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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IQ demodulation from specific rate

We have an acquisition hardware in our lab that acquires and digitizes data from a source generating band-limited signal in the MHz range. It samples the signal at a rate of 4 times the center ...
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1answer
154 views

BER based transmitter gain

Are there any direct relation formula between BER and Transmitter gain. The higher the transmitter gain is, the better the BER performance is. In here, I want to plot graph for the BER based on ...
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429 views

Complex bandpass filter giving quadrature signal

I have found a technique detailed on page 34 & 35 of this thesis. In this, the author states a complex bandpass filter can be derived by first making a prototype real valued IIR filter, then ...
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1answer
613 views

Instantaneous Frequency Estimation by Hilbert Transform - Theoretical Justification and Proof

I would like to better understand why the instantaneous frequency estimation by Hilbert transformation works (and especially why it doesn't work / lead to precise results in many cases). The ...
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827 views

real refractive index from Kramers Kronig relation

I have a measurement of the complex part of the refractive index $k$ (where the refractive index is $m = n + i\,k$) measured at a nonlinear grid of wavelengths or frequencies that span several orders ...
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0answers
411 views

Connections between quantum field theory and signal processing

I've been working with quantum field theory on the basis of it being a stochastic signal processing formalism for a number of years. The projection to fourier components within the forward light-cone ...
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715 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 (...
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1answer
232 views

Does the instantaneous frequency contradict the uncertainty principle?

The uncertainty principle states that there is a trade off between time and frequency. So, finding frequency components at specific time is impossible. However, the instantaneous frequency measure the ...
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25 views

How to quantify a deterministic system?

So let me layout my question and the thought process on solving it. Say, we have some system, and we want to see how deterministic the system is. By that I mean, I mean if I put some signal (real ...
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1answer
79 views

Symmetries of analyticity / zero self-correlation

I seek to understand symmetry properties of analytic sequences, without referring to frequency domain: what criteria must a complex sequence $x[n]$ satisfy to be analytic? Framed alternatively, such a ...
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2answers
107 views

Nyquist Frequency and Window Length

The Nyquist theorem states that the sampling rate must be twice the highest frequency to be observed. How does the length of the interval play into this relationship? The main resource that I found ...
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0answers
51 views

Hilbert Transform on split datastream produces phase flip

this is my first post here! I'm trying to do phase correction on a signal from a linear CCD (2048 pixels, 10bit per pixel, 250kHz linerate) in an FPGA. Therfore I need to generate an analytical ...
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30 views

How to construct marginal Hilbert spectrum

Suppose $f$ is a signal of duration $t_d$ sampled each $0.01 sec$. After employing empirical mode decomposition (EMD) to $f$, $n$ number of intrinsic mode functions (IMF) would be extracted. Using ...
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736 views

Plotting Hilbert and Marginal Spectra in Python

I am using the PyEMD package for python 3.6. I want to create a 2d plot of hilbert spectrum (x: Time, y: Frequency, Colorbar: Amplitude) and the Marginal Spectrum (x: Frequency, y: Amplitude) I can ...
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55 views

Discrete Hilbert transform enhancements?

Consider the Discrete Hilbert Transform, which takes a sequence $u[n]$ defined on the interval $-M\leq n\leq M$ and returns the discrete convolution $$\tilde u[n]=\sum_{i=-M}^Mu[i]h[n-i]$$ where the ...
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125 views

Compute hilbert transform from DCT- FFTW3 REDFT00

My problem is similar to this but not the same. Edit: Here is a description of Neumann boundary conditions for differential equations: Neumann-type boundary conditions means derivatives are ...
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0answers
997 views

Hilbert Huang Transform: Negative value in instantaneous frequency

I'm working on Hilbert Huang Tranform and have a question on computation of instantaneous frequency. I'm using HHT toolbox by Patrick Flandrin for EMD and computing IF manually. Problem is that I am ...
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177 views

How to get the phase offset from the instantaneous phase

The phase components of a signal that they are got from the Fourier Transform, are simply, the phase offset of each sinusiod. Which is the $\phi$ in equation $1$. However, in case of Hilbert transform,...
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994 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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187 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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1answer
119 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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34 views

Get Hilbert marginal spectrum with emd package in python

I want to get the Marginal Hilbert Spectrum in Python using the emd package. You can estimate the Marginal Hilbert Spectrum as where, and A(ω,t) is the time-dependent amplitude modulation and ω ...
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38 views

How to prove that the integral of Hilbert transform is not equal to the Hilbert transform of the integral?

To prove that $\int_{-\infty} ^\infty \mathcal{H}(g(t))(t)\text{d}t\neq\mathcal{H}(\int_{-\infty} ^\infty g(t) \text{d}t)$, where $\mathcal{H}(\cdot)$ is the Hilbert transform operator My approach to ...
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77 views

Symmetries of discrete analytic signals

Defining "analytic" as $x_a[n]$, where $X_a[k] = \text{DFT}(x_a[n])$, and $$ X_a[k < 0] = 0, \tag{1} \label{1} $$ what time-domain properties, such as symmetry or norm, are guaranteed for ...
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88 views

Instantaneous amplitude of a constant frequency sine wave?

I am playing around with the Hilbert transform using Python's scipy.signal.hilbert package to better understand what the various instantaneous properties are given different input signals. One input ...
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94 views

Decoding images from NOAA satellite APT signals

I've been working on a decoder for these APT images for a while now. I started years ago, in Python, and was able to implement a working decoder quickly. A few months ago, I came back to the project ...
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1answer
29 views

Implementing an L-System conversion from R2 to R1 for symmetric, square matrices

I have been reading for some time about L-Systems, and specifically the Hilbert Space filling curve. I am interested in writing a function to convert upper-triangular matrix coordinates into an ...
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1answer
70 views

Is there a way to break down a signal into its respective phases (4 in this case) to be later analysed individually

Is there a way to extract amplitude information but over 4 phases of the same frequency. That is, if the frequency is known could I extract amplitude peaks (between given values)in the time domain in ...
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27 views

Phase of complex nonsinusoidal signals

What's the best method for calculating phase of complex nonsinusoidal signals? I've tried using Hilbert transform, but I've found that my results change drastically depending on the amount of data I ...
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62 views

Bandwidth in the filter-Hilbert method

I understand that the Hilbert transform on broadband data produces uninterpretable results. And so we first bandpass the data, and then run the Hilbert transform. My question is, how wide can the ...
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106 views

Audio experiment with intermodulation by multiplying two analytic signals

1) First, I describe intended processing with a basic case: Let's say on left channel I have a sin wave with frequency F1, and constant amplitude A1. Then on right channel a sin wave with frequency ...
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145 views

Passband filter before Hilbert transform

I have a .wav file of human speech sampled at 48kHz. Before making the analytic signal with: hilbert(s_real) lets say in range 200 - 3,500 Hz, I probably need to do pass-band filtering, say 300 - 3,...
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4k views

Hilbert Transform - C or C++ code implementation

For a minimum phase system relationship of magnitude response to phase response is: In the search for C code implementation I have found a ht.c file on www.physionet.org. However, this code specifies ...
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73 views

What is the relationship between signal and its analytical version?

Hilbert transform is used to transfer signal into analytical signal. But why after the transform, the envelop and instant frequency (if the signal is monogenic) can be calculated. What is happened in ...
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386 views

Problem executing Hilbert transform on $x$-$y$ plot in MATLAB

I have a wav signal I have imported into MATLAB, and I would like to find its envelope. I want to do this via the Hibert transform. But whenever I try to find the Hilbert transform of the signal I ...