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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21 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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45 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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11 views

How can single low-resolution have multiple high-resolution versions?

I'm trying to prove the fact that the super-resolution problem is ill-posed problem. As having a single low-resolution image we can generate multiple high-resolution images. which also known by ...
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1answer
62 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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9 views

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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2answers
62 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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3answers
345 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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1answer
31 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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17 views

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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1answer
78 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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56 views

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
20 views

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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2answers
89 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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5answers
520 views

Multi-channel audio upsampling interpolation

I have a four-channel audio signal from a microphone tetrahedral array. I wish to upsample it from 48 kHz to 240 kHz. Is there a preferred interpolation method for audio? Does cubic ...
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24 views

delayed result in sinc upsampled signal

I have implemented an infinite kernel sinc interpolation. For some signals I notice an artifact, visible at the right end of the plot. I am wondering: is it a bug in my code or a phenomenon usual for ...
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2answers
101 views

What Does 'Zero Order Hold' and 'First Order Hold' Mean?

While studying the Image Magnification in spatial domain, I have come across this definition of Image Magnification by Replication: Replication is a zero order hold where each pixel along a scan ...
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2answers
58 views

Alignment of 2 Set of Samples from Different Sensors

If we measure the heart rate of a subject with two different devices, which have big different sampling rates then how we can compare their outcomes. For instance, one of the devices has the sampling ...
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95 views

signal interpolation (upsampling) by factor 2

The task is to interpolate the signal by increasing the sampling rate by factor 2. Matlab has a dsp.FIRHalfbandInterpolator function. Let's try using it. ...
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1answer
137 views

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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38 views

Zero padding frequency domain data for improving time domain resolution before inverse FFT

I am working in MATLAB with measured data from a VNA. The bandwidth is 1 GHz from 5-6 GHz with 801 samples in the frequency domain. Everywhere I have read that I need to split the data into 2 parts at ...
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1answer
35 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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1answer
93 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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2answers
114 views

Frequency response of numerical differentiation by polynomial interpolation / finite difference

One can use polynomial interpolation (or finite difference) to do numerical differentiation. However, there seems to be a surprising lack of interest in obtaining frequency response of this numerical ...
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1answer
68 views

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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2answers
87 views

Interpolation of audio for new frames

I am trying to upsample a video by existing frame interpolation techniques. In the process, I realize that I also need to interpolate the audio signal for the new frames so that the audio signal is in ...
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1answer
102 views

Upsampling signal using convolution-based interpolation filters

I am currently reading this paper which discusses several image interpolation methods, such as nearest neighbor and linear interpolation, using convolution filters. I first want to do this in 1D with ...
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1answer
53 views

Having Glitches trying to use a Sinc Function Interpolation on a Signal, by chunks of 1024 samples

I am trying to interpolate a signal using a third party lib that performs Sinc Function Interpolation on a signal. It works well if I input all the samples at once but introduce phase distortion if I ...
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1answer
88 views

Why is interpolation a time varying system

I was reading about interpolation (Interpolation and Decimation of Digital Signals - A tutorial Review, Ronald E. Crochiere) and found that Interpolation filter is a time varying system. Can someone ...
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1answer
41 views

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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1answer
294 views

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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1answer
230 views

Low pass filtering of an upsampled(zero inserted) signal

I have been working on interpolation in python from quite some time. The input signal is a sinusoid signal sampled at 933KHz. I am upsampling the signal by a factor of 5 and later using an FIR ...
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1answer
323 views

Implementation of a Variable Fractional Delay with Lagrange Interpolation using Farrow Structure

I am writing a C++ simulation software working in time domain. I generate regularly sampled data, and need them to be delayed, in "real-time", by a variable fractional delay. This is a pretty common ...
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1answer
32 views

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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77 views

Resampling or interpolating non-uniform 2D measurements

I am not sure what I should call what I am looking for, but I have some measurements that have 2 independent variables and I would like to get an interpolated value at a specified x,y coordinate. My ...
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0answers
103 views

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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1answer
51 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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2answers
74 views

Image Interpolation Using the Yule Walker Equations

I have been studying about the Yule-Walker equations for prediction of a time series data from knowledge of past values of the series. Is there any way I can use the same in an image to exploit the ...
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1answer
101 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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2answers
111 views

Radix2 fft - zero padding output size

With zeros padding the FFT radix2 has different input size than output. How to deal with that? I see two solutions but not sure which one is better/appropriate. Maybe you know some other and better ...
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1answer
180 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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1answer
225 views

Interpolated FIR filter group delay

I'm trying to design a digital low pass filter with a narrow transition band. My sampling rate is 25 kHz, the cut off frequency is 60 Hz & the transition band width is 4 Hz. I'm looking for about ...
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1answer
81 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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2answers
2k views

How does nearest neighbour, bilinear and cubic interpolation work in images?

More math is appreciated for each of the methods and references are appreciated. I have tried understanding from Wiki and matlab link but don't understand how the translation matrix is being used ...
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1answer
311 views

Signal Resampling by a non integer factor with convolution

to start I am a newbie in signal processing, I just started a month ago so please be as detailed as possible. From what I understood to resample a signal by a non integer factor you can do an ...
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3answers
127 views

Detect the beginning of an increasing signal

After denoising and cleaning, I get amplitude signals like this (y-axis: dB): On bottom left of each of these 3 graphs, you can see a noise floor (nearly "horizontal line"). This noise floor ...
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1answer
164 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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1answer
370 views

Sample Rate Conversion between 32K and 44.1K

I would like to know what are possible/typical efficient implementations (preferably in fixed-point DSP) of synchronous sample rate conversion between 32KHz and 44.1KHz (audio applications). Also, I'd ...
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2answers
301 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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1answer
293 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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1answer
51 views

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 ...