I have modulation in signal:
How to find the distance between the centers of two modulations in [s]?
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I have a signal (points in frequency domain (nanometers, then converted to tera hertz; along with magnitude level in mW). My signal looks like the attached pic. I would like to know a way to calculate the center frequency.
One theory suggests finding the -3dB cutoff frequencies on both ends. However, I could not find how to do that. So, please tell me how to calculate the -3dB cutoff frequencies so that I can apply te following formula- (f1+f2)/2
or suggest me a better way of finding the center frequency.
You could perform this measurement as an OBW measurement. - 3dB is when you half the total signal power by 50%. (in Watts)
The way to do it manually is to get the whole signal spectrum in an excel table, for example 1000 points, measure the total power, Ptot, and start adding the power by the lowest frequency until you reach 25% of Ptot. The frequency at that point will be Flow. Do the same, but starting from the top frequency until you reach 25% of Ptot. it will be Fhigh. The center will be (Flow + Fhigh)/2.
Sorry if it's not very clear but if you look for OBW measurements You should find better explanations on the net. Most of modern spectrum analyzers have this function built in.
Simple question:
Is the Euclidean distance admissible in a 15 puzzle if we assume a block can move in 8 directions (Horizontal, vertical, diagonal), at the same cost?
No; distance needs to be a direct cognate to the number of steps in your state graph. Consider the case of a single set of move choices: up-left and up are each a single step; Euclidean distance will tell you that up-left is more expensive.
This will expand to cases fatal to your optimal solutions. For instance, moving three tiles in sequence across a main diagonal is only three steps, but Euclidean distance makes that to be more than four (3*sqrt(2)).
Suppose that I have two cameras. I don't know exactly the poses of these two cameras. So their rotation matrice denoted as R1 and R2, respectively, are unknown. But I know the relative angles of these cameras along three axes. I mean if the angles along three axes of the two camera are (alpha1, betta1, gamma1) and (alpha2, betta2, gamma2), then the relative angles of these camera (deltaX, deltaY, deltaZ)=(alpha2-alpha1, betta2-betta1, gamma2-gamma1) are known.
My question is that can we form a "relative" rotation matrix R12 so that R2=R12*R1?
Because there're many methods to construct a rotation matrix. And the results of these methods are different (I'm still don't understand why can a camera have different rotation matrices). In this case, I construct the rotation matrix by multiply three rotation matrix along three axes. More specifically, R=RzRyRx.
As I test with the code in Matlab,
R(alpha2, 0, 0)*R(alpha1, 0, 0)=R(alpha1+alpha2, 0, 0).
But
R(alpha2, betta2, gamma2)*R(alpha1, betta1, gamma1) != R(alpha1+alpha2, betta1+betta2, gamma1+gamma2).
Thanks!
I want to know what a single sample of audio data (uncompressed PCM) represents.
It is a number, but what exactly is that number and how come it can be converted back to audio?
For example if it is a 4-bit sample, does 0 represent absolute silence and 15 represent max volume?
If it is volume, what frequency are we talking about? How is the information about the frequency stored?
In songs we can hear various instruments (frequencies) at the same time, meaning each frequency is somehow stored in a single sample. How is that done?
Audio is just a curve which wobbles up/down with time going left/right. At a given point in time a Sample is a measure of the curve height. Silence is when the curve does not wobble ... it just goes flatline ... at value zero with a Sample value of 0 (more accurately the middle value of its range from max to min) ... when curve reaches its maximum height up or down that stretch of audio is the loudest possible
The notion of normalization is important ... the absolute range of curve values (maximum up or down) is arbitrary ... could be anything ... lets say max is 15 and minimum is 0 ... remember silence is no wobble so middle of max up/down silence would be about 7
Curves can be encoded into any number of bits ... this roughly maps into how many horizontal lines you dice the curve into ... more lines more bits so greater accuracy in value of your Sample of curve height
A sin or cos curve is considered a pure tone ... Joseph Fourier proved an arbitrary curve (audio or otherwise) can be stored in the form of a set sin curves of (A) various volumes (max up/down) (B) various frequencies (C) various phase offsets ... interestingly this transformation works in either direction : from a curve of arbitrary shape into a set of above (A/B/C) or from a set of (A/B/C) back into synthesizing a curve of arbitrary shape (this is how audio synthesizers work)
Information about frequency storage is baked into the curve shape ... its all about how often the curve wobbles up/down ... lazy wobbles taking a long time to cross from below to above the middle line are low frequency ... a stretch of tightly spaced squiggles implies a high frequency squawk
When a microphone records multiple people all talking at once or various instruments all emitting their own sounds we have many simultaneous frequencies yet the recording somehow just works - How ? think of what happens inside the microphone ( or to your flat eardrum ) ... its coil can be considered as a flat surface (a 2D surface ) which can only get sloshed up or down period ... either only moves back and forth ... this is an arbitrary curve ... one curve which at a point in time has a value of its height as it progresses from max to min
I have two questions.
I have three sensors in 3D measuring distance of one single target point. I know the sensor location in 3D and all distances between them and target. How can i find the unknown point? ( I got three circle euqtion, which doesn't make sense to solve?)
It is the inverse of the above question. I know the target point in 3D and all distanctes for 3 sensors. I know relative distance between three sensor also. How can i find the position of this three sensors. I can have multiple target points with known distances.
There is an equation for the 3-D, three-point case at http://en.wikipedia.org/wiki/Trilateration; I think http://en.wikipedia.org/wiki/Multilateration answers the inverse question you posted.