# 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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### 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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### 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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### 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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### Pre-envelope of an FM signal $s(t) = A\cos[\omega_ct + B\sin(\omega_xt)]$ [duplicate]

I want to ask a question about pre-envelope of an FM wave: $$s(t) = A\cos[\omega_ct + B\sin(\omega_xt)]$$ Can someone explain briefly how we calculate the pre-envelope of this signal?
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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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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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### What is the origin of the line shape in a Marginal Hilbert Spectrum

When calculating the marginal Hilbert spectrum of a discretely sampled harmonic oscillation (sine wave), I have found that the peak in the spectrum has a roughly Lorentzian line shape, albeit ...
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### Why does the Marginal Hilbert Spectrum of an anharmonic oscillator have two peaks?

I've been looking at the marginal Hilbert Spectra of both the simple harmonic oscillator and the anharmonic Morse oscillator. I have found that while the SHO has a marginal spectrum with a single and ...
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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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### Calculating Marginal Hilbert Spectrum across IMFs using mhs() in MATLAB

I'm working on an EEG dataset from which I need to extract the power of five different frequency bands. I'm doing this by performing Hilbert Transform on the ICA activations from performing channel-...
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### What is the relationship between a signal's Marginal Hilbert Spectrum and Fourier Spectrum?

I am looking at the differences between Marginal Hilbert spectra and Fourier spectra and I was wondering what the mathematical relationship is between them and under what conditions they become ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### Not able to reach minimum phase using Hilbert transform

My problem is pretty simple, I've designed a magnitude response and I would like to find the corresponding minimum phase filter. I'm using the code below and unless there is a bug my eyes don't want ...
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### Ideal Discrete Time Hilbert Transformer with constant group delay

Let's assume we have an ideal discrete time Hilbert Trasnformation system (90-degree phase shifter) with a frequency response over one period: H(e^{jw}) = \left\{ \begin{array}{ll} -j & \...
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### Fourier Transform of the Hilbert Transform of cos(t) (using Fourier time-shifting property)

If $x(t)=cos(t)=\frac{1}{2}e^{jt}+\frac{1}{2}e^{-jt}$, then $X(\omega)=\pi \delta(\omega-1)+\pi \delta(\omega+1)$. If \$y(t)=cos(t-\frac{\pi}{2})=\frac{1}{2}e^{j(t-\frac{\pi}{2})}+\frac{1}{2}e^{-j(t-\...
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### How does the power spectrum of the amplitude envelope depend on its underlying carrier frequency?

when looking at the amplitude envelope of an oscillation (see red trace in Figure below), it seems to me as if the frequency content of the envelope depends on the the frequency of the underlying ...