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1answer
76 views

How to extract IF (instantaneous frequency) from Discrete Hilbert Transform?

The continuous time Hilbert transform is $$\hat x(t) := x(t) + j\left( p.v. \left\{\frac{1}{t\pi} \ast x \right\} (t)\right)$$ where $$ \theta(t) = \tan^{-1}\left( \frac{ p.v. \left\{\frac{1}{t\pi} ...
0
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1answer
39 views

Instantaneous phase calculation problems

I am currently struggling with a problem when calculating the instantaneous phase of a wavefield using a 1D Hilbert transformation. The scheme is as follows. 1D Hilbert transformation of wave field ...
0
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1answer
33 views

The error between the theoretical value and the simulation value of imaginary part of the FFT results

As we know, a complex analytic signal can be obtained through Fourier transformation of a real value function, and the imaginary part can be reconstructed by Hilbert transform of real part. But I have ...
0
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1answer
23 views

Hilbert transformer's phase in .AC simulation

I don't understand this: the HT works as it should but in an .AC simulation, the phase shows up like this (wrapped): Why doesn't it look like a constant -90deg phase, like in a differentiator? ...
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0answers
41 views

Instantaneous power estimation by discrete hilbert transform - how far does it smooth?

In my research area, instantaneous power in a specific frequency band is commonly estimated by the following procedure: Apply a bandpass filter on the raw signal (e.g. 80-90Hz bandpass). Estimate ...
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0answers
18 views

Testing whether instantaneous phase algorithm works 2D

I need to calculate the instantaneous phase $\phi$ of a 2D wave field $U$ in C which can be derived by one of two 1D Hilbert transforms $H$: $$ q(x,z) = H_1[U(x,z)] = 1/\pi \int_R U(x-\zeta,z) ...
2
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1answer
85 views

Analog Hilbert transformer

I know the FIR approach, I have seen IIR, to, but I'd like to know if it's possible to implement a Hilbert transformer in analog domain, i.e. with integrators instead of delays. Is it possible? If ...
1
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0answers
41 views

How to get the quaternionic analytic signal of a image?

The 2D discrete image signal's quaternionic fourier transform can be described as F(u,v), and its 2D analytic signal often be described as: $$ F_q(u,v) = (1 + \mbox{sgn}(u))(1 + \mbox{sgn}(v)) F(u,v) ...
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2answers
87 views

Compensate for phase shift of Hilbert transform

I'm using Octave and trying to use the "instfreq" function from the time frequency toolbox which requires an analytic signal input. To get this analytic signal I'm using the Octave function "hilbert" ...
0
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1answer
56 views

Gibbs phenomenon in Hilbert transform

I have just read that the Gibbs phenomenon can cause artifacts in the use of Hilbert transforms for audio processing applications, but the reference contained no more specific information. Can anyone ...
0
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1answer
90 views

Discrete Hilbert transformation of a spatial signal

first of all, sorry for this basic question in signal processing, I'm pretty new in this field and have been stuck in a situation a little beyond my expertise. The idea is to derive the instantaneous ...
1
vote
1answer
140 views

What are the mathematical consequences of a discrete signal living in Hilbert space?

I am doing the Coursera course on DSP by Prandoni and Vetterli, and was excited to learn that we can use the tools of vector spaces to analyze discrete signals. At this early point in the course the ...
3
votes
1answer
258 views

Why do we read that Hilbert transform can be used for envelope detection?

We can often read that Hilbert transform is useful for envelope detection (e.g. Hilbert transform to compute signal envelope?) I have done some tests with various soundfiles, and ...
1
vote
1answer
619 views

Hilbert-Huang Transform Implementation

I am looking for a implementation of Hilbert-Huang Transformation. Ideally, in Java, but any language with similar syntax would prove useful. Could someone point me to a specific implementation, ...
5
votes
1answer
370 views

Precisions on Hilbert Huang transform

After investigating signal analysis methods based on empirical mode decomposition (EMD), I found that recent developments are mostly related to the Hilbert Huang transform (HHT) and the Local Mean ...
2
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2answers
226 views

Why do envelope extraction before pitch detection?

I am referring to this report on pitch estimation. The author does envelope extraction using Hilbert transform before applying AMDF. What is the advantage of doing that? Is speech a narrowband ...
3
votes
1answer
104 views

What is a complex helical sequence?

Matlab says x = hilbert(xr) returns a complex helical sequence, sometimes called the analytic signal, from a real data sequence. How did the name ...
5
votes
1answer
1k views

What exactly is a complex envelope?

I have seen this be mentioned a couple of times in some books I read, so I want to make sure. Is the complex envelope simply the summation of the real and quadrature components of a signal, whereby ...
3
votes
1answer
735 views

Hilbert transform filter for audio applications: Using IIR half-band parallel all pass structure

Does anyone have any experience designing wideband IIR Hilbert transform filters with audio applications in mind? I am using the filter for single side band modulation audio effects discussed in this ...
3
votes
2answers
781 views

How do I find the Hilbert transform (qudrature) of a discrete signal by convolution with a Hilbert kernel?

Given a discrete real signal $ f_{re}(t) $ the (complex) analytic signal is given by: $ x(t) = f_{re}(t) + j*f_{im}(t) $. I want to calculate $f_{im}(t)$: the quadrature by convolving with a Hilbert ...
2
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2answers
602 views

Derive minimum phase from magnitude

With the desired magnitude of a transfer function in the frequency domain in C++ as described below what is the correct corresponding minimum phase? In general how does one derive the correct minimum ...
2
votes
1answer
589 views

How to find the envelope of a wide-band signal?

I would like some feedback on possible techniques that one may use to determine the envelope of a broad-band time domain signal. I have heard anecdotally, that it is not as straight-forward as it ...
0
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1answer
2k views

Envelope of time domain signal // Hilbert transform

to get the envelope of a time domain signal, s(t), I use the absolute of its analytical time domain signal. But there occur the problem that sometimes the envelope is not as desired a true envelope ...
2
votes
1answer
604 views

Matlab Hilbert Transform in C++

I asked this at Stack Overflow, they told me to come here. First, please excuse my ignorance in this field, I'm a programmer by trade but have been stuck in a situation a little beyond my expertise ...
5
votes
1answer
299 views

Hilbert transform: analytic signal

I want to observe how the signal's phase changes over time and I know Hilbert transform can be used here to get the analytic signal, from which I can extract the amplitude and phase. I know that to ...