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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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Hilbert transform of symbolic function in Matlab

I have a signal of the form $f(\omega,x) = g(\omega) e^{i \omega (x +c)},$ for $g: [\omega_1 , \omega_2] \rightarrow C, \, x\in R$ and some constant $c.$ I want to get the function $$ F (\omega,x) = \...
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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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45 views

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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What is k and n in this Discrete Hilbert Transform formula and how to use it with a time series?

I have a time series and I need to find the Discrete Hilbert Transform of that. This paper says that about the Hilbert Transform. Suppose I have a time series f(t)...
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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 ...
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Hilbert Transformer processing block by block

I am processing audio and trying to obtain a 90º phase shift when processing block by block. I have implemented a Hilbert Transformer (from Lyon's 3rd. Ed. & MATLAB). MATLAB code below (I believe ...
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How to handle edge effects with EMD (HHT)?

In the application of the Huang Hilbert Transform (HHT) (or aka EMD, Empirical Mode Decomposition), there is the notable challenge of handling the edges (boundaries) of the signals; as noted in the ...
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Quadrature component - condition on equivalent lowpass signal

I have a question regarding the equivalent lowpass signal $x_{LP}$ of a bandpass signal $x(t)$ and the quadrature component. I'd like to find a condition on $x_{LP}(t)$ and $X_{LP}(f)$ such that the ...
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Hilbert Transform in C provides possibly strange results

I am calculating some signals that depend on the Hilbert Transform and, after following various guides online and SO, my function looks like this: ...
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Hilbert Transform of a sine Function with Quadratic Argument $\sin(At^2 + Bt + \pi/4)$

I am looking for the Hilbert transform of the following function: \begin{equation} \mathcal{H}\bigg\{ \sin\Big(At^2 + Bt + \frac{\pi}{4}\Big) \bigg\} \end{equation} where $A$ and $B$ are constants ...
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How to implement Discrete time FIR Hilbert transformer filter?

I want to implement FIR Hilbert transformer filter in Matlab.
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Phase shift of all-pass bi-quadratic filter

Does anybody know how to derive this phase function for that all-pass filter structure? Many papers re-print them, and corresponding chart as well. But nobody mentions that at normalized frequency 0....
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Digital Derivative

I need to calculate the derivative of a digital signal (sinusoidal). In one of the papers they have mentioned Gilbert transformation is used to calculate the derivative. But I have searched in the net ...
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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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Can the instantaneous frequency be always derived from an analytic signal?

Instantaneous frequency can be defined as a derivative of an instantaneous phase of an analytic signal which can be nicely seen in practice in this example from Scipy's documentation. But it seems ...
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Extracting positive frequencies of discrete-time signal

Convolution in the time domain is the same as multiplication in the frequency domain. My data is sampled at 200 Hz, which means that the Nyquist frequency is 100 Hz, and all frequency content is <=...
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207 views

Plotting Hilbert Spectrum from Hilbert Huang Transform

Before anyone calls it a repeat post from past posts. I'd like to point out I've read all of those; however, I have questions on making a hard coded version of the hilbert spectrum. I do indeed have ...
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Denoising a signal

I'm starting hydraulic experiments, where I'd have to measure velocity in an unsteady flow with a device called Acoustic Doppler Velocimeter. In DSP terms, I'd have a nonstationary signal in a shape ...
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Inverse DFT of $-i\pi \text{ sgn}(f)$

the following MATLAB code should plot the iFFT of $-i \pi sgn(f)$ which has to be $\frac{1}{t}$ in continuous time. As you can see, the output kinda looks like a 1/x function, but is modulated. How ...
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Phase response of a FIR Hilbert transformer

The graph below shows a linear phase response of FIR Hilbert transformer with a constant diff of -0.06135923. I am not sure if I understand the concept of the phase response correctly, but as the ...
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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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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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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 ...
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The Instantaneous Frequencies from IMF Aren't Consistent with Its Spectrum

I'm trying to find the instantaneous frequencies for one of the Intrinsic Mode Functions (IMFs) I extracted from the original signal using Hilbert-Huang Transform. So, I got the following spectrum for ...
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Measuring acoustic phase difference between two receivers

I am trying to measure the acoustic phase difference between two sensors 30cm apart each other. The sampling frequency is 20kHz, and my interest frequency is about 1700 Hz. The below is how I ...
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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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542 views

Hilbert transform of unit step function

How to calculate Hilbert transform, if it exists, of the signals like $u(t)$, $sgn(t)$. What properties should a function satisfy for existence of Hilbert transform. Absolute integrability of a ...
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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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Demonstrate that $x(t)$ and $\hat{x}(t)$ are orthogonal

I have to demonstrate that a function $x(t)$ and his Hilbert's transform are orthogonal, it is said: $$\int^{\infty}_{-\infty} x(t) \cdot \hat{x}(t) dt = 0$$ I have tried the exercise using Parseval'...
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Extracted envelope via Hilbert Transform is tracking the signal

I am trying to extract the envelope of the signal shown in blue, which is the low-pass filtered output of a second-order system. Low-pass filtering was done in order to reduce measurement noise. To be ...
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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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Hilbert Spectrum vs. STFT

If I wanted to plot a spectrogram of a signal, I would by default use the Short Time Fourier Transform. However, the Hilbert transform does something similar: it lets us calculate instantaneous ...
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Hilbert transform of sinusoid — apparent contradiction

The arrow "$\xrightarrow{\mathcal H}$" denotes a Hilbert transform: $$\cos(\omega t)\xrightarrow{\mathcal H} \sin(\omega t)$$ happiness. But $$\cos(\omega t) = \cos(-\omega t) \xrightarrow{\...
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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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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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400 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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545 views

Hilbert transform with a sliding window

I have a input voltage signal which has disturbances present in it. I am actually discretizing the input signal into say $1300$ samples and taking Hilbert transform of the signal by taking $N$ samples ...
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591 views

Hilbert Transform of an FM Signal

The Hilbert Transform of an Amplitude Modulated signal returns the envelope of the signal. What does the Hilbert transform of a Frequency Modulated signal return? How can I use the Hilbert Transform ...
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125 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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221 views

What is proof of Basic Hilbert Transform?

Attached is the question. Need to find the output for signal x(t).
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852 views

In-Phase and Quadrature components of low-pass equivalent of a band-pass signal?

I was wondering what is the physical meaning of IN-PHASE and QUADRATURE components? In the context of low-pass equivalent of band-pass signals. Any help is appreciated!
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101 views

How to solve this equation (about complex envelope)?

I am a beginner of digital signal processing. In my research project, I need to calculate this equation which is below. $$ e(t) = \Re \Big\{z(t) \, e^{j \omega_0 t} \Big\} $$ I know the $e(t)$ and I ...
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Struggling to implement this simple algorithm for ECG wave delineation

I'm trying my best but my maths isn't good enough to implement the algorithm as outlined in this paper in python. It for detecting the onset and offset of a wave on an ECG, and it's using a well ...
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92 views

Link between LTI systems and square-integrable functions eigenfunctions

I'm trying to study on my own a little bit of functional anaylsis. I try to summarize the main concepts (without being rigorous) that I learnt. Correct me where and if I'm wrong. In Hilbert spaces ...
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Conditions for which the Hilbert transform returns a correct phase

I'm quite new to signal analysis, and I'm currently trying to understand under which conditions a Hilbert transform can be used to compute the correct instantaneous phase and enveloppe of a given ...
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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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520 views

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 ...
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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 ...