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7
votes
3answers
73 views

How to build a phase shifter with arbitrary phase shift

Fred, a DSP engineer, goes to his favorite DSP store to do some shopping. Fred: Hi, I'd like to buy a phase shifter. Shop assistant: Hmm, what exactly do you mean? Fred: Well, you know, if you put ...
0
votes
1answer
19 views

Demodulating upper sideband (USB) signals

A modulating signal $m(t)= \sin(2 \pi \nu_m t)$ is transmitted via a carrier of frequency $\nu_c$ using upper sideband (USB) modulation. Show that the USB modulated signal can be demodulated using a ...
3
votes
2answers
58 views

Useful natural “Hilbert-like” $n$-uples and $n$-fold "analytic signals

If $\mathcal{H}$ denotes the Hilbert transform, the analytic signal of a signal $x(t)$ is $$x_a(t) = x(t) +\imath \mathcal{H}(x(t))\,.$$ The real and imaginary parts form Hilbert pairs. Are there ...
0
votes
2answers
40 views

Hilbert transform linearity

Explain why the Hilbert transform of $f(t)=\operatorname{sinc}(at) \cos(2 \pi \nu_c t)$ is $$\hat{f} (t) = \operatorname{sinc} (at) \sin(2 \pi \nu_c t),$$ where $0<a<\nu_c.$ Attempt: I have ...
0
votes
1answer
41 views

Hilbert FIR Filter for Q - Matching Filter for I

For an ultrasound application, I am collecting data from an ADC using high spec Altera FPGA which grabs data and can then do some DSP processing that would be otherwise too slow for a desktop to do. ...
1
vote
1answer
36 views

Hilbert transform from analytic signal

Show that the Hilbert transform of $h(t) = m(t) \cos(2 \pi \nu_c t)$ is $$\hat{h} (t) = m(t) \sin(2 \pi \nu_c t),$$ where $m(t)$ is a real valued, band-limited function (i.e. we have Fourier ...
1
vote
2answers
72 views

Hilbert transform pair proof

I am looking for the proof that the Hilbert transform of $\displaystyle\frac{\sin(at)}{at}$ is given by $$\frac{\sin^2(at/2)}{at/2}.$$ How do we prove this? This is a $\operatorname{sinc}(at)$ ...
-1
votes
1answer
33 views

Code for a wavelet based hilbert transform? [closed]

I normally implement the Hilbert transform using the Fourier transform. I have noise related issues I want to solve. Does anybody have an (apodized) implementation of the Hilbert transform handy, ...
1
vote
1answer
56 views

Very-short Hilbert transform FIR (or “recursive”) approximations

Hilbert transform is a quite sensitive topic here, since Gabor's paper, Theory of Communication, J. Inst. Electr. Engineering, London, 1946. Perhaps even more important than the Fourier transform. ...
1
vote
1answer
34 views

What is the relation between hilb and Hilbert transform in MATLAB?

In MATLAB, there is a command called hilb(n) which it says gives a Hilbert matrix of order n. Is this matrix the one used for ...
1
vote
1answer
55 views

Is Hilbert transform not defined for complex signals?

Is Hilbert transform not defined for complex signals? In MATLAB, the function hilbert ignores if you give a complex sequence as input. Why?
0
votes
1answer
87 views

Hilbert Transform from FFT?

For a school project, I'm working on a software-defined radio transmitter intended for the HF amateur radio bands. I'm planning to support SSB transmission with the formula $$f(t) = m(t) \cos(2\pi f_\...
1
vote
1answer
101 views

Relationship between the Real and Imaginary parts of a LTI causal system

Prelude I am writing an elaborate text on the relationship between the real and imaginary parts of a LTI causal system and how stability, causality and analyticity imposes various constraints on its ...
0
votes
1answer
50 views

Pre-envelope of ${\Pi}_{a}(t)\cos(2{\pi}f_{0}t)$

I want to find the pre envelope of $$x(t) = {\Pi}_{a}(t)\cos(2{\pi}f_{0}t)$$ where I found the Fourier transform to be $$ \begin{align} X(f) & \triangleq \mathfrak{F}[{\Pi}_{a}(t)\cos(2{\pi}f_{...
0
votes
1answer
27 views

Given the absolute value of a function, find hilbert pairs that make it up

This might be a solved problem (or a known unsolved problem) because it is related with finding a causal signal that has a desired magnitude response. $$F(f)=R(f)+iI(f)$$ $$F(f)=R(f)+i \int^\infty_{-...
0
votes
1answer
20 views

Pulse shaping and Baseband filtering

I'm slightly confused about baseband pulse shaping. Let's assume I have a complex data vector in an arbitrary complex constellation (QAM for example). I would like to pass this complex vector through ...
3
votes
2answers
98 views

Is the Hilbert transform computable “losslessly”?

The Hilbert transform is a procedure that can be used to perform a 90° phase shift on a signal. Is the computation of (a discretized) Hilbert transform a "lossless" process? I.e. it merely phase ...
0
votes
0answers
39 views

what is the difference between EMD and EEMD dealing with HHT?

I have been going through a lot of articles on HHT and EMD. I came across EMD and EEMD. I am not getting a clear picture on the differences between the EMD (Empirical Mode Decomposition) and EEMD (...
0
votes
1answer
64 views

Addition of two signals in polar coordinates

There is quadrature detector which receive radio signal and return its amplitude and instantaneous phase after performing hilbert transformation and transferring the signal to zero frequency. The main ...
0
votes
4answers
174 views

Design Hilbert filter at matlab (pure 90 phase and magnitude 0db)

I need to design a filter able to take a measurement of alternate current and shift the phase of the input by 90°. The filter should work between 40 and 60Hz and at this range should have unity ...
10
votes
6answers
855 views

Meaning of Hilbert transform

I understand the Fourrier Transform which is a mathematical operation that lets you see the frequency content of a given signal. But now, in my comm. course, the professor introduced the Hilbert ...
4
votes
2answers
178 views

Difference between these two digital down conversion methods

I can think of two possible methods of digital down conversion. One seems superior to the the other for most cases, but I'd like to get some DSP experts' comments on the practical differences between ...
0
votes
3answers
97 views

What is the minimum number of time points recommended for accurate instantaneous phase estimates using the Hilbert transform

I have two time series. The two series look like they follow the same function, but one appears to lag slightly behind the other. I would like to determine if there are phase differences between the ...
0
votes
1answer
119 views

Is real-time Hilbert envelope feasible?

Is the Hilbert envelope (analytic signal) feasible to be calculated in audio frames/blocks in real-time, when using FFT with windowing. What I'm specifically concerned with is that how does it not ...
0
votes
0answers
138 views

Signal reconstruction in FMCW radar

I am doing fmcw radar simulation. I have an output of mixer and from that I want to reconstruct the amplitude and phase of the signal. Therefore, I am taking hilbert transform and by the ...
1
vote
0answers
103 views

Hilbert transform of a bandpass signal

I have a bandpass signal x. I am taking hilbert transform of it. I want to reconstruct amplitude and phase of the signal.Therefore, i am using Hilbert transform. ...
1
vote
0answers
151 views

Hilbert Transform, filters - two different phase graphs

Relationship between magnitude response and phase response for minimum phase is: Phase plots are obtained from Hilbert transform of real magnitude values. Input to Hilbert transform was a vector (...
2
votes
3answers
1k views

Calculate and interpret the instantaneous frequency

I'm new to the principle of calculating the instantaneous frequency, and came up with a lot of questions on it. You find them all in a bullet-point list at the end of this text. The text might be a ...
0
votes
1answer
109 views

Filters - Hilbert Transform and Absolute Value of Magnitude Response

Following relationship between magnitude response and phase response for minimum phase: I have implemented in C++ code using the Hilbert Transform C code from file found online ht.c. However, I am ...
0
votes
0answers
670 views

Hilbert Transform - C or C++ code implementation

For a minimum phase system relationship of magnitude response to phase response is: In the search for C code implementation I have found a ht.c file on www.physionet.org. However, this code ...
2
votes
1answer
218 views

What is the reason for filtering out the negative frequencies of a signal?

I am reading this tutorial. Quoting the lines from the topic "Analytic signals and Hilbert transform filters": the corresponding analytic signal $ z(t)=x(t) + j {\cal H}_t\{x\}$ has the property ...
1
vote
1answer
1k views

How to plot the Hilbert Spectrum in Hilbert-Huang transform?

I'm working on integral transforms for a science initiation project and i got to do a work on the Hilbert-Huang transform. I've seen on the internet that, after one found the IMFs with the EMD method,...
0
votes
0answers
42 views

What is the relationship between signal and its analytical version?

Hilbert transform is used to transfer signal into analytical signal. But why after the transform, the envelop and instant frequency (if the signal is monogenic) can be calculated. What is happened in ...
1
vote
1answer
166 views

Generating I/Q samples from a real signal

My understanding is that if I have a real signal, it can be called as the 'I' component and its Hilbert transform can be called the 'Q' component. Due to the property of Hilbert transform, 'I' and 'Q'...
1
vote
1answer
264 views

How to extract IF (instantaneous frequency) from Discrete Hilbert Transform?

The continuous time Hilbert transform is $$\hat x(t) := x(t) + j\left( p.v. \left\{\frac{1}{t\pi} \ast x \right\} (t)\right)$$ where $$ \theta(t) = \tan^{-1}\left( \frac{ p.v. \left\{\frac{1}{t\pi} \...
0
votes
1answer
67 views

Instantaneous phase calculation problems

I am currently struggling with a problem when calculating the instantaneous phase of a wavefield using a 1D Hilbert transformation. The scheme is as follows. 1D Hilbert transformation of wave field $...
0
votes
2answers
170 views

The error between the theoretical value and the simulation value of imaginary part of the FFT results

As we know, a complex analytic signal can be obtained through Fourier transformation of a real value function, and the imaginary part can be reconstructed by Hilbert transform of real part. But I have ...
0
votes
1answer
38 views

Hilbert transformer's phase in .AC simulation

I don't understand this: the HT works as it should but in an .AC simulation, the phase shows up like this (wrapped): Why doesn't it look like a constant -90deg phase, like in a differentiator? ...
1
vote
0answers
220 views

Instantaneous power estimation by discrete hilbert transform - how far does it smooth?

In my research area, instantaneous power in a specific frequency band is commonly estimated by the following procedure: Apply a bandpass filter on the raw signal (e.g. 80-90Hz bandpass). Estimate ...
2
votes
1answer
366 views

Analog Hilbert transformer

I know the FIR approach, I have seen IIR, to, but I'd like to know if it's possible to implement a Hilbert transformer in analog domain, i.e. with integrators instead of delays. Is it possible? If yes,...
1
vote
0answers
139 views

How to get the quaternionic analytic signal of a image?

The 2D discrete image signal's quaternionic fourier transform can be described as F(u,v), and its 2D analytic signal often be described as: $$ F_q(u,v) = (1 + \mbox{sgn}(u))(1 + \mbox{sgn}(v)) F(u,v) ...
1
vote
2answers
385 views

Compensate for phase shift of Hilbert transform

I'm using Octave and trying to use the "instfreq" function from the time frequency toolbox which requires an analytic signal input. To get this analytic signal I'm using the Octave function "hilbert" ...
0
votes
1answer
183 views

Gibbs phenomenon in Hilbert transform

I have just read that the Gibbs phenomenon can cause artifacts in the use of Hilbert transforms for audio processing applications, but the reference contained no more specific information. Can anyone ...
0
votes
1answer
209 views

Discrete Hilbert transformation of a spatial signal

first of all, sorry for this basic question in signal processing, I'm pretty new in this field and have been stuck in a situation a little beyond my expertise. The idea is to derive the instantaneous ...
2
votes
1answer
162 views

What are the mathematical consequences of a discrete signal living in Hilbert space?

I am doing the Coursera course on DSP by Prandoni and Vetterli, and was excited to learn that we can use the tools of vector spaces to analyze discrete signals. At this early point in the course the ...
3
votes
1answer
477 views

Why do we read that Hilbert transform can be used for envelope detection?

We can often read that Hilbert transform is useful for envelope detection (e.g. Hilbert transform to compute signal envelope?) I have done some tests with various soundfiles, and ...
1
vote
1answer
2k views

Hilbert-Huang Transform Implementation

I am looking for a implementation of Hilbert-Huang Transformation. Ideally, in Java, but any language with similar syntax would prove useful. Could someone point me to a specific implementation, ...
5
votes
1answer
805 views

Precisions on Hilbert Huang transform

After investigating signal analysis methods based on empirical mode decomposition (EMD), I found that recent developments are mostly related to the Hilbert Huang transform (HHT) and the Local Mean ...
2
votes
2answers
622 views

Why do envelope extraction before pitch detection?

I am referring to this report on pitch estimation. The author does envelope extraction using Hilbert transform before applying AMDF. What is the advantage of doing that? Is speech a narrowband ...
3
votes
1answer
213 views

What is a complex helical sequence?

Matlab says x = hilbert(xr) returns a complex helical sequence, sometimes called the analytic signal, from a real data sequence. How did the name ...