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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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 ...
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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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132 views

A cubic interpolation function: folkloric copypasta or clever trade-off?

I've been reading on interpolation methods recently and I have come across an implementation of cubic interpolation that is leaving my head scratching. Every other variant and example of cubic ...
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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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Natural cubic spline interpolation versus cubic BSpline interpolation?

An answer here seems to shows the algorithm Mathematica uses to compute: ...
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112 views

Efficient double upsampling of a pure real tone

Has anyone seen this trick before? Let's say I'm working with a real pure tone signal that's dangerously close to Nyquist. So, I want to upsample it by a factor of two to move it near the four ...
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106 views

Why is my time domain interpolation via zero-padding in frequency domain wrong?

Since the process can be applied in either domain to increase the sampling rate in the other domain, I am trying to apply zero-padding in frequency space to recover a 'cleaner' interpolated signal in ...
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Frequency response and sampling theorem for triangular function

The triangular function is defined as follows: $h_l(x) = \begin{cases}1-|x|,&|x|<1;\\0&\text{otherwise}.\end{cases}$ According to ccrma.stanford.edu: "If the output of the interpolator ...
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84 views

Find continuous signal given a condition on its samples

Let $x(t)$ be band-limited with $B = \omega_m$. Sampling gives us $$x(nT_s) = \begin{cases} 1, & n = 0 \\ 0, & n \not = 0 \end{cases}$$ And $\omega_s = 2\omega_m = \frac{2\pi}{T_s}$. Find ...
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Why the plots of spline and cubic interpolation are exactly same? [closed]

I am trying to watch difference between cubic interpolation and spline interpolation using matlab plot but i am getting same plots in both cases using interp1 ...
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1answer
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How to transform a signal to go through specific points?

I have a 1d signal obtained using a Fourier based resample method (TDIFDZP) for which the resampled points don't necessarily go through the original samples. I want to transform the upsampled signal ...
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171 views

Using a low pass filter to interpolate signal

In my DSP university textbook, the interpolation process is described as follows: In order to represent a baseband signal $x[k]$ at an increased sampling rate with the same shapes of its time-...
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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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57 views

Sinc Interpolation Artifacts

I have written a program that uses sinc interpolation to resample some data. The general algorithm is a that I compute the previous N values and the next N values to get a new sample at a non-integer ...
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54 views

Determine impulse resonse of First Order Hold (FOH)

Question, how can I determine the impulse response function of a first order hold? On Wikipedia it is simply stated as: $$ h_{\mathrm{FOH}}(t)\,= \frac{1}{h} \mathrm{tri} \left(\frac{t}{h} \right) =...
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obtain envelope of spectrum

To extract a 2001-sampled envelope of magnitude of the spectrum of a signal, I have divided the frequency axis into 2001 intervals. In each interval, I find the 3 largest spectrum magnitude values ...
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what are some possible reasons of having duplicates in sensor signal? resulting in stair-step signal?

I am using an cellphone application to record cellphone gyroscope signal. I put the sampling rate to "fastest" which means the highest sampling rate the cellphone is able to do. What is strange is ...
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42 views

Reconstruction using sinc

The signal that I produce above. What is the reason for it to slide to the right? In oversampling at Nyquist rate can I make like below picture ? do you think the signal i produced at nyquist rate is ...
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Types of interpolation used for reconstruction in DSP?

What are the different types of interpolation used in DSP for reconstruction of analog signal from discrete/digital signal I am able to somehow learn two types of interpolation 1st is "zero order ...
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1answer
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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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207 views

Reconstructing/interpolating small regions of a bandlimited signal by taking the fewest possible samples

I have a signal which is bandlimited and can be sampled at arbitrary continuous positions. The value at any position is given by an expensive computation. I need to do some further computation on ...
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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
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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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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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256 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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74 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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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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71 views

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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281 views

Effect of Resizing (Up Scaling) an Image on the Ability to Detect / Recognize Objects

I work in a research lab and am currently setting up a system to image objects approximately 30 microns in diameter with a 250x USB microscope, then use image subtraction to isolate the objects as ...
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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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26 views

resample interpolation decimation filters algorithm

I'm creating a program in order to perform Resample, Interpolation and Decimation Frequency. ...
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46 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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166 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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1answer
71 views

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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183 views

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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447 views

Sinc interpolation in spatial domain

I have tried to perform sinc interpolation (in 1D) with the following Matlab code: ...
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1answer
65 views

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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