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Questions tagged [analytic-signal]

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2answers
90 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....
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2answers
173 views

Block diagram for a complex impulse response

I have this question regarding digital systems which might not handle sinusoidal signals in general. So let us say that I have a system with impulse response $h(n) = \{1+j, -1, 2j \}$ with first ...
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0answers
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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3answers
234 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_\...
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1answer
114 views

Improving template with instantaneous amplitude

Given some recording (containing both the signal of interest and some Gaussian noise), can we improve our template (or model) of the signal using the analytic signal of the recording? For example, a ...
1
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0answers
45 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 ...
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1answer
68 views

Separate Complicated Signal into Exponential Components

This morning, I asked a similar question about separating simple signals - with constant frequency - into exponential components. User @AndreasH suggested that a hilbert transform can do this as ...
2
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1answer
50 views

Separate Simple Signal into Exponential Components

Everyone here should be familiar with the trignonometric identity $$2 \cos(x)=e^{jx}+e^{-jx}$$ Let's say I have a real world analog signal given by the following function $$x(t)=2\cos (\omega_1 t)$$...
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1answer
207 views

CODECS used for VoIP calls

I am trying to self-study audio codecs and I am trying to understand the difference between CODECS that come under AMR-WB, SuperWB and EVS vs. AAC-LD (MPEG-4). When is the former used and when is the ...
1
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1answer
270 views

Definition of minimum-phase system

I saw a couple of definitions for minimum-phase in different textbooks and I'm trying to understand what the implication of each of them. The first definition I saw was: An invertible system which ...
0
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1answer
693 views

QAM Constellation Construction - Basic 4/8 QAM

I wanted to know how to construct the set of amplitudes/phase for QAM modulation. I saw that a QAM signal can be represented as: $$ s_m(t)=A_{mi}g(t)\cos(2\pi f_c t)-A_{mq}g(t)\sin(2\pi f_c t) $$ ...
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1answer
1k views

How to “draw” the function/wave to send symbols using QAM?

Say you have the following 8QAM constellation diagram: Say, you want to send the sequence: 001 110 101 000 001 How would you draw the function/wave containing the symbols? My problem in ...
2
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0answers
255 views

Connections between quantum field theory and signal processing

I've been working with quantum field theory on the basis of it being a stochastic signal processing formalism for a number of years. The projection to fourier components within the forward light-cone ...
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1answer
655 views

How can I determine the complex envelope of a signal when knowing the analytic signal?

Consider a signal $x(t) = \sum A_i \sin(2\pi(f_c+f_i) t + \theta_i),\, i=1\ldots N,$ and its analytic signal $Z_x(t) = x(t) + j\mathcal H[x(t)]$. I want to describe the complex envelope (equivalent ...
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1answer
149 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 ...
2
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1answer
241 views

Compute real signal from a discrete analytic signal

I have a 128MHz-wide down converted signal that gets processed in a FPGA via a polyphase filter bank to give 8x16 MHz baseband analytic signals. How do I convert this analytic signal to a real-valued ...
1
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1answer
1k 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 ...
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4answers
9k 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 ...
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2answers
422 views

Recover signal from its spectral amplitude and envelope

I am given an amplitude spectrum (no phase) and the envelope of a signal. What I know about the original signal is, that it can be thought of as wavepacket like structure (sinusoids under a bell curve)...
2
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2answers
1k views

Teager-Kaiser Operator vs. Hilbert Transform

Since a couple of months I started working on the extraction (estimation) of signal frequency and amplitude components by means of two different time-frequency approaches, namely the Hilbert transform ...
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0answers
71 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 ...
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1answer
229 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 ...
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0answers
921 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 ...
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0answers
176 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) ...
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2answers
130 views

number of possible component in sinusoidal model

Suppose that we have the following model $y(t) = A_1\sin(\omega_1 t+\phi_1) + A_2\sin(\omega_2 t+\phi_2) + ... + A_p\sin(\omega_p t+\phi_p) + z(t)$ My question is not related to how to determine the ...
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0answers
434 views

FFT of complex envelope

I have I and Q samples of a time domain signal, sampled at a rate T, both of length L. I create the complex envelope, C = sampleI+j*sampleQ. Then take the FFT of ...
0
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2answers
457 views

How to create a band limited signal of sine waves that is nearly uniform distributed

I would like to create a signal that is nearly uniform distributed (as depicted in Figure 1). It must consist of some single sine waves (e. g. 400 Hz, 430 Hz, 500 Hz) or a random band limited signal (...
2
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2answers
178 views

Can signal processing be applied successfully to price data from financial markets?

Price/volume data from financial markets are like signals. Can these information be applied to signal processing to generate profits successfully?
1
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2answers
606 views

understanding analytic signals

I know that a function $f_a\in \text{L}^2(\mathrm{R})$ is an analytic signal if its Fourier transform is 0 for negative frequencies, i.e. $\hat{f_a}(\omega)=0$ if $\omega<0$. We can characterize ...
2
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1answer
129 views

Revert anayltic signal(length(N/2)) to real signal (length(N))

As a beginner in signal processing, i'll try to explain my problem most thoroughly. I'll firstly explain the idea of the transformation the real valued data has undergone. This includes the ideas and ...
2
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2answers
515 views

Prevent negative image with BPSK modulation in a complex signal

In a baseband complex signal, I need to generate a BSPK modulated signal at a given frequency. If I generate a CW at this frequency, all is good. However, when I then BPSK modulate the CW, I get a ...
2
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1answer
8k views

Envelope of time domain signal // Hilbert transform

to get the envelope of a time domain signal, s(t), I use the absolute of its analytical time domain signal. But there occur the problem that sometimes the envelope is not as desired a true envelope ...
2
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1answer
336 views

Spectrum and Spectrogram explanation

I'm reading this material but I don't understand this example: "An example of a 94% overlap transform processing could be demonstrated by a 279 sample frame with 262 samples overlapped from each ...
3
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0answers
792 views

calculate root mean square, ratio of power, constant false alarm, … of a signal

I am new to Digital Signal Processing, and am reading a paper. I don't know how they can extract some features from signal, like root mean square (RMS), Constant False Alarm Rate - CFAR, Mean Value ...
5
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1answer
1k views

Hilbert transform: analytic signal

I want to observe how the signal's phase changes over time and I know Hilbert transform can be used here to get the analytic signal, from which I can extract the amplitude and phase. I know that to ...
3
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1answer
157 views

signals comparison metrics

Am new to signal processing and was wondering when given two signals, what are the widely used statistical analysis methods to understand the relationship between them?
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3answers
884 views

How should I pre-process a real valued signal in order to use Kay's estimator?

I have 100,000 samples of a signal $x[n]$ that was sampled at 20kHz. The data is vibration data from a rotating machine, and contains a significant spectral component related to the speed of the ...