7 votes

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

The baseband QAM signal is complex, and the only way to draw it is by doing two drawings, one for the in-phase (real) component, and one for the quadrature (imaginary) component. The passband QAM ...
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6 votes
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Real and complex low pass equivalent of band-pass signal

It's not true that any real-valued band pass signal can be written as shown in your first equation: $$s(t)=A(t)\cos(\omega_c t)\tag{1}$$ The most general representation of a real-valued band pass ...
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4 votes

Calculate and interpret the instantaneous frequency

At least f2 and f3 seem to work appropriate on a pure chirp signal, but all methods, including f2 and f3 seem to fail horrible, when it comes to more than one frequency in the signal. In reality ...
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4 votes

Calculate and interpret the instantaneous frequency

Not really an answer but maybe helpful: Personally I found that the concept of instantaneous frequency is only useful for sufficiently narrow band signals. Consider the simple example of two steady ...
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4 votes
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I Q sampling and baseband version of analytic signal

The problem in your derivation is the way you discard the high frequency components. Note that $\hat{s}(t)$, the Hilbert transform of the bandpass signal $s(t)$, has frequency components around $\...
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3 votes
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Magnitude of the analytic signal

By definition, the magnitude of the analytic signal $s_a(t)$ can always be considered the envelope of the signal in a purely mathematical sense, simply because the real-valued signal is given by $$s(t)...
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3 votes
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Obtain I/Q Components from a Real Signal On the Fly - Hilbert Transform or Digital Downconversion?

[Update: I mentioned a possible +3dB processing gain by including the Hilbert Transform prior to DDC for the case of a real IF signal in the first version of this post, which @MattL questioned so I ...
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3 votes
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Separate Simple Signal into Exponential Components

Your problem seems to be finding the analytic signal to a given real signal. What you apparently need is the Hilbert transform. This will allow you to "recreate" the imaginary part of $y(t)$ from the ...
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3 votes

Definition of minimum-phase system

one thing about a non-minimum phase system (with a rational transfer function), is that it can be thought of as the series concatenation (or cascade) of a minimum-phase system, having identical ...
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3 votes

QAM Constellation Construction - Basic 4/8 QAM

You can choose any mapping that you desire from your unique data sequences to the symbol locations on the QAM constellation. It is common and usually best to Gray-code the mapping such that only one ...
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3 votes
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Phase change rate of human speech

I will not address the question whether or not it is meaningful to compute the instantaneous frequency of a speech signal. Instead I will show you a better method for computing the instantaneous ...
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2 votes
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Teager-Kaiser Operator vs. Hilbert Transform

This paper may be of interest: David Vakman, "On the Analytic Signal, the Teager-Kaiser Energy Algorithm, and Other Methods for Defining Amplitude and Frequency." IEEE Trans. Signal Processing. (1996)...
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2 votes

Calculate and interpret the instantaneous frequency

Sorry to provide an answer a year after the fact, but I stumbled across this post while searching for articles on this very topic. Your questions reflect the widespread disagreements and ...
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2 votes
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Pulse shaping and Baseband filtering

Your complex baseband signal before modulation is given by $$s(t)=\sum_{m=-\infty}^{\infty}a_mh(t-mT)\tag{1}$$ where $a_m$ are the complex symbols, $h(t)$ is the impulse response of the transmit ...
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2 votes
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CODECS used for VoIP calls

Let me put in an unconnected form things about audio codecs. Audio can be music or speech (discluding ultrasound, sonar etc). Music is wideband and requires high-fidelity. Speech has a lower ...
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  • 26.7k
2 votes

Block diagram for a complex impulse response

A digital system with complex input and complex output has a block diagram in which the various arrows carry complex signals, each register holds a complex number, each multiplier computes the product ...
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2 votes
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Is real-time Hilbert envelope feasible?

As with most things in Engineering the answer is "depends on your requirements". In general you can't do a perfect Hilbert transform unless the signal is strictly periodic (see http://andrewduncan.net/...
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2 votes
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Why use complex envelope to model raw measurements?

'Imaginary' is a misnomer; they 'exist' as much as reals do. As for the envelope: it provides a meaningful representation of phase and amplitude over time, not otherwise doable with reals alone. To ...
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2 votes
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Analytic Signal Block in Simulink Gives Reduced Amplitude for the Imaginary Part

If the filter has a fixed order then increasing the sampling rate will make its response scale with frequency, thus the transition width increases relative to the sampling frequency. For example: if $...
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2 votes

Envelope detection in MATLAB

The Hilbert is not at all difficult to implement in practice for narrow band signals (we just need to introduce a perfect quadrature phase shift and maintain the amplitude balance-and with a single ...
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1 vote

Magnitude of the analytic signal

Using your notation for the (complex valued) analytic signal; $$s(t) = x(t) + j \hat{x}(t) = |s(t)| e^{j \phi(t)} \tag{1}$$ where $x(t)$ is the message signal and $\hat{x}(t)$ is its continuous-time ...
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  • 26.7k
1 vote

Determine the haar wavelet function is linear or nonlinear

Linearity can play at different levels in this context: The Haar wavelet functions are piece-wise affine (constant), not linear (but sometimes people call affine "linear"). Any standard ...
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1 vote

Phase shift of all-pass bi-quadratic filter

First of all, that formula for the phase has a sign error, at least if $\alpha$ is defined as in the diagram of the filter structure. Second, your phase plot shows a jump from $-\pi$ to $\pi$, which ...
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1 vote
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Block diagram for a complex impulse response

It depends on the orthonormal basis you are using to perform the modulation. In general, we use $\sin()$ and $\cos()$, since they are orthogonal and we are familiar with them. But actually you could ...
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  • 4,872
1 vote

Phase change rate of human speech

instead of calculating angle (from the real and imaginary parts), unwrapping the wrapped angle, and computing a difference, the better way is to compute the difference from the real and imaginary ...
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1 vote

Improving template with instantaneous amplitude

Since I don't really know what you're using software-wise, I just whipped up a really short demo in GNU Radio Companion. This uses a PLL in a live processing demo: If you're inclined to play around ...
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1 vote

Separate Complicated Signal into Exponential Components

Hilbert transform method from your earlier question and Jason R's answer should still work. What you are interested in is extracting the instantaneous phase of your function. For a signal $x(t)$ this ...
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  • 4,034
1 vote

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

With constant amplitudes and phases, this becomes a simple exercise: First, go to the spectral domain $$ X(f) = \mathcal{F}\{x(t)\}=\sum A_i \frac{1}{2j} (\delta(f-(f_c+f_i)-\delta(f+(f_c+f_i))\exp(...
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1 vote

Compute real signal from a discrete analytic signal

@user85858302: If designing a complex-valued bandpass filter is the solution to your problem, you can design such a filter without using the Hilbert transform. Start by using your favorite method for ...
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1 vote

Calculate and interpret the instantaneous frequency

Wow, what a huge question. I'm going to answer the not-so-important question first: And one last, not so important question, why is it that most papers I find on instantaneous frequencies are from ...
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