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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117 views

One-sided waveforms in both time and frequency?

Can a complex signal be one-sided (causal in time and positive only spectrum in frequency) in both domains? I understand that a function can't have finite support in both domains, but what if both ...
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Cut-off frequency for Low-pass filters in Arctangent Demodulation

According to literature, the arctan-demodulation method commonly used in Radio-frequency radar systems is the one shown below: Is there a rule of thumb regarding the cut-off frequency of these Low-...
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How an algorithm for measuring the analytic signal (Hilbert transform) gives us complex value at the end?

I have a question about the following codes for measuring analytic signal (Hilbert transform). Here,the time domain signal (x) is a real value signal. After making fft it becomes complex (X). Then it ...
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131 views

Implementing FIR Hilbert Transformer in Python

I want to implement FIR Hilbert Transformer in Python using window method. I'm new to digital signal processing so please point out to me all mistakes you notice. Ideal Hilbert transformer is ...
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47 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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104 views

Envelop detection using matlab hilbert function

I am trying to detect the envelope of a high-frequency signal (similar to below) using Matlab Hilbert function This is my output It generally follows the envelope, but there is a high-frequency ...
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66 views

Proof of Bedrosian's theorem

I was looking for a straightforward proof for Bedrosian's theorem which says the Hilbert transform of the baseband signal times the passband signal is the original baseband signal times the Hilbert ...
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31 views

Implementation of Hilbert Spectrum in MATLAB

I am trying to implement this equation on Matlab, where i have wj values in the form of an array, cumtrapz command of MATLAB implements this, but its confusing which way is exact. such as cumtrapz(t,...
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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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1answer
107 views

Negative instantaneous frequency with hilbert transform using scipy hilbert

When I produce a chirp signal with a duration of 2 sec, sampling frequency of 200Hz, with frequencies ranging from 20Hz-100Hz, I get negative instantaneous frequencies using the scipy(Python) Hilbert ...
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How does the Hilbert Transform extract the in-phase and quadrature phase components of a real passband signal?

I am taking an intro to radar signal processing course and we are discussing the Hilbert Transform and how it take a real input and its output is analytically complex. I'm trying ) how a radar ...
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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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Validity of an argument that two transfer functions are minimum-phase based on their ratio being minimum-phase

Update I think the essence of my question below is this: If the ratio of two transfer functions may be represented exactly as a minimum-phase filter (MPF) plus a pure delay (in the title, I simply ...
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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
87 views

Relation between Fourier phase and Analytic Signal Phase

Do you know if there is a relation between the phase of the Fourier Transform and the phase of the Analytic signal? I mean, if i have a signal s(t) then... ...
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Something like Hilbert Transform to obtain arbitrary Phase Shift? [duplicate]

I was wondering if there is something like a Hilbert Transform but that can implement an arbitrary phase shift to every frequency component. I mean, I know that the magnitude response of a "...
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Difference between Analog IQ sampling and creating IQ digitally

In the context of wideband receiver design, what are the advantages and disadvantages of Analog IQ sampling vs creating IQ digitally (with Hilbert transform)? Why do we use different ADCs to create ...
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Extrapolation of band-limited frequency data

I'm now studying "How to do accurate transform from band-limited frequency data specifically S-parameter data of high speed interconnect to the causal impulse response in time domain. There are ...
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1answer
207 views

Hilbert transform in the frequency domain

As I know, the Hilbert transform $$ H(x(t))=\frac{1}{\pi t}\star x(t) $$ in time domain is equal to $$ -j \operatorname{sgn}(f) \cdot X(f) $$ in frequency domain. so I tried simple example using ...
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Magnitude of the analytic signal

It's well known that magnitude of the analytic signal for narrowband signals gives the envelope. For example we can demodulate AM signal by abs(hilbert(s_AM)) in ...
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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
253 views

Design causal FIR filter to approximate hilbert transform

I'm attempting to design an FIR filter that approximates the Hilbert transform in order to get a $90^{\circ}$ phase shift and unity gain. However, I'm having trouble adjusting the filter to make it ...
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Obtain Envelope and Pitch curves of my Singing Voice

I wish, in real time, to hum into a mic and produce via dsp the envelope and pitch of what I am humming, before outputting these two signals to my analog synth. This synth takes a gate and a cv signal....
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Terminology for instantaneous phase of magnitude component of complex signal

In my field, we deal with data that are originally complex-valued. Typically, researchers convert their data from real + imaginary to magnitude + phase, and then discard the phase data (i.e., we ...
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292 views

Inverse Hilbert Transform

The Hilbert Transform of a 1D/real-valued vector signal returns the analytic signal, x, from a real data sequence, xr. The analytic signal x = xr + jxi has a real part, xr, which is the original data, ...
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Finding causal impulse response given the imaginary part of the frequency response

I understand that I would need to calculate inverse Discrete Time Fourier Transform (iDTFT) to find $h(n)$. Since $h(n)$ is real, iDTFT of the imaginary part of $H(e^{j\omega})$ gives the odd part of ...
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How to I obtain the real part of a an Analytic Signal when the real and imaginary parts have been delayed by different amounts

A real audio signal (0-3 KHz) is processed by a Hilbert filter to obtain the Imaginary component. Both the real signal and the imaginary are delayed but by different amounts. I want to obtain the real ...
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48 views

Different number of modes while performing the EEMD (Ensembled Empirical Mode Decomposition)

I am performing an Ensemble Empirical Mode Decomposition (EEMD). I wrote a MATLAB routine to perform the EMD. I noticed that when adding white Gaussian noise to the input signal, sometimes I obtain a ...
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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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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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Question about Hilbert transform of a cosine signal

In the paper entitled "On instantaneous frequency", it is claimed that the Hilbert transform of a signal in the form of $A(t)cos(\phi(t))$ would result in $A(t)sin(\phi(t))$, where $A(t)$ is ...
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Question about Hilbert transform

Hilbert transform of a function $g(t)$ which is defined in time domain, would result in another function in time domain. Is there any other transformation like Hilbert that the results be in time ...
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Is $ H\left\{x_h(t)\right\} = H\left\{x\left(t-\frac{\pi}{2w_c}\right)\right\} $ where $H$ is Hilbert transform

Accordind to my understanding of the following: $$H\left\{X(f)\right\} = -j\;sgn(f)\; X(f) \qquad(1)$$ my work so far: since $ x_h(t) = x\left(t-\frac{\pi}{2w_c}\right)$, Their Hilbert ...
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Hilbert transform with scipy.signal

I'm coding with python and I just started to use the Hilbert transform from scipy.signal. Consequently, to check the result I got I tried to verify a property of ...
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1answer
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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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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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141 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
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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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120 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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Wind Turbine Vibration Analysis: Which approach?

I'm analysing vibration data from 4 wind turbines (WTs). 8 different sensors are sampled at 25.6 kHz for 10 seconds once a day. I have data from around 400 days (intervals). The plot underneath is for ...
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1answer
106 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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359 views

realtime software 90 degree phase shift a sinusoidal signal

I would post this to stack overflow but it seems to me more like a signals and systems problem, which EE's thrive on. I need a realtime system implemented in software that can generate a sinusoid ...
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1answer
556 views

Getting hilbert transform of IQ signal

Im new to communications so this may be a stupid question, but I am somewhat confused. I am trying to train an automatic modulation classification (AMC) algorithm on IQ data from the RadioML dataset. ...
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Hilbert transform Use as a Single Sideband Frequency Translator in Analog communication

How Hilbert transform helps us in communication? What is the practical significance of it? Specifically how is the Hilbert Transform used to create single side-band frequency translators?
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Obtain I/Q Components from a Real Signal On the Fly - Hilbert Transform or Digital Downconversion?

I'm planning to build a data acquisition system for a software-defined radio receiver. Basically, it just uses an ADC which samples an analog signal and send the signal to a processor. And then a ...
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1answer
857 views

How do I convert a sampled complex signal to a real signal?

I’m writing a Soapy SDR plugin for the FL2K-SDR. Soapy SDR expects plugins to produce and consume IQ samples. However, the FL2K-SDR driver consumes only real samples. I know you can convert a real ...
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121 views

Relationship between real and imaginary part of a real-valued and causal system

I have one question about the real part of a real-valued and causal system with the imaginary part of its Fourier transform given by $$\textrm{Im}\big\{X(e^{j\omega})\big\}=3\sin(2\omega)-2\sin(3\...
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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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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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Noise sensitivity of the (classical) Empirical Mode Decomposition routine

I tried to apply a MATLAB Empirical Mode Decomposition routine to denoise a signal, basically retaining only the last IMFs, with a criterion based on the mode energy. To validate the routine, I have ...