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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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Fractional Frequency Shifting a Discrete Signal in the Frequency Domain

In our current hardware-based signal processing pipeline, we have a time-domain signal $x[n]$ that we want to frequency shift by $f_0$. To do this, we multiply the signal by a complex exponential in ...
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Plotting the Frequency Response of Zero-Order Hold

I'm trying to find the frequency response and the DC gain, then plot the response and find the cutoff frequency from the graph. I start off with the impulse response $$h(t)= 1 ; 0\leqslant t\leqslant ...
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Why is this Python implementation of trigonometric interpolation not working properly?

Consider a signal $u_j, j = 0, 1, \dots, N-1,$ sampled on an evenly-spaced grid of points, $x_j$. Define the discrete Fourier transform of $u_j$ by $$U_k := \frac{1}{\sqrt{N}} \sum_{j=0}^{N-1}u_je^{-(...
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Performing Sample-Rate Conversion on Subchunks of an Audio Signal

I have implemented sample-rate conversion (SRC) from scratch in my hobby music player, and it worked fine. However, originally, the music player loaded entire audio files into memory and performed the ...
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1 vote
2 answers
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Symbol Timing Recovery with Fractional Sample per Second

I'm trying to write symbol timing recovery loop and taking help from "Digital Communications A Discrete-Time Approach" by Miachel Rice. MATLAB communication toolbox has also implemented the ...
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How to implement interpolation by convolution for rotation of an image by an angle which is not a multiple of 90 degrees?

I know that the usual way to perform rotation of an image is to compute the new pixel coordinates by multiplying with a rotation matrix $ \begin{pmatrix}x_{rot} \\ y_{rot} \end{pmatrix} = \begin{...
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Why does upsampling and interpolation by convolution introduce a shift compared to imresize?

For purposes of understanding the process - not for any practical purpose for which I could use imresize - I wanted to show that 2x upsampling followed by convolution with an appropriate kernel (...
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2 answers
55 views

Good interpolation functions for downscaling magnitude spectrums

I'm trying to downscale a 1D FFT (for displaying an audio spectrogram, like this: My question is, assuming that I have, say, a 512 bands spectrum, what would be the most recommended interpolation ...
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1 vote
1 answer
60 views

Resample signal and start from a different point with numpy.interp

I am trying to resample a signal in Python, only by giving the new and the old step. My function works fine until here. But now I want to start the resampled signal at a specific point other than the ...
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3 votes
3 answers
269 views

Interpolation FIR filter output spectrum

I've inherited some FPGA code implementing an interpolation by 2 with a FIR low pass filter. The code came with a cocotb test bench that also models a filter (scipy.signal.lfilter) and then compares ...
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Sinc Based Multi Dimension Signal Resampling on the Fourier Spectrum (DFT)

As a generalization of the following questions: The Proper Way to Do Sinc Downsampling (DFT Downsampling) for Uniformly Sampled Discrete Signals with Finite Number of Samples. The Proper Way to Do ...
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4 votes
1 answer
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Applying 2D Sinc Interpolation for Downsampling in the Fourier Domain (DFT / FFT)

Related to The Proper Way to Do Sinc Downsampling (DFT Downsampling) for Uniformly Sampled Discrete Signals with Finite Number of Samples, how can one apply Sinc downsampling in the DFT / FFT domain ...
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0 answers
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How to find the kernel of the convolution?

I'm trying to solve the following exercise: Image A was doubled by linear interpolation. The magnification was performed in two stages. In the first stage, add about zero pixel to the image between ...
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1 answer
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Applying 2D Sinc Interpolation for Upsampling in the Fourier Domain (DFT / FFT)

Related to The Proper Way to Do Sinc Upsampling (DFT Upsampling) for Uniformly Sampled Discrete Signals with Finite Number of Samples, how can one apply Sinc upsampling in the DFT / FFT domain for a ...
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1 vote
1 answer
67 views

Downsampling an image using sinc interpolation?

I have a discrete image of size $2^N \times 2^N$ which I would like to iteratively downsample to produce a pyramid with image sizes $2^k\times 2^k, \, k=0,\ldots,N$. That is, each subsequent image ...
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1 vote
0 answers
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1D Interpolating subdivision for wavelet lifting schemes

I am looking into wavelet lifting methods first introduced by Swelden, and explained in this paper: Build your own wavelets at home. In this paper (in chapter 2 specifically), they discuss ...
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3 votes
2 answers
121 views

Interpolation by zero padding FFT

I'm currently studying the book Vibration-Based Condition Monitoring (second edition) by Robert Bond Randall. I'm trying to implement in Matlab an algorithm to "increase" the sample rate for ...
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3 answers
93 views

Sinc Interpolation between output samples of FFT

Let's say I'm designing a spectrum analyzer. While doing this I take the FFT of the real time data with the FFT size of 2048. Is there a way to increase the resolution in the frequency domain after ...
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1 vote
1 answer
79 views

Spectral Interpolation vs Linear Interpolation

What is the main edge of using a spectral method (Spectral Intp/Trigonometric Intp) for upsampling or downsampling a signal in comparison to using a linear (Trilinear Intp) method to do the same? I ...
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-1 votes
1 answer
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Change Amplitude Magnitude after Interpolation Algorithm

I try to implement interpolation algorithm. I code this using MATLAB. Firstly, I create a signal and I upsample my signal using zero padding. ...
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1 answer
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Undo finite difference with arbitrary timesteps

I'm wondering if there is a way to undo a finite difference filter with arbitrary timesteps. In the simplest case of a two-sample finite difference of a time-series $x[n]$, \begin{equation} y[n] = x[n]...
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5 votes
1 answer
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The Proper Way to Do Sinc Upsampling (DFT Upsampling) for Uniformly Sampled Discrete Signals with Finite Number of Samples

Given a signal $ \left\{ x [ 0 ], x [ 1 ], ..., x [ N - 1 ] \right\} $ what would be the correct way to upsample it in the frequency domain (Sinc interpolation)? Note: Added as a request by the answer ...
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How to change the samplimg rate with interpolation and decimation?

I have a wav file at a 44.1KHz. I'm trying to change the sampling frequency to 1.26MHz. For that, I need to use interpolation and decimation, and so I did, but I'm getting odd results back. It seems ...
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1 vote
0 answers
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3D interpolation of a volume with irregular upsampling

Given a collection of 2D slices which as a whole corresponds to a 3D volume (medical image of an organ), I only take specific slices (i.e. I replace the ones I dont want with zeros) and so, I end up ...
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1 answer
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Interpolation of complex signal

I'm struggling with particular (corner) case of interpolation of complex signal, in connection with OFDM modulation. While I assume that guard sub-carriers are always used, I'm studying a case when ...
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1 vote
1 answer
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Constrained interpolation/smoothing of multi-dimensional time series

Consider an $N$ dimensional time series $x_i(t),~i\in\{0,1,\cdots, N-1\}$ where $x_i(t)$ is smooth. It turns out that for all $t$: $x_i(t)>x_{i-1}(t)$. The multi-dimensional series is sampled at ...
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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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1 vote
1 answer
71 views

How do I confirm that range cell migration correction was done correctly? Is there a way to check this graphically without looking at the signal data?

I am implementing the Range Doppler Algorithm for a Synthetic Aperture Radar project and I am at the step where I must perform Range Cell Migration Correction. This step involves creating a sinc ...
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1 vote
1 answer
77 views

oQPSK/QPSK conversion with fractional interpolation

I once used a GNU Radio QPSK receiver for oQPSK demodulation. All I did was to "forcefully" delay the Q channel by half the symbol time. At the time, I was using a discrete number of samples ...
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2 answers
90 views

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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2 answers
205 views

Impulse response of linear interpolation in discrete time

I'm trying to understand interpolation in discrete time. We know that for linear interpolation we use h(t)=triangle waveform. When we talk about linear interpolation in discrete time, I'm using ...
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1 answer
100 views

How does upsampling/interpolation/oversampling help with noise shaping?

That's all, Why does upsampling improve the resolution and signal-to-noise ratio? What makes it so good for noise-shaping
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0 answers
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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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2 votes
0 answers
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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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1 vote
0 answers
111 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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4 votes
3 answers
621 views

Seamless looping of a signal without pops

I'm trying to seamlessly loop an audio signal. When I loop the current audio signal I have, I hear audible clicks or pops right as it loops back to the beginning. I want to be able to loop the audio ...
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4 votes
3 answers
259 views

How to find peak value of an analog signal efficiently after sampling in the digital domain?

I have a bandlimited analog signal for which I want to find the peak value in real time. The signal is sampled and processed digitally at just enough sampling rate. Since the peak of the analog signal ...
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1 vote
0 answers
88 views

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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1 vote
2 answers
82 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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1 vote
1 answer
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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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2 votes
1 answer
342 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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-1 votes
1 answer
220 views

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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0 answers
88 views

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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1 vote
1 answer
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Can multi-rate operations of decimation and interpolation can be used to implement a rate change by a factor an irrational number?

I know that common rates are integer values like 2 or 3, but can multi-rate operations of decimation and interpolation can be used to implement a rate change by a factor of an irrational number? ...
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0 votes
1 answer
104 views

Spectral peak location estimation using complex DFT

In this paper a simple method to estimate a spectral peak is proposed, by using quadratic interpolation between three samples of the DFT of the signal. Namely, the position of the peak relative to the ...
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1 vote
2 answers
238 views

Is there a way to use decimation or linear interpolation to shrink or stretch an audio signal in the time domain?

I am able to shrink/stretch an audio signal using Python code for a phase vocoder, as well as the stretchAudio function from Matlab's Audio Toolbox. Although both methods do indeed alter the audio ...
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1 vote
1 answer
67 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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1 vote
1 answer
114 views

What are some really accurate ways to get the value of a peak (local maximum) given some points around it? (To be used for autocorrelation peaks.)

I have looked everywhere on the internet for this and, surprisingly, haven't found much useful information. Given 3 or more points closest to a peak (local maximum) what are some of the most accurate ...
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1 vote
1 answer
1k 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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2 votes
2 answers
204 views

HRIR interpolation using VBAP

1) Problem description I am trying to implement a 3D audio simulator in Python. I am using the HUTUBS dataset as HRIR database (more informations here: https://depositonce.tu-berlin.de/handle/11303/...
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