modification

I'm working on a pitch modification plugin involving resampling, and want the quality to be as high as possible. I currently use windowed sinc interpolation and lowpass filter where required. I ...
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37 views

A basic question about bilinear interpolation

I have a basic question about "Bilinear Interpolation". How to derive the bilinear interpolation formula of 4 pixels arranged as follows: And if the bilinear interpolation is applied to ...
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1answer
37 views

Difficulty absorbing Idea of interpolation?

I am trying to develop my understand of interpolation and signal reconstruction and uptill now i have understood that there are 3 commonly studied types of interpolation 1)Zero order hold ...
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1answer
39 views

piecewise-quadratic vs piecewise-cubic vs higher order polynomial interpolation?

There is a question available on DSP SE that mentions types of interpolation used for signal reconstruction but there isn't any mention about the difference between piecewise-quadratic,piecewise-cubic ...
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1answer
86 views

Zero order hold interpolation and Nearest-neighbor interpolation?

Is there any difference between Zero order hold interpolation and Nearest-neighbor interpolation I want to perform zero order hold interpolation in MATLAB,but there isn't any information about zero ...
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1answer
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Streaming windowed sinc interpolation/resampling: trying to understand a Rust implementation

I'm working on a fork of the Rust dasp library, which is intended to be a DSP toolkit that abstracts over samples/frames/signals, and contains a number of functions ...
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Efficient Method for Interpolating between bins in FFTW

I'm working on some oscillator classes right now and perform FFT around 100 times per second. The issue I'm running into is interpolating between the bins so there is not a noticeable change from each ...
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Bilinear Interpolation Algorithm for up-sampling 2D images

In keras it is possible to use UpSampling2D layer to up-sample an image. You can use Bilinear Interpolation. Given an image ${h\times w}$ it is possible to increase its size in ${h*k\times w*l}$, ...
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After upscaling a signal what noise metric to use for noise qualification

If I have a 2d signal (like image) and interpolate (linear) it to get an upsampled signal, how can I qualify the noise, with which metric? STD changes between the signal and its'upsampled counterpart ...
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standard deviation of two constant noised signals related through interpolation

Let us say say we have a noised constant signal and want to evaluate the standard deviation (std) of the noise. We calculate the std of the said noised signal and call it $\sigma_1$. Now we process ...
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102 views

minimum oversampling factor for D/A converter

Consider a D/A converter for audio signals consisiting of a zero-order-hold interpolator followed by a continuous-time lowpass filter with positive passband between 0 and 20KHz and stopband starting ...
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Interpolationg phase and magnitudes, Transformation function

I am trying to filter signal x(n), n = 150. I made a filter with few frequency points on the x axis , [-11., -9., -3., -2., -1., 1., 2., 3., 9., 11.]) ...
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Wasn't Wikipedia errata on DFT/Trigonometric interpolation polynomial

https://en.wikipedia.org/wiki/Discrete_Fourier_transform "Trigonometric interpolation polynomial" Section. Shouldn't the middle term in the second line be? $$ \cdots + X_{[(N-1)/2]} e^{i\ ( ...
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Zero-padding or Interpolation in 3D FFT

I'm trying to perform a FFT of a 3D regular grid and then compute the bin average (in spherical shell bins) of the Fourier transformed grid. The problem is that the resulted vector is very noisy as I'...
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1answer
563 views

What is the “bilinear interpolation kernel” in personlab paper?

please excuse my ignorance in computer graphics, but what is this bilinear interpolation kernel in the personlab paper page 6 equation (1)? Here it is: $$ h_k(x) = \frac{1}{\pi R^2}\sum_{i=1:N}p_k(...
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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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1answer
264 views

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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1answer
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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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resample interpolation decimation filters algorithm

I'm creating a program in order to perform Resample, Interpolation and Decimation Frequency. ...
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52 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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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 ...