Questions tagged [hilbert-transform]

Hilbert Transform is an operator of a function of time or frequency domain that, unlike the Fourier Transform, returns a function in the same domain. The Hilbert Transform of $ x \left( t \right) $ essentially preserves magnitude and shifts the phase of all positive frequency components by -90° (Also shifts the phase of all negative frequencies by +90°).

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14
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2answers
2k views

How to build a phase shifter with arbitrary phase shift

Fred, a DSP engineer, goes to his favorite DSP store to do some shopping. Fred: Hi, I'd like to buy a phase shifter. Shop assistant: Hmm, what exactly do you mean? Fred: Well, you know, if you put ...
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8answers
50k views

Meaning of Hilbert Transform

I understand the Fourier Transform which is a mathematical operation that lets you see the frequency content of a given signal. But now, in my comm. course, the professor introduced the Hilbert ...
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1answer
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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 ...
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1answer
1k views

What is the easiest, most straight-forward way to prove this about minimum-phase filters?

Using the "unitary" or "ordinary frequency" or "Hz" convention for the continuous Fourier Transform: $$ \begin{align} X(f) \triangleq \mathscr{F}\{x(t)\} &= \int\limits_{-\infty}^{\infty} x(t) \, ...
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2answers
3k 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 ...
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1answer
2k 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 ...
4
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2answers
375 views

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

I have a signal (saved on disk) that I would like to take the Hilbert transform of, but it's too large to fit in memory (all at once). I would like to cut it into blocks and take the transform of each ...
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1answer
118 views

phase difference detection

For application of syncing sampling clock phase to carrier phase of received signal where the received signal is sampled with 10 times the carrier phase and modulated with the PSK shown in the figure (...
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1answer
1k views

Pre-envelope of ${\Pi}_{a}(t)\cos(2{\pi}f_{0}t)$

I want to find the pre envelope of $$x(t) = {\Pi}_{a}(t)\cos(2{\pi}f_{0}t)$$ where I found the Fourier transform to be $$ \begin{align} X(f) & \triangleq \mathfrak{F}[{\Pi}_{a}(t)\cos(2{\pi}f_{...
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6answers
8k views

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

In mathematics you can take the double derivative, or double integral of a function. There are many cases where performing a double derivative models a practical real-world situation, like finding the ...
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2answers
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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 ...
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4answers
1k views

Compression algorithms specific to complex signals

I am looking for (lossy or lossless) compression algorithms dedicated to complex signals. The latter could be composite data (like the left and right for stereo audio), a Fourier transformation or an ...
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3answers
294 views

Phase change rate of human speech

I have a .wav file of human speech, sampled at 48kHz, with useful signal up to 5kHz, and almost no noise. If I do Hilbert transform in MatLab, I get the Analytic signal: $$ s_\mathrm{a}[n] = s_\...
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1answer
8k 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 ...
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5answers
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Why is Scipy implementation of Hilbert() function different from Matlab implementation of the function?

I am trying to fit Hilbert envelop to a high frequency ultrasonic signal of frequency 250 KHZ and sampling rate 12000000. Raw signal looks like below: . I used hilbert() function from scipy.signal ...
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1answer
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Hilbert transformer and minimum-phase

I can't find out if it possible to compute the minimum-phase response corresponding to a given magnitude response using a Hilbert transformer. Is that possible? When I write Hilbert transformer I ...
3
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1answer
810 views

Discrepancies between FFT-based Hilbert Transform and FIR filter results

I compared the results of Hilbert Transform as provided in scipy.signal.hilbert() (which is uses I/FFT as you can see in the source code) with its approximation implemented as FIR filter using coeffs ...
2
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1answer
180 views

Given Gain function, how to design a causal, stable and minimum phase IIR filter?

I am given $|H(\omega)|$, I wonder if minimum phase stable causal filter is unique and how to calculate it.
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2answers
4k views

Hilbert transform pair proof

I am looking for the proof that the Hilbert transform of $\displaystyle\frac{\sin(at)}{at}$ is given by $$\frac{\sin^2(at/2)}{at/2}.$$ How do we prove this? This is a $\operatorname{sinc}(at)$ ...
2
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1answer
197 views

Hilbert transform from analytic signal

Show that the Hilbert transform of $h(t) = m(t) \cos(2 \pi \nu_c t)$ is $$\hat{h} (t) = m(t) \sin(2 \pi \nu_c t),$$ where $m(t)$ is a real valued, band-limited function (i.e. we have Fourier ...
2
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1answer
47 views

Conditions for analytical signal reconstruction with the Hilbert Transform (HT)

I'm new to the Hilbert Transform, I was reading the paper: "SISAR Imaging - Radio Holography Signal Reconstruction Based on Receiver-Transmitter Motion", and the next sentence was written in the paper:...
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1answer
102 views

Why does the Hilbert-Huang transform not suffer from the uncertainty principle, and what are the implications of this?

I have been studying the Hilbert-Huang transform, which I understand is a frequency analysis technique that uses the adaptive IMFs basis components to decompose a signal using EMD. I understand that ...
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4answers
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Design Hilbert filter at matlab (pure 90 phase and magnitude 0db)

I need to design a filter able to take a measurement of alternate current and shift the phase of the input by 90°. The filter should work between 40 and 60Hz and at this range should have unity ...
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0answers
663 views

Hilbert Transform, filters - two different phase graphs

Relationship between magnitude response and phase response for minimum phase is: Phase plots are obtained from Hilbert transform of real magnitude values. Input to Hilbert transform was a vector (...
2
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1answer
7k views

How to plot the Hilbert Spectrum in Hilbert-Huang transform?

I'm working on integral transforms for a science initiation project and i got to do a work on the Hilbert-Huang transform. I've seen on the internet that, after one found the IMFs with the EMD method,...
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1answer
245 views

Computational burden of EMD/Huang-Hilbert vs wavelet

I am working on an online application of signal processing and pattern recognition. It involves sampling the signal at 2 MS/s, extracting features and classifying. My classifier has pretty good ...
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2answers
116 views

Fourier Transform of sampled reflectance measurements

Goal: Calculate the complex index of refraction ($\hat n = n +jk)$ from reflectance measurements. Data: Reflectance measurements for various materials were taken with a FTIR (Nicolet™ iS50 FTIR, ...
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1answer
53 views

minimum-phase phase via Hilbert transform returned values

Following my previous question: HRIR Minimum phase I managed to compute the minimum-phase phase of a FIR filter (in my particular case, HRTF filters). However I am not sure of the phase values ...
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1answer
712 views

Hilbert transform properties

Here Its says Hilbert transform is a non-causal,linear,and time-invariant system How can I prove it mathematically? wikipedia says the input output relation like this $$\boxed{y(t)=\frac{1}{\pi}\...
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0answers
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Does the EEMD (Ensemble Empricial Mode Decompsition) also reduce the sensitivity to noise?

EEMD (Ensemble Emprical Mode Decomposition) was introduced to improve the problem of mode mixing and mode splitting of the classical EMD (Emprical Mode Decomposition). How much does the EEMD reduce ...
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1answer
579 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 ...