10
votes
Accepted
Numerically Controlled Oscillator (NCO) for phasor implementation?
The NCO is a cyclical counter that can go on indefinitely but is otherwise similar to what you suggest in that you are increment n to set the output rate. It basically is a look up table of all the ...
- 51.3k
7
votes
How to calculate critical damping of a system with two springs and a damper (or two springs and two dampers)?
Re-writing the strain-stress equation
$$
0 = E_1Ɛ + \frac{η(E_1+E_2)}{E_2}\dot{Ɛ} - \frac{η}{E_2}\dot{σ} - σ
$$
for displacement/restoring force variables
$$
0 = E_1x + \frac{η(E_1+E_2)}{E_2}\dot{x} + ...
- 1,729
6
votes
Accepted
Allan Variance vs Autocorrelation - Advantages
My current work involves the design details of atomic clocks where we use the Allan Variance and Allan Deviation (ADEV) extensively. The primary point is that it can be used for non-stationary ...
- 51.3k
5
votes
Accepted
Freeform band-limited waveforms
this paper was done long before i had MATLAB. the drawings are poor, but the math (at least in this revision, which is what you should use) is spot on.
send me an email address (to my ...
- 20.7k
5
votes
Accepted
How do I stabilize my oscillating system?
First, combine your two variable set of first order differential equations into a single variable second order one.
$$ \frac{d^2y}{dt^2} = c \frac{dx}{dt} = acy + bc $$
$$ \frac{d^2y}{dt^2} - acy = ...
- 7,560
4
votes
Denoising Oscilloscope data the right way [python3]
If you are simply interested in plotting the data then any data reduction technique would do,even if it appears to be crude.
Effectively, the plotting function itself will not plot all the data, ...
- 10.7k
3
votes
Accepted
polyBLAMP anti-aliasing in C++
First of all, if your phasor oscillator has a step discontinuity (as opposed to a ramp one) at $\phi\bmod 1 = 0$, then you should use the four-point, fourth order polyBLEP residual, not the fifth-...
3
votes
What is the moment when all oscillators aligned to make a jump called?
I think the word/phrase you are looking for is "discontinuity" / "discontinuity in the source signal". Although a jump is always a discontinuity, a discontinuity is not always a jump. When it isn't ...
- 7,560
3
votes
What is the moment when all oscillators aligned to make a jump called?
It is the time of maximum constructive interference of the derivatives of the harmonics. That's a physics term, but widely known.
- 13.5k
3
votes
Emulating an analog Oscillator in DSP
That's a fairly broad question.
I'm eager to understand how one might emulate an analog oscillator digitally.
If you really want to model an analog circuit this is typically done by using ...
- 44.7k
2
votes
Accepted
How to account for multiple signals in the input to a Kalman filter
The kinematic filter (which is mathematically a polynomial Kalman filter) has the ability to track any signal as long as the sampling rate is high enough, because when it's so, the complex motion of ...
- 28.2k
2
votes
How to implement a digital sawtooth oscillator?
Refer to think link, and use the truncated phase word directly (no look-up-table needed):
Numerically Controlled Oscillator (NCO) for phasor implementation?
- 51.3k
2
votes
Accepted
How to look at Rubidium frequency standard using the oscilloscope?
From the Oscilloscope, I want to check 1PPS and 10MHz from the Rubidium frequency standard, How to do that?
Not at all.
From your oscilloscope's product page:
Accuracy: 200 ppm
That's ...
- 30.7k
2
votes
Accepted
Resonance circuit peak filter with unity stopband in MATLAB
You have designed a bandpass filter, i.e. it does not allow any frequency far way from the resonance to pass. As far as I understand, you want a filter, that does not change the signal in the stopband,...
- 6,218
2
votes
Generate loopable sine wave cycle for given frequencies
Your clicks are coming from two sources. The wavetable and the hardware.
If you are looking to create a simple little instrument that produces tones by playing back a wavetable, then there is no way ...
- 10.7k
2
votes
Accepted
What is the moment when all oscillators aligned to make a jump called?
Phasor Alignment : The individual frequency component phasors of the square wave are aligning, but I don't think this is a well-defined (or previously-defined) term.
- 25.7k
2
votes
How to recover frequency and damping coefficient from superposition of damped oscillators?
If you are absolutely sure that you have a signal that is the superposition of damped oscillators then you can simply track their evolution in time.
...
- 10.7k
2
votes
NCO loses lock after a while for certain values of alpha
I will assume that your PLL is purely digital. Is that correct?
I assume your PLL consists of 3 blocks
The first block calculates the phase of your incoming signal (the signal you wanna lock to).
...
- 3,777
2
votes
How do I stabilize my oscillating system?
An empirical approach:
I'm adding a new answer as it is completely different in nature.
It seems you have a system you are studying where you can vary one parameter (or more?) to control the ...
- 7,560
2
votes
How to recover frequency and damping coefficient from superposition of damped oscillators?
There is an actual group of methods that deal exactly with this: the so-called High Resolution Methods. They are based in covariance of the signal and are very efficient separing noise from sinusoidal ...
- 21
2
votes
Accepted
What equation predicts the amplitudes of harmonics from a square/triangle/sawtooth/pulse oscillator?
This is what Fourier series are all about. Under relatively mild conditions, a $T$-periodic function $f(t)$ can be represented as an infinite sum of complex exponentials:
$$f(t)=\sum_{k=-\infty}^{\...
- 90k
2
votes
Accepted
Emulating an analog Oscillator in DSP
Here's the other common method for an oscillator of any waveshape. It comes from this more general file implementing wavetable synthesis with up to 3 axes of control. A simple oscillator has 0 axis ...
- 20.7k
2
votes
Emulating an analog Oscillator in DSP
Because you say you are emulating an oscillator rather than simulating an oscillator, I assume that your definition of it "acting right" is that it gives some desired result, rather than ...
- 12.7k
2
votes
Accepted
Specific de-trending method for damped oscillation?
In Prony's method you're taking a signal and extracting a system characteristic polynomial from it. In $z$-domain terms, you have a known signal $x(n)$ with a $z$ transform
$$X(z) = \frac{N(z)}{P(z)} ...
- 12.7k
1
vote
Accepted
Output of marginally stable systems
A second-order system without damping (such as an ideal LC circuit) will not produce any output without input and with zero initial conditions. It will produce output only if there is either a non-...
- 90k
1
vote
Output of marginally stable systems
An ideal LC circuit has no resistance, and hence no resisitive loss mechanism. Therefore if it starts to oscillate (due to, for example, a non-zero initial voltage or current stored in the L or C), ...
- 28.2k
1
vote
Detect when signal starts oscillating
As far as I can tell from the graph, the variance of the signal goes up substantially under "oscillation" conditions. So, monitor the variance over a rolling window. High variance indicates ...
- 191
1
vote
Is there any special when all Fourier components have the same angle?
sine waves all have zero crossings at the same phase of $0$ or $\pi$ and have a peak (or valley) with a phase of $\pm\tfrac{\pi}{2}$.
cosine waves all have zero crossings at the same phase of $\pm\...
- 20.7k
1
vote
How do I stabilize my oscillating system?
Converting the model to a state space model
$$
\begin{pmatrix}\dot x\\\dot y\end{pmatrix} = \begin{pmatrix}d &a\\ c &0\end{pmatrix}\begin{pmatrix}x\\y\end{pmatrix} +
\begin{pmatrix}1\\ 0\end{...
- 522
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