55 votes
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Is deep learning killing image processing/computer vision?

On the top of this answer, you can see a section of updated links, where artificial intelligence, machine intelligence, deep learning or and database machine learning progressively step of the grounds ...
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47 votes
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Meaning of Hilbert Transform

One application of the Hilbert Transform is to obtain a so-called Analytic Signal. For signal $s(t)$, its Hilbert Transform $\hat{s}(t)$ is defined as a composition: $$s_A(t)=s(t)+j\hat{s}(t) $$ The ...
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31 votes
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What are advantages of having higher sampling rate of a signal?

Sampling at a higher frequency will give you more effective number of bits (ENOB), up to the limits of the spurious free dynamic range of the Analog to Digital Converter (ADC) you are using (as well ...
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23 votes

Replacing "e" in Euler's formula with another number

Say you're interested in $$M^{j2\pi f_0 t}. \tag{1}$$ Note that $$M = e^{\log M},$$ so $(1)$ can be written as \begin{align} M^{j2\pi f_0 t} &= \left( e^{\log M} \right) ^ {j2\pi f_0 t} \\ &= ...
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22 votes

Is deep learning killing image processing/computer vision?

First, there is nothing wrong with doing grad work in image processing or computer vision and using deep learning. Deep learning is not killing image processing and computer vision, it is merely the ...
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22 votes

Is there any practical application for performing a double Fourier transform? ...or an inverse Fourier transform on a time-domain input?

No, taking the Fourier transform twice is equivalent to time inversion (or inversion of whatever dimension you're in). You just get $x(-t)$ times a constant which depends on the type of scaling you ...
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  • 80.4k
21 votes
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Why doesn't sampling a periodic continuous-time signal yield a periodic discrete-time signal?

If the ratio between your sampling frequency and the frequency of your signal is irrational, you will not have a periodic discrete signal. Assuming you have a 1-kHz sine wave and you sample at 3000*...
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18 votes

Meaning of Hilbert Transform

In layman terms, the Hilbert transform, when used on real data, provides "a true (instantaneous) amplitude" (and some more) for stationary phenomena, by turning them into "specific" complex data. For ...
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17 votes

Is there any practical application for performing a double Fourier transform? ...or an inverse Fourier transform on a time-domain input?

Whilst taking the Fourier transform directly twice in a row just gives you a trivial time-inversion that would be much cheaper to implement without FT, there is useful stuff that can be done by taking ...
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16 votes
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Is there any practical application for performing a double Fourier transform? ...or an inverse Fourier transform on a time-domain input?

"Is there any practical application?" Definitely yes, at least to check code, and bound errors. Especially for huge data or a large number of iterations "In theory, theory and practice ...
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15 votes

Why Does the DFT Assume the Transformed Signal Is Periodic?

There are already some good answers, but I still feel like adding yet another explanation, because I consider this topic extremely important for the understanding of many aspects of digital signal ...
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15 votes

What's the noise in this signal ? (Beginner question)

From the spectrogram (frequency domain plot) you have a large signal at 60 Hz and harmonics. This will be mains pickup if this was recorded in a area with a 60 Hz mains supply. On the upper time plot ...
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14 votes

Why does a longer observation time improve DFT resolution, but repeating a signal does not?

Why is this not equivalent to simply observing the signal for 1 period, and then paste it together N times? It's only equivalent if certain conditions are met. Let's look at a single sine wave with ...
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13 votes

How to learn MUSIC algorithm?

Read the original paper: Schmidt, R. O. "Multiple Emitter Location and Signal Parameter Estimation." IEEE Transactions on Antennas and Propagation. Vol. AP-34, March, 1986, pp. 276–280 You may also ...
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13 votes
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Shift a signal by fraction of a sample

There's a good overview article which appeared in 1996 in the IEEE Signal Processing Magazine: Splitting the unit delay: tools for fractional delay filter design. The nice thing about it is that there'...
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13 votes

Is deep learning killing image processing/computer vision?

No Deep Learning isn't killing Image Processing. You need huge datasets and lots of computational resources to do deep learning. There are plenty of applications where it is desirable to be able to do ...
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13 votes

Is deep learning killing image processing/computer vision?

Today we had a discussion with a friend of mine. It was a rainy day here in Munich, while a large portion of Europe was having a kind of sunny atmosphere. People were sharing photographs in social ...
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13 votes

Is there any practical application for performing a double Fourier transform? ...or an inverse Fourier transform on a time-domain input?

2D Fourier transform (2D DFT) is used in image processing since an image can be seen as a 2D signal. E.g. for a grayscale image $I$, $I(x,y)=z$, that means that at the coordinates $x$ and $y$ the ...
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13 votes

What's the noise in this signal ? (Beginner question)

Your difficulty does not arise out of a lack of common sense (if any); rather, the reason is that the problem is not well specified. To be able to tell signal from noise, you need to know something ...
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12 votes
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How to calculate Signal-To-Noise Ratio

If you can get input signal when it doesn't contain any useful signal (I mean only noise is presented), you can estimate average noise power at first. Simply find a power of such a signal: $P_n=1/N \...
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12 votes
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Accessing Maximum Value from a Singular Value Decomposed Matrix

The SVD Decompose the image into the (One way to look at it) many matrices. For instance, given an Image $ I $ its SVD is given by: $$ I = U S {V}^{T} = \sum_{i=1}^{\textrm{rank}(I)} {s}_{i} {u}_{i} {...
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12 votes
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Periodicity of a constant signal!

As you say, the constant function is periodic. A signal $x(t)$ is said to be periodic with period $p$ or to have a period $p$ if there exists a $p>0$ such that $x(t+p)=x(t)$ for all real numbers $t$...
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11 votes

Why Does the DFT Assume the Transformed Signal Is Periodic?

It comes from the definition of the time domain signal: $$ x \left[ n \right] = \sum_{k = 0}^{N - 1} X \left[ k \right] {e}^{\frac{2 \pi i n k}{N}} $$ You can see by definition that $ x \left[ n \...
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11 votes
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Power of a Discrete time signal

The power of a discrete-time signal $x[n]$ is given by $$P_x=\lim_{N\rightarrow\infty}\frac{1}{2N+1}\sum_{n=-N}^{N}|x[n]|^2$$ which is identical to the first formula in your question. The second ...
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11 votes

Show others how I hear myself

The most practical attempt that I am aware of is by Won and Berger (2005). They simultaneously recorded vocalizations at the mouth with a microphone and on the skull with a homemade vibrometer. They ...
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  • 231
10 votes

Meaning of Hilbert Transform

The analytic signal produced by the Hilbert transform is useful in many signal analysis applications. If you bandpass filter the signal first, the analytic signal representation gives you information ...
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10 votes

Meaning of Hilbert Transform

A transform (FT or Hilbert, etc.) doesn't create new information from nothing. It only represents the information already present in a different way. The "information we get", or the added ...
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10 votes
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Show others how I hear myself

It is not impossible but it is not going to be a walk in the park too. What you would be trying to do is to add to the voice signal, those vibrations that are delivered to the ear via the bones and ...
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10 votes

How can a signal be both periodic and random?

Most realistic signals are both random and periodic. For example, you can modulate a harmonic oscillator with a slow enough random signal that moves its frequency around a $\mu_{f}, \sigma_f$. This ...
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