Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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°).

0
votes
1answer
21 views

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 ...
1
vote
1answer
81 views

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: ...
5
votes
1answer
100 views

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 ...
0
votes
1answer
43 views

How to implement Discrete time FIR Hilbert transformer filter?

I want to implement FIR Hilbert transformer filter in Matlab.
0
votes
2answers
61 views

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....
-1
votes
1answer
66 views

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 ...
1
vote
0answers
152 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 ...
1
vote
1answer
37 views
2
votes
2answers
217 views

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 ...
0
votes
1answer
58 views

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 <=...
1
vote
1answer
145 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 ...
1
vote
3answers
181 views

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 ...
1
vote
2answers
106 views

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 ...
0
votes
3answers
96 views

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 ...
0
votes
0answers
44 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,...
2
votes
3answers
196 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_\...
2
votes
1answer
224 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 ...
0
votes
1answer
100 views

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 ...
0
votes
0answers
88 views

Hilbert transform spectrum and discrete impulse response

The impulse response of a filter implementing the hilbert transform is $ f_H(t)=\frac{1}{\pi t} $ (see hilbert transform on wikipedia) which seems to be kind of a "smooth" function as long as $ t \neq ...
0
votes
1answer
126 views

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 ...
3
votes
1answer
253 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 ...
1
vote
2answers
443 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 ...
1
vote
0answers
228 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 ...
0
votes
0answers
158 views

Hilbert Transform - Convolution of Discrete Frequency Sweep

I am hoping to recover the phase and then the time-domain of a received signal. I performed a frequency sweep at various positions from 2.41 GHz to 2.49 GHz in steps of 100 MHz. There are no time ...
1
vote
3answers
82 views

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'...
0
votes
0answers
28 views

Stress analysis via Voice Signals (EMD, Hilbert Transform etc.)

I have several questions about our graduation project's voice signal processing part: 1) Is it necessary to use Hilbert Transform to get IMF's after the execution of EMD with input of WAV. file? 2) ...
0
votes
2answers
346 views

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 ...
3
votes
3answers
2k views

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 ...
0
votes
0answers
202 views

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 ...
6
votes
2answers
876 views

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{\...
1
vote
0answers
34 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 ...
2
votes
1answer
77 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 ...
0
votes
0answers
45 views

equivalency between cross-spectrum and covariance of band-limited analytic signals

I have worked out through experimentation that for phase-shifted pure sinusoids $x(t)$ and $y(t)$ of frequency $f$, the (complex) cross-spectrum $\Gamma_{x,y}(f)$ is numerically equivalent to the ...
1
vote
1answer
330 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}\...
0
votes
2answers
457 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 ...
1
vote
1answer
435 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 ...
1
vote
1answer
103 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 ...
0
votes
1answer
186 views

What is proof of Basic Hilbert Transform?

Attached is the question. Need to find the output for signal x(t).
1
vote
1answer
754 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!
0
votes
1answer
94 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 ...
3
votes
1answer
288 views

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 ...
2
votes
1answer
90 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 ...
4
votes
1answer
494 views

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 ...
1
vote
0answers
63 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 ...
3
votes
1answer
389 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 ...
3
votes
0answers
194 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 ...
1
vote
0answers
475 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 ...
1
vote
0answers
130 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,...
1
vote
2answers
182 views

Why does Hilbert filter distorts the shape of the signal?

If all the harmonics composing a the signal are shifted by the same amount, this would be the same as sampling later or earlier in time. I think. Take a simple pulse train as an example. If Fourier ...
2
votes
1answer
157 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 ...