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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Is there a relatively easy way to detect likely real-time peaks in discrete-time data?

Let's say I have a set of data over time, t: [0, 4, 6, 7, 7, 6, 4, 0] It seems likely that this data would peak at ...
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268 views

Ideal Reconstruction of Upsampled Signal

Problem: The signal $cos(2\pi14100t)$ is sampled at $F_s = 400 Hz$. It is then upsampled with a factor 3 and then reconstructed ideally with a new frequency $F = 500 Hz$. I now want to find the new ...
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419 views

Calculate interbeat intervals

I'm currently reading a paper and I can't seem to make sense of a certain part. A link to the paper: removed The part I don't quite get is on page 286 (after the part where they explain their filters)...
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Interpolated FIR filter (from Oppenheim and Schafer's Discrete-Time Signal Processing, 3rd ed)

[from Discrete-time Signal Processing by Oppenheim and Schafer, 3rd ed., p.196] Two questions: In this context, the filter with system function represented by Eq. (103) is called an interpolated FIR ...
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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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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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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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2k 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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864 views

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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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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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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Extrapolate a 2D array using Fourier Transform

I need to extrapolate a given 2D array to a larger domain, keeping the spatial frequency. This is the original field: (the data file in numpy npz format and a Jupyter notebook to plot it can be found ...
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319 views

What's wrong with this Whittaker-Shannon-Kotel’nikov interpolation implementation?

I tried to implement Whittaker-Shannon-Kotel’nikov interpolation formula but I get unexpected results: the reconstructed signal lags with respect to the original. I know that I can not expect a ...
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568 views

difficulties implementing windowed sinc interpolation (C++)

I'm currently trying to implement a windowed sinc interpolation. I've already written some code for that, but it only seems to work for cases where phaseInc <= 1.0 (phaseInc = outSampleRate / ...
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Isosurfaces from three dimensional column data: methods

I have just been asked the following question, and I somehow felt short of smart answers. You are given a series of $N$ triplets of values ($P_1$, $P_2$, $P_3$), pertaining to physical measurements. ...
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Interpolation of missing audio signal in a video sequence

Suppose there is a video sequence and there are some frames for which the audio data is missing. I want to interpolate the missing audio data on the basis of the correlation of the audio signal with ...
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Bilinear interpolation implemented by convolution

I read the paper Deep Feature Flow for Video Recognition https://arxiv.org/abs/1611.07715. In Sec.3, the author implements bilinear interpolation like this: $$f_i^c(p)=\sum\limits_{q}G(q,p+\delta p)...
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Question on Levinson's proposed discrete form of Wiener filter

The whole foundation of Levinson's discrete version of Wiener filter is based on the assumption of stationarity of a time series, and aims to predict a value based on the past observed values. Now, if ...
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82 views

What is the right way to interpolate a 2D grid?

Let's say I have a 2D grid of temperature measurements in some area and I want to estimate the temperature at some point between the samples. Or at every point, which would basically amount to ...
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153 views

interpolate 1D signal depending on 3D parameter space

I have a 1D array of data d(x,p) in which a number of "bumps" or "dips" appear and/or move in the spacial dimension x, depending ...
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1answer
103 views

Online interpolation of temporal signal

I have a signal generated from an accelerometer, what I want to do is to receive the incoming signal and check if it is in a certain interval, if it is then I can apply interpolation on it(but ...
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443 views

Relationship between interpolation accuracy, impulse response and frequency response

Global interpolation or sinc interpolation is an ideal filter since its frequency response is a rect function. The impulse response of this filter is the sinc function (same as the coefficients of the ...
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472 views

Interpolation and decimation

I have a sinusoid in continuous time, with a frequency of 18kHz, it is sampled ideally with a continuous to discrete convertor, with a frequency of 27kHz. After that, we change the sampling speed in ...
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668 views

How to smooth (or interpolate) phase of FFT and reduce data points

I am writing some code for audio analysis, and have currently got two signals with FFT performed on them. I get the phase of my complex array by using: ...
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Most natural interpolation to simulate increasing distance?

Background: I'm generating multiple datasets with varying scales of resolution to simulate taking pictures from varying distances and then comparing image classification performances. For example ...
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543 views

frequency translation or pitch shifting through linear interpolation in frequency domain

I want to perform pitch shifting with the method described in NEW PHASE-VOCODER TECHNIQUES FOR PITCH-SHIFTING, HARMONIZING AND OTHER EXOTIC EFFECTS. Basically, it involves: Locate the spectral peaks ...
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399 views

Resampling scattered data with MATLAB's $\tt interp$ and $\tt resample$

I am recording acceleration data with an MPU6050 connected to a Arduino1 and stored on a SD. Here you can find the code. I need to calculate the FFT of an acceleration signal that was not sampled ...
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416 views

DTFT reconstruction

I have a sampled DTFT. If we assume that there isn't aliasing in time domain, what is the best way to reconstruct DTFT from its equidistant samples? I though about Dirichlet interpolation. Do you know ...
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169 views

Accurate Image Resizing

I need to resize an image using bilinear interpolation and create an image pyramid. I will detect corners at the different levels of the pyramid and scale the pixel co-ordinates so that they are ...
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234 views

Inter-point interpolation using FIR filter

Suppose I have discrete noisy signal $X = (0.096, -0.0632, 0.351, 0.531, 0.360, 0.006, -0.320)$ sampled at discrete time points $T = (1, 2, 3, 4, 5, 6, 7)$. Filtering (zero-padded) $X$ with ...
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3answers
162 views

FIR estimator for IIR system

Suppose that we have a dynamical system of which the impulse responses are infinite (IIR). Now I found methods on papers (http://dx.doi.org/10.1109/9.839942) estimating states or outputs of such a ...
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What is the difference between Linear Interpolation factor and Sampling rate conversion factor?

I have come across sampling rate conversion factor, which is given by: S_factor = F_new/F_old If F_new > F_old, then s_factor > 1 ...
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Modeling multipath distortion and shifting by fractions of a sample

I am working on modelling some FM transmitted signals, and I'm trying to figure out how to model the effects of multipath channels. The most obvious method is to delay the signal by some integral ...
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PSNR of two images of different size in matlab

I performed bicubic interpolation on a 256*256 image(img) dest = interp2(img,'bicubic') and i got a 511 * 511 image.I want to compute PSNR of a 512 * 512 image(...
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Frequency response of discrete time system involving interpolation and resampling

I am working on a problem towards calculating frequency response of discrete time system(does interpolation followed by resampling) which looks like: x(n) is fed to linear interpolator(h(t) = ...
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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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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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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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73 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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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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191 views

How to correctly use sinc interpolation in Matlab?

What is the right way to use sinc interpolation for a given discrete signal $x[n]$? Following is the sinc interpolation formula: $$x(t) = \sum_{n=-\infty}^\infty x[n] \mathrm{sinc}\left(\frac{t-nT}{T}\...
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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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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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Natural cubic spline interpolation versus cubic BSpline interpolation?

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