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23 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 ...
Matt L.'s user avatar
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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 ...
leftaroundabout's user avatar
16 votes
Accepted

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 ...
Laurent Duval's user avatar
12 votes
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How to build a phase shifter with arbitrary phase shift

Nice question! It uses one of my favorite trig identities (which can also be used to show that quadrature modulation is actually simultaneous amplitude and phase modulation). The impulse response of ...
MBaz's user avatar
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12 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 ...
SheppLogan's user avatar
12 votes
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Can humans hear Hilbert transform in audio?

Can humans hear Hilbert transform in audio? Generally no. The human auditory system is fairly insensitive to monaural phase shifts. "Monaural" means "same phase shift for both ears&...
Hilmar's user avatar
  • 46.3k
12 votes

What information does the Hilbert transform give?

If the OP is interested in what is the practical purpose of the Hilbert Transform, the rest of this post applies. Similar to the Fourier, Laplace, and Z transforms, the Hilbert Transform can be used ...
Dan Boschen's user avatar
11 votes
Accepted

Hilbert transform of sinusoid -- apparent contradiction

The error lies in the assumption that if $g(t)$ is the Hilbert transform of $f(t)$, then the Hilbert transform of $f(-t)$ must be $g(-t)$. This is not the case. Let $f^-(t)=f(-t)$. Then we have $$g(...
Matt L.'s user avatar
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11 votes
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Is there a relation between an analytic signal (signal processing) and an analytic function (complex analysis)?

There is a relationship between these two concepts. Let the complex function $f(z)$ be analytic on and inside a simple closed curve $C$ in the complex plane. Then Cauchy's integral formula states that ...
Matt L.'s user avatar
  • 90.6k
10 votes

Why Hilbert Transform is terrible choice for amplitude demodulation of broadband signals?

It's not only a matter of "broadband or not": The Hilbert estimate degrades for multi-component signals - that is, whatever we can't draw without lifting our pen, left-to-right, in time-...
OverLordGoldDragon's user avatar
9 votes
Accepted

Does analytic signal have positive instantaneous frequency?

It is not the case that the instantaneous frequency of an analytic signal is always positive. In general, the instantaneous frequency can become negative, also for analytic signals. I'll show this ...
Matt L.'s user avatar
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8 votes

How to build a phase shifter with arbitrary phase shift

MBaz's answer is correct. I would just like to add another way of thinking about it, of course leading to the same result: Note that this system can be approximated quite well in a practical (...
Matt L.'s user avatar
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8 votes
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Why is Scipy implementation of Hilbert() function different from Matlab implementation of the function?

It works fine for me: ...
endolith's user avatar
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8 votes
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How do I convert a sampled complex signal to a real signal?

So the point is that "classically", communications theory tends to be done in complex baseband, i.e. signals centered around 0 Hz, but not necessarily symmetric in spectrum. When you want to ...
Marcus Müller's user avatar
7 votes

IIR Hilbert Transformer

This is achievable with two parallel all pass filters. The two all pass filters synthesize an odd ordered low pass filter whose pass band extends from -90º to +90º in the z-domain. (I will discuss ...
Robby Wasabi's user avatar
7 votes
Accepted

Envelope detection using matlab hilbert function

This must be an artifact in the way the OP has generated the waveform (all those details are not provided) as I get different results as detailed below using the ...
Dan Boschen's user avatar
6 votes

Compression algorithms specific to complex signals

Complex signals are a special case of multidimensonal signals (where the dimension is two). A lossy approach tackling compression of multidimensional signals is vector quantization. A very good ...
msm's user avatar
  • 4,305
6 votes

IIR Hilbert Transformer

I have insufficient reputation to answer in the comments, so here goes: I believe Olli calculated his coefficients using some kind of genetic algorithm (I don't know the details). All I did was plot ...
Ross Wilkinson's user avatar
6 votes
Accepted

Hilbert transform too large to store (out of core processing)

I would use a linear phase FIR Hilbert transformer, and use block processing, such as the overlap-add method. That means that you partition the input signal into contiguous non-overlapping blocks and ...
Matt L.'s user avatar
  • 90.6k
6 votes

Demonstrate that $x(t)$ and $\hat{x}(t)$ are orthogonal

You have to use the following form of Parseval's identity: $$\int_{-\infty}^{\infty}x(t)y^*(t)dt=\int_{-\infty}^{\infty}X(f)Y^*(f)df\tag{1}$$ where $^*$ denotes complex conjugation, and where $X(f)$ ...
Matt L.'s user avatar
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6 votes
Accepted

Discrepancies between FFT-based Hilbert Transform and FIR filter results

There are several reasons why the two results don't match: the coefficients of the FIR Hilbert transformer are wrong the FIR Hilbert transformer is too short to even come close to the performance of ...
Matt L.'s user avatar
  • 90.6k
6 votes

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

To answer the second question, in digital communications there is a technique in use in cellphones right now that makes good use of applying the IFFT to a time-domain signal. OFDM applies an IFFT to ...
myeslf's user avatar
  • 61
5 votes
Accepted

Hilbert FIR Filter for Q - Matching Filter for I

Clay Turner has an interesting couple of papers. what you want to do is compute (using MATLAB firpm() or firls()) two filters ...
robert bristow-johnson's user avatar
5 votes

Meaning of Hilbert Transform

This question already has many excellent answers, but I wanted to include this very simple example and explanation from this page that massively cleared up the concept and usefulness of the Hilbert ...
dkv's user avatar
  • 181
5 votes

Meaning of Hilbert Transform

As already explained in other answers that Hilbert transform is used to get anaytic signal which can be used to find envelope and phase of signal. Another way of looking Hilbert transform is in ...
pulkit's user avatar
  • 61
5 votes

In-Phase and Quadrature components of low-pass equivalent of a band-pass signal?

i will call the bandpass signal: $$\begin{align} y(t) &= \Re \Big\{ (x(t) + j\hat{x}(t)) \, e^{j \omega_0 t} \Big\} \\ \\ &= x(t) \cos(\omega_0 t) - \hat{x}(t) \sin(\omega_0 t) \\ \...
robert bristow-johnson's user avatar
5 votes

Hilbert Transform in C provides possibly strange results

I am not a signal processing expert, but I have made it a good practice not to mix concepts. There is something called the Hilbert Transform, and there is an analytic signal. Here is what I do to ...
Cesar's user avatar
  • 61
5 votes

Not able to reach minimum phase using Hilbert transform

More taps. You don't have anywhere near enough taps for a filter that steep. Start large with 8192 or so cut to desired accuracy, if needed Due to the low number of tabs you are seeing the effect of "...
Hilmar's user avatar
  • 46.3k
5 votes
Accepted

Question about Hilbert transform

TLDR: if the time variable $t$, and its dual variable ($f$, $\tau$) in the expression of the bivariate kernel have the same homogeneity, (I believe that) you can call it a time-domain ...
Laurent Duval's user avatar
5 votes
Accepted

Envelope detection using hilbert transform

To be clear, the Hilbert Transform in MATLAB does not actually return the Hilbert Transform, but returns the Analytic Signal given as: $$x_a(t) = x(t) + j \hat x(t)$$ Where it is the imaginary ...
Dan Boschen's user avatar

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