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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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1answer
711 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
348 views

Resampling: how many samples to zero-stuff or down sample?

I am a little confused about how resampling works with one filter. I get why you choose the lower nyquist cutoff when you combine both interpolation and decimation for resampling by a rational ...
2
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1answer
567 views

Practical vs ideal lowpass interpolator

Consider a signal with a sample rate $f_s = 44.1$ kHz. Let us upsample the signal by a factor of $L = 2$ and interpolate the zeros. An ideal lowpass interpolator would have a gain of $L$ and a cutoff ...
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1answer
117 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 ...
2
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3answers
460 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 ...
2
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1answer
276 views

Interpolation formula for two dimensional signal reconstruction in the frequency domain from polar samples

In the book, Advanced Topics in Shannon Sampling and Interpolation Theory by Robert J. Marks II, one may find an interpolation formula for reconstructing a two dimensional signal from regular polar ...
2
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1answer
329 views

Compute real signal from a discrete analytic signal

I have a 128MHz-wide down converted signal that gets processed in a FPGA via a polyphase filter bank to give 8x16 MHz baseband analytic signals. How do I convert this analytic signal to a real-valued ...
2
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1answer
2k views

Convolution Based Image Interpolation

From a book, I learned that image interpolation (or upsampling) can be written as a convolution like this: $$g(i,j) = \sum_{(x,y)}f(x,y)h(i-rx,j-ry)$$ while $r$ is the upsampling rate. But I have a ...
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0answers
47 views

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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0answers
31 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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0answers
36 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 ...
2
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0answers
167 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 ...
2
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0answers
198 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 ...
2
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0answers
350 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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4answers
2k views

DFT Frequency domain analysis and interpolation

I have a 2 part question, one may be related to why I'm not understanding the other. A while back, I remember some professor saying that for the $N$ point DFT frequency domain, the values for $k$ ...
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0answers
673 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 ...
2
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0answers
140 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 ...
2
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1answer
3k views

Interpolation of a gray scale image in matlab [closed]

I want to fill the black areas with the value of neighboring pixels. Kind of interpolation. Can any one suggest me how Can I do in matlab.
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5answers
642 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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2answers
133 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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2answers
787 views

Interpolation vs Interpolation Filter?

Hi guys, I've been reading some papers on - how to remove ghosting artefacts from the Fourier Slice theorem applied to a 3D discrete image volume. The papers mention that in order to remove ghosting ...
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2answers
203 views

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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5answers
10k views

Output gain when upsampling and downsampling

Do the processes of upsampling and downsampling affect the magnitude of the transform of a signal? And if not, why am I seeing everywhere that a filter with gain different from 1 is applied after up/...
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3answers
1k views

Designing a 2x interpolation filter for audio

I want to perform 2x interpolation on an audio signal sampled at 44.1KHz by upsampling the signal by adding a zero after each original sample and then using a lowpass filter to interpolate the results....
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1answer
70 views

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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2answers
210 views

Interpolation techniques for extremely limited hardware

I am trying to playback samples on a retro-computer. The hardware is extremely limited, so I am forced to use software PWM as my main method of playback. The limitations of the platform mean that I ...
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3answers
4k views

Upsampling - What purpose does the interpolation filter have?

I want to apply some nonlinear processing to a signal, namely: I want to implement a tube emulation which adds warmth/harmonic distortion to a digital audio signal. I am worried about aliasing, so I ...
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3answers
1k views

Interpolating irregularly missing data points of regularly spaced data

If I have a set of regularly spaced sample data (spacing $\delta x$) and some of my data is missing (zero) but not at regular intervals, i.e. $[a_0, (missing), (missing), (missing), a_4, a_5, (...
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1answer
296 views

Why does Fourier zero-fill interpolation pad the middle frequencies?

In this: http://dspguru.com/dsp/howtos/how-to-interpolate-in-time-domain-by-zero-padding-in-frequency-domain the author says that we can interpolate a signal by zero-padding the middle frequencies in ...
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2answers
892 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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2answers
180 views

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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2answers
437 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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2answers
466 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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2answers
1k views

Mathematical justification for zero padding?

This question asks what's the point of zero padding. The accepted answer is certainly very insightful, but I don't understand a big chunk of it: Zero padding allows one to use a longer FFT, which ...
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2answers
143 views

Explanation relevant to the filter response ($\mathrm{sinc}$ interpolation) - Equation $(2)$ in my question

At present, I am learning the theory of operation of resampling for bandlimited periodic discrete signals using $\mathrm{sinc}$ interpolation. I am developing a design flow and having difficulty in ...
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1answer
86 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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1answer
127 views

Why would FFT interpolation using zero-padding undershoot the true frequency of a single tone sinusoid?

Why would FFT interpolation by zero-padding or using the Chirp Z-Transform produce a maximum at a bin that corresponds to a frequency less than the input frequency of a single tone sinusoid? I am ...
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1answer
725 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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2answers
272 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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2answers
7k 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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2answers
371 views

Spline-Based Adaptive Interpolation Filters?

My understanding of interpolation specific to resampling applications is limited to the concept of inserting zeros, then designing a filter to minimize distortion in the passband and reject the images ...
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1answer
655 views

Does Zero Padding Work as Advertised?

I have trouble accepting the merits of zero padding in the frequency domain to give more points in FFT. Wonder if anyone else has similar thoughts. The mathematical 'proof'for the validity of zero ...
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2answers
2k views

Resampling an audio signal

I am trying to resample an audio signal in my application. It will be between 48kHz and 96kHz audio (both upsampling and downsampling). Looking at the Wikipedia page for resampling I see there are ...
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1answer
405 views

Fractional/Interpolating Delay Line still sounding glitchy

I'm trying to implement a simple digital delay line. I want it so that when the user changes the delay amount, it sounds smooth and not glitchy. Currently I'm implementing a fractional delay line but ...
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2answers
1k views

Sinogram Fourier Analysis Doesn't Show Clear Bow Tie Shape

I'm working on finding the center of rotation of a set of test tomographic projections in order to perform 2D reconstruction. I'm trying to implement the algorithm to find center of rotation as ...
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1answer
1k views

Variable sample rate interpolation

I have a set of data over which I would like to interpolate, with a sampling rate say about $f_0$ Hz with a significant uniform random sampling jitter, such that it's more or less: $$f_0 - \frac{1}{4}...
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1answer
1k views

How to downscale an image with interpolation by a factor larger than interpolation kernel size?

I'm experimenting with image resizing techniques and algorithms. Specifically, I'm significantly downsizing images, e. g. from 2048x1536 to 64x48 - 32 times. Now, say I'm using a 4x4 kernel. Right now ...
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1answer
25 views

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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1answer
62 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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1answer
118 views

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 ...