Interpolation is a method of constructing new data points within the range of a discrete set of known data points.

learn more… | top users | synonyms

1
vote
2answers
27 views

Philosophy of perfect inter-sample interpolation

How would you define perfect (inter-sample) interpolation, and is it possible? To quote Armifinn's prior answer: "I guess the most important result is that for signals with bandwidth limitation, ...
1
vote
2answers
58 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 ...
3
votes
1answer
40 views

Whittaker-Shannon ($\mathrm{sinc}$) interpolation for a finite number of samples

Given an infinite number of samples $(N)$, a higher (or lower) number of samples $(cN)$ can be derived using sinc interpolation followed by sampling. How can this be applied to finite length signals? ...
0
votes
1answer
59 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 ...
1
vote
1answer
46 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 ...
0
votes
0answers
20 views

OFDM Channel estimation using pilots

I'm simulating various scenarios of channel estimation using pilots in OFDM. The FFTSize and number and position of pilots may vary but the pilot scheme is identical, meaning that pilots exist in ...
0
votes
2answers
34 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 ...
0
votes
1answer
51 views

Closed-form expression for Whittaker-Shannon interpolation for non-bandlimited signals

For a bandlimited signal $x(t)$ that is reconstructed after Nyquist-sampling at intervals $T$, $$x(t) = \sum_{k=-\infty}^{\infty} {x[k]\textrm{sinc}\left(\frac{t-kT}{T}\right)}$$ where $x[k]$ = $x(...
4
votes
2answers
134 views

Zero, First, Second … nth-order Hold

The rectangular function is defined as: $$\mathrm{rect}(t) = \begin{cases} 0 & \mbox{if } |t| > \frac{1}{2} \\ \frac{1}{2} & \mbox{if } |t| = \frac{1}{2} \\ 1 & \mbox{if } |t| < \...
0
votes
0answers
32 views

non integral (sub sample) delay estimation using interpolation [duplicate]

Integral sample delay can be obtained directly from peak of cross correlation. How to obtain non integral delay. Is there some other interpolation technique (apart from parabolic) which estimates the ...
0
votes
2answers
58 views

Zero-order interpolation problem

Let $x_c(t)=\cos(\omega_0t)$. This signal is sampled with $\omega_s$, which is greater than the Nyquist rate. It is then interpolated with a zero-order interpolator. The signal obtained is $y_c(t)$. ...
-1
votes
2answers
122 views

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/...
0
votes
3answers
49 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 ...
0
votes
2answers
46 views

Interpolated impulse response for fraction delay?

I need to find a way to create some fractional delay in a signal processing application that I am working on. Separately to this, I have been messing around with basic filter design (despite reading ...
1
vote
1answer
36 views

Cut-off frequencies for fractional sample rate adjustment

We have a signal sampled att 22 kHz that we want to interpolate to 40 kHz. So we can do this by upsampling by a factor 20, then downsampling by a factor 11. My question regards the choice of cut-off ...
0
votes
1answer
75 views

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 ...
1
vote
1answer
196 views

Why upsample before modulation?

We're doing a project in which we're sending an OFDM frame, modulated to some appropriate carrier, over a channel. Before modulating, we are instructed to upsample and low-pass it. Is there a good ...
1
vote
1answer
70 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 ...
0
votes
0answers
23 views

Type FIR LPF for Interpolation

I know this, input discrete function $$ x[n]= x0,x1,x2,x3 $$ then according to zero padding wtih $L=3$ my $z[n]$ will be $$ z[n]=x0,0,0,x1,0,0,x2,0,0,x3,0,0 $$ following this: http://fourier.eng....
0
votes
0answers
27 views

Temporal Interpolation of Spectra

The signal of interest to me is the ocean wave height as a function of time at a particular location. Its power or variance spectrum is estimated by buoys at regular time intervals. Specifically, ...
1
vote
1answer
52 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 ...
1
vote
1answer
56 views

Perform inverse distance weighting interpolation using multiple images matlab

I have a total of 4 highly identical grayscale images, where image1 is taken as the reference image, the rest of the images are to be used to enhance image1. My objective is to enlarge the image to 2 ...
2
votes
1answer
110 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 ...
0
votes
3answers
135 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....
1
vote
4answers
130 views

Basic method for 2x oversampling?

I would like to know if the following method of 2x oversampling is correct: Interpolate: Take an original signal sampled at 44100Hz as input Upsample by adding a zero after each original sample to ...
2
votes
1answer
93 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
votes
1answer
56 views

Interpolate/Decimate with a single filter?

This is not a homework question (I'm out of school now 2 years). I'm thinking, let's say you have 2 systems, one at 32khz and the other at 48khz and you want to go between the two. Is there a way to ...
0
votes
0answers
35 views

Comparing AR coefficients derived from different sampling rates

I'm interested in comparing the coefficients of AR processes computed from different dynamic texture videos. That is, $A_1$ and $A_2$ are the $d \times d$ coefficients for dynamic texture videos 1 and ...
0
votes
2answers
111 views

Interpolation based on sinc function

I implemented an interpolation method in C++ based on this equation ...
0
votes
1answer
32 views

How to interpolate complex array (FT)?

I do Fourier Transform for an image, then consider line(slice) in FFT image. When that slice isn't parallel neither x- not y-axis, coordinates are not integer. E.g. slice can hold indices ...
1
vote
4answers
282 views

Estimate Delay of a Known Signal Delayed by Sub Sample Resolution

Given a known signal $ x \left( t \right) $ and its delayed version $ y \left(t, \tau \right) = x \left( t - \tau \right) $. Both are sampled by Sampling Frequency $ {F}_{s} $ to generate the signals $...
5
votes
4answers
169 views

Sampling Theorem illustration

Can someone please explain the illustration (figure 1.19) at the bottom of this image? It looks like there are four sampling points but I don't understand what the different curves represent. Actually ...
1
vote
1answer
66 views

Chosing polyphase interpolation coefficients

I'm writing code for a 3x polyphase interpolator using a total of 9 coefficients. This is organized as 3 parallel FIR branches with 3-taps each that are summed at the 3x sampling rate. The problem I ...
0
votes
0answers
26 views

How to reduce polynomial?

I have some 4 polynomials like this. these equation is made by polyfit() from MATLAB tool. ...
0
votes
2answers
40 views

Sinc interpolation looks weird

blue is how I tried to sinc interpolate. why would something like this happen?
0
votes
2answers
102 views

sinc interpolation using fft

Lets say I want to double the number of points in an array f. I had the idea to do this: F=fft(f);N=length(f); FF=[F(1:N/2) zeros(1,N) F(N/2+1:N)]; f=ifft(FF); ...
0
votes
1answer
54 views

Best way to approximate a curve?

I have a curve like this one: I need a function to approximate this curve, but I need that the function be a low order function (less than 5). What is a good way to obtain what I expect? Thanks!
0
votes
1answer
57 views

Is a cubic Lagrange interpolation tensor product the same as bicubic interpolation?

I just implemented some interpolated texture sampling by sampling the 4x4 nearest pixels then doing Lagrange interpolation across the x axis to get four values to use Lagrange interpolation on across ...
1
vote
0answers
22 views

How to shift with spline interpolation?

I have a sampled pulse shape: $ h = [1, 0.5]$ and I do not know what is its real underlying continuous-time pulse. I want to compute the samples of $h(t-\Delta t)$. If I write the continuous pulse ...
0
votes
0answers
92 views

Optimal signal sampling reduction method : Decimation, interpolation or both?

I have a function with an equation: \begin{equation} C(t)=1.6925\left(\exp^{-0.136t}- \exp^{-1.192t} \right) u(t) \end{equation} where u(t) is a unit-step function. Then, denoting the Fourier ...
1
vote
0answers
37 views

How to proceed with this convolution problem?

If $$\alpha_k = \sum_l a_l \ \ g((k-l)T-l\Delta T)$$ $$s_k = \sum_l \alpha_l \ \ q((k-l)T+k\Delta T)$$ where $a_l \in \pm1$ and $g(t) = \frac {\sin(\pi t/T)}{\pi t/T}$ and $q(t) = \frac {\sin(\pi t/(...
3
votes
1answer
260 views

How to apply a Butterworth filter to data of varying sample rate?

I am trying to apply a Butterworth bandpass filter to accelerometer data of my smartphone. However, the accelerometer samples I receive do not come at regular intervals. Sample frequency varies ...
1
vote
0answers
149 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 ...
-1
votes
1answer
41 views

linear interpolator replacement for the sinc function

How to find an optimum linear interpolator replacement for the ideal sinc function? The reason is for the hardware implementation ease. For example when I use sinc interpolation: ...
1
vote
2answers
136 views

How to compare the qualities of two interpolation (image resizing) algorithms?

I am implementing image resizing algorithms (Bilinear, Bicubic, Lanczos and a few others). How do I quantitatively compare them? I am thinking of considering a large sample of images and running ...
0
votes
2answers
326 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 ...
2
votes
0answers
87 views

How to subsample shift with sinc interpolation?

Does anybody know of a way to shift data by a fraction of a sample by using sinc interpolation? For example, shift an image to the right by 0.1 pixels. I'm struggling to find a formula or reference ...
2
votes
1answer
216 views

Difference between subsampling and downscaling (image)?

I know that there are many ways to upscale (interpolate) an image using bilinear, bicubic, sinc... Somehow, these same algorithms can also be used to downscale an image. But when it comes to ...
0
votes
1answer
194 views

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 ...
1
vote
2answers
79 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 ...