13 votes
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Multi-channel audio upsampling interpolation

Does cubic interpolation (or any other) have any advantages over linear for the specific case of audio? You'd use neither for audio. The reason is simple: The signal models you typically assume for ...
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11 votes
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What is the difference between cubic interpolation and cubic "Spline" interpolation?. How to use it for upsampling purpose?

The difference between cubic interpolation as described in your question and cubic spline interpolation is that in cubic interpolation you use 4 data points to compute the polynomial. There are no ...
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9 votes
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Zero, First, Second ... nth-order Hold

This is not the case. First of all, a second-order hold would use three sample points to compute an interpolation polynomial, but your suggested impulse response $\text{tri}(t)\star\text{tri}(t)$ is ...
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9 votes
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Shannon interpolation formula for downsampled data with an "almost ideal" low pass filter

I don't get your downsample step when you downsampled by factor $M$. Let me go from scratch with the spectrum visualization below, with time domain, continuous frequency domain and discrete frequency ...
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9 votes
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Is interpolation of an audio signal to increase frequency resolution possible?

The (very) short answer is no, interpolation does not increase resolution: no new data, no new information (Note that strictly speaking, the usage of "resolution" is not appropriate ...
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8 votes

Sampling Theorem illustration

This plot depicts how to convert your digital signal back to the analog one, using $\mathrm{sinc}$ functions. The nice property of these functions used in this process, is that maximum of each ...
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8 votes

Proving Nyquist Sampling Theorem for Strictly Band Limited Signals (Whittaker Shannon Interpolation Formula)

Approaching The Sampling Theorem as Inner Product Space Preface There are many ways to derive the Nyquist Shannon Sampling Theorem with the constraint on the sampling frequency being 2 times the ...
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8 votes
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What Does 'Zero Order Hold' and 'First Order Hold' Mean?

We need to assume the reader knows some basic stuff to answer that. Let's give it a try. Lets understand the sentence - Zero / First Order Hold. We have the Zero / ...
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8 votes
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Seamless looping of a signal without pops

But is this good practice? Yes, that's a perfectly reasonable approach. Will this will work for all types of signals I might have ? There are a LOT of signals out there and there is always an ...
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7 votes

Sinc Interpolation Using DFT (FFT)

Doing DFT based interpolation has to keep 3 principles: Keep the zeros outside the data (Looking form $ -\pi $ to $ \pi $). Namely add zeros to the higher frequencies. If it is real signal, keep the ...
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7 votes
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Unexpected Result When Using Sinc Interpolation

Since Sinc based Interpolation requires you to know the data at any point. Hence it is not feasible. You might do a Truncated Sinc Interpolation. The artifacts you're seeing can be caused by a kernel ...
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7 votes

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

An alternative explanation of what the function $g(u)=\sum_{m\in\mathbb{Z}}\operatorname{sinc}(u-mN)$ is. First, note that $$g(u)=\sum_{m\in\mathbb{Z}}\operatorname{sinc}(u-mN)=\text{sinc}(u) \ \...
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7 votes
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Signal values we will 'miss' between sampling instances during sampling of band limited signals

I don't have a real answer but I have the feeling that this result will help you out: Bernstein's inequality says that, if the signal $x(t)$ is bandlimited to $|f|\leq B$, then $$\left| \frac{\textrm{...
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7 votes
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Can you decimate / downsample a signal in frequency domain just like you can interpolate / upsample it?

Your interpolation operation is an upsampling operation with subsequent low-pass filtering. This translates to zero-padding in the frequency domain. Given your original signal $x[n]$, you upsample it ...
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7 votes

Effects of linear interpolation of a time series on its frequency spectrum

Duane Wise and i wrote a paper back in the 90s that we presented to an AES convention that spelled out how to model time-domain polynomial interpolation (of which linear interpolation is an example) ...
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7 votes
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Alignment of 2 Set of Samples from Different Sensors

There are 2 main factors here: Aligned timeline Namely each sample has time stamp taken with the same reference time. The lower sampling rate is high enough according to the sampling theorem Namely ...
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7 votes
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The Proper Way to Do Sinc Downsampling (DFT Downsampling) for Uniformly Sampled Discrete Signals with Finite Number of Samples

Interpolation in Frequency (DFT Domain) The implementation is well known. In MATLAB it will be something like: ...
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7 votes
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Interpolation FIR filter output spectrum

Everything is operating just as it should and this looks like a fine interpolation. The spectral noise floor in the proximity of the signal is not changing (there is no noise summing there -it is the ...
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  • 37.1k
6 votes
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What is the Concept of MATLAB Function Polynomial Interpolation?

It is basically an approach choice. Inside the math is identical. Usually, when doing Least Squares curve fitting, you're not looking for the Polynomial coefficients but a scaled version of them. For ...
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6 votes
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Sinc Interpolation Using DFT (FFT)

If N is odd it's a bit simpler: FF=2*[F(1:(N+1)/2),zeros(1,N),F((N+3)/2:N)]; ff=real(ifft(FF)); This is very close to what you ...
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6 votes
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Basic method for 2x oversampling?

Interpolation (sampling frequency 44.1 kHz ➔ 88.2 kHz) Your original 44.1 kHz sampled signal has frequencies up to 22.05 kHz, so you should lowpass filter at 22.05 kHz after dilution with zeros. Your ...
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6 votes
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Why upsample before modulation?

The reason is aliasing. Because the modulation is digital, on the discrete signal, the sampling frequency should be high enough that the channel's frequency band does not extend beyond the Nyquist ...
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6 votes
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Estimation / Reconstruction of an Image from Its Missing Data 2D DFT

For simplicity I will show an approach Id' use on 1D signal (A row of real world image). You will be able to extend it and I will add few remarks on how you can even gain from having 2D data. The ...
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6 votes
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Why do we need to increase sampling frequency at the transmitter?

Three reasons to increasing the sampling rate further are 1) To relax the requirements of the post D/A conversion filtering for image rejection. 2) Increase signal SNR by spreading quantization ...
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6 votes

Why Zero Padding in the Center of the DFT Interpolates / Upsamples the Signal (Sinc Interpolation / DFT Interpolation / Periodic Interpolation)

What you are experiencing is technically called interpolation by DFT; i.e., interpolating a time-domain sequence $x[n]$ by properly zero filling the middle portion of it's DFT $X[k]$ (and taking the ...
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5 votes
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Bicubic Interpolation

Here pretty good explanation. I'll start by consider the 1D case of cubic interpolation (because its easier to explain) and then go onto the 2D case. The basic idea of cubic interpolation is to ...
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Interpolate/Decimate with a single filter?

Yes, you can interpolate and decimate at the same time. This is called "resampling". If you google resampling you will find lots of information about it. And yes, your reasoning about resampling is ...
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5 votes

Zero, First, Second ... nth-order Hold

so this is why i think an $n$-th order hold is a $\operatorname{rect}\left( \frac{t - T/2}{T} \right)$ convolved against itself $n$ times. Wikipedia isn't the final reference of all things, but there ...
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5 votes
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Interpolate DFT Coefficient of a Frequency That Is Not in the DFT Bin

If you need very specific frequency you should either use the Discrete Fourier Transform (DFT) definition or the Goertzel Algorithm. Yet, if you need higher resolution Grid, you can use many off the ...
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5 votes

Signal values we will 'miss' between sampling instances during sampling of band limited signals

Observations I have used +1 and -1 in the sequence instead of your 1 and 0. With $\alpha=1$, the band-limited continuous function $f_m(T)$ in your first two figures (with the above mentioned ...
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