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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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### Physical meaning of a signal with 4 IMF?

If a signal is composed of four implicit mode functions, where the last one is a constant residue, does the instantaneous frequecy of the signal have physical meaning?
9 views

### 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 ...
32 views

### 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 ...
63 views

### Hilbert transform with strange behavior

I am taking the Hilbert transform of a signal in Matlab and I don't understand part of the result. Below are the complete signal $z(t)$ and phase $\phi(t)$, obtained with ...
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### Is there any practical application for performing a double Fourier transform? …or an inverse Fourier transform on a time-domain input?

In mathematics you can take the double derivative, or double integral of a function. There are many cases where performing a double derivative models a practical real-world situation, like finding the ...
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### Get FIR Hilbert coefficients from Matlabs envelope() function

How can I get the used Hilbert filter coefficients from the Matlab function envelope()? ...
63 views

### Non-Linear, Non-Stationary spectral analysis methods! When and where?

I have been reading about non-linear non-stationary signal analysis methods and it seems to do this type of analysis the go-to method is the Empirical Mode Decomposition (EMD), then Hilbert Transform (...
161 views

### Python Hilbert does not seem to calculate the envelope

I am following the example from: https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.hilbert.html And although I can replicate their example, it does not work with my data. This is the ...
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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 ...
76 views

### 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 ...
64 views

### 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 ...
34 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 ...
366 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: ...
684 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 ...
262 views

### 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....
111 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 ...
383 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 ...
37 views

### How to prove $\int_{-\infty}^{\infty}x^2(t)dt=\int_{-\infty}^{\infty}\hat{x}^2(t)dt$ where $\hat{x}(t)$ is the Hilbert Transformation of $x(t)$ [closed]

$\hat{x}(t)$ is the Hilbert Transform of $x(t)$. Can anybody help me proving the above.
361 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 ...
73 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 <=...
277 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 ...
543 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 ...
128 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 ...
321 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 ...
75 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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### 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 ...
101 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 ...
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}\...
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 ...