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.
Related
I want to design a score or signature function based on a time series signal. Usually, the signal has ups and downs.
For a given time window, I desire to design the score function based on the number of times it fluctuates, the duration of the fluctuations, and the magnitude of the fluctuations. I am wondering what kind of math I can use to design the function. I am not sure if the statistical features (mean, median, and so on) would be enough to design unique function such that two time windows would be distinguishable.
Thanks!
Summary statistics will not give you what you want... but it can still be useful.
Things you can try:
Zero crossings on the signal will give you number of fluctuations. You'll have to use some central tendency value to move the signal about the 0 line in order to do this. Alternatively you can use FFT on the original to find the harmonic frequency as part of the score.
Could define the duration of fluctuations as the difference between zero crossings divided by two (since one fluctuation will reach the 0-line twice).
Magnitude can be done by finding the local minima and maxima - check out some packages with peak finding functions. You might want to use the mean or median to rule out local minima and maxima that fall on the wrong side of the line. Alternatively, finding the zero crossings on the derivative signal and then mapping them back to the original will give you all the local minima and maxima as well.
I have become a part of this infinite question of how to estimate position from accelerometer data achieved by an Inertial measurement unit. I am wondering how to compensate for integration ''drift'' during linear movement using Kalman filtering.
At this moment I got my acceleration in a fixed coordinate system and all movements are in know directions with no change in angular position.
So at this point we got acceleration in 3D (x-y-z) in known directions, an acceleration in x will yield for zero acceleration in y and z and so on. Assuming perfect conditions, which are not the case, of course some noise with be added to the other directions when moving in one direction but lets ''leave'' this out at this point. In addition, It is important to note that the system only has to estimate a limited period, approximately about 1 second using a sampling freq of 512 Hz.
It also important to note that I have compensated for the offset (gravity and misalignment of the accelerometer in the IMU) and bias of the acceleromter data when static. Meaning when the sensor is non-moving all my readings are constant zero before going into the Kalman filter.
To more characterize my problem I have this graph to illustrate my problem with drift. This is estimations on 5 seconds to more show what I'm struggling with.
Position-estimation-drift-problem
Here we are looking into a movement in one direction, the movement are 20cm movement in y direction which in my case are forward relative to my starting position.
Is there a way to reduce/eliminate this drift when integrating my signal. For instance assume something about drifting when my sensor is non-moving. Or to compute using some correction in my Kalman algorithm to subtract or add to my estimated velocity and position. The system does not have to run in real time so any tuning bias compensation can be adjusted for looking back into the data. But I would be preferable if it was possible to take new measurements with slightly different movements and not tune more then needed.
Finally where/how can I compensate for this, in the Kalman algorithm or before/after, or should I be in for a disappointment already?
If I left out some important information please ask so i can elaborate more, an at last any thoughts/ideas are welcome!
Remember I do only need to estimate for second’s worth of time so my hope is that this makes it more achievable, but i might be wrong?
I can only guess/suggest few tricks, but you will probably get some significant error if you only based on accelerometer.
seems that detecting motionless is not resetting the speed, just acceleration (according to your graph) so this should be an easy fix
if we are talking an a car/other type of surface motion with contact / friction, your motionless can be set by characterizing the noise of in motion/self sensor noise
kalman parameters may be off
run multiple kernels and average results (may also try particle filter)
if its not for online application you can also try fitting offsets/drift and reduce them by assuming there is not motion in constant speed or other approaches that can replace the kalman filter which is designed for real time best estimation.
error seems a-symmetric in time, just run it in both directions (:
what are you measuring at 512 Hz??? maybe you can better model it
I can go on and on but if you supply data and code, it would be much easier.
Good luck,
Lev
I have a requirement where I have to verify the transmit power out of a device as measured at its connector is within 2 dB of its expected value over 95% of test measurements.
I am using a signal analyzer to analyze the transmitted power. I only get the average power value, min, max and stdDev of the measurements and not the individual power measurements.
Now, the question is how would I verify the "95% thing" using average power, min, max and stdDev. It seems that I can use normal distribution to find the 95% confidence level.
I would appreciate if someone can help me on this.
Thanks in anticipation
The way I'm reading this, it seems you are a statistical beginner, so if I'm wrong there, the rest of this answer will probably be insultingly basic, and I'm sorry.
Anyway, the idea is that if a dataset is normally distributed, and all the observations are independent of one another, then 95% of the data points will fall within 1.96 standard deviations of the mean.
Do you get identical estimates of average power every time you measure, or are there some slight random differences from reading to reading? My guess is that it's the second. If you were to measure the power a whole bunch of times, and each time you plotted your average power value on a histogram, then that histogram of sample means would have the shape of a bell curve. This bell curve of sample means would have its own mean and standard deviation, and if you have thousands or millions of data points going into the calculation of each average power reading, it's not horrible to assume that it is a normal distribution. The explanation for this phenomenon is known as the 'central limit theorem', and I recommend both the Khan academy's presentation of it as well as the wikipedia page on it.
On the other hand, if your average power is the mean of some small number of data points, like for instance n= 5, or n= 30, then assumption of a normal distribution of sample means can be pretty bad. In this case, your 95% confidence interval around the average power goes from qt(0.975,n-1)*SD/sqrt(n) below the average to qt(0.975,n-1)*SD/sqrt(N) above the average, where qt(0.975,n-1) is the 97.5th percentile of the t distribution with n-1 degrees of freedom, and SD is your measured standard deviation.
Im fairly new to onset detection. I read some papers about it and know that when working only with the time-domain, it is possible that there will be a large number of false-positives/negatives, and that it is generally advisable to work with either both the time-domain and frequency-domain or the frequency domain.
Regarding this, I am a bit confused because, I am having trouble on how the spectral energy or the results from the FFT bin can be used to determine note onsets. Because, aren't note onsets represented by sharp peaks in amplitude?
Can someone enlighten me on this? Thank you!
This is the easiest way to think about note onset:
think of a music signal as a flat constant signal. When and onset occurs you look at it as a large rapid CHANGE in signal (a positive or negative peak)
What this means in the frequency domain:
the FT of a constant signal is, well, CONSTANT! and flat
When the onset event occurs there is a rapid increase in spectrial content.
While you may think "Well you're actually talking about the peak of the onset right?" not at all. We are not actually interested in the peak of the onset, but rather the rising edge of the signal. When there is a sharp increase in the signal, the high frequency content increases.
one way to do this is using the spectrial difference function:
take your time domain signal and cut it up into overlaping strips (typically 50% overlap)
apply a hamming/hann window (this is to reduce spectrial smudging) (remember cutting up the signal into windows is like multiplying it by a pulse, in the frequency domain its like convolving the signal with a sinc function)
Apply the FFT algorithm on two sucessive windows
For each DFT bin, calculate the difference between the Xn and Xn-1 bins if it is negative set it to zero
square the results and sum all th bins together
repeat till end of signal.
look for peaks in signal using median thresholding and there are your onset times!
Source:
https://adamhess.github.io/Onset_Detection_Nov302011.pdf
and
http://www.elec.qmul.ac.uk/people/juan/Documents/Bello-TSAP-2005.pdf
You can look at sharp differences in amplitude at a specific frequency as suspected sound onsets. For instance if a flute switches from playing a G5 to playing a C, there will be a sharp drop in amplitude of the spectrum at around 784 Hz.
If you don't know what frequency to examine, the magnitude of an FFT vector will give you the amplitude of every frequency over some window in time (with a resolution dependent on the length of the time window). Pick your frequency, or a bunch of frequencies, and diff two FFTs of two different time windows. That might give you something that can be used as part of a likelihood estimate for a sound onset or change somewhere between the two time windows. Sliding the windows or successive approximation of their location in time might help narrow down the time of a suspected note onset or other significant change in the sound.
"Because, aren't note onsets represented by sharp peaks in amplitude?"
A: Not always. On percussive instruments (including piano) this is true, but for violin, flute, etc. notes often "slide" into each other as frequency changes without sharp amplitude increases.
If you stick to a single instrument like the piano onset detection is do-able. Generalized onset detection is a much more difficult problem. There are about a dozen primitive features that have been used for onset detection. Once you code them, you still have to decide how best to use them.
I have a question regarding how to determine the Duration of notes given their Onset Locations.
So for example, I have an array of amplitude values (containing short) and another array of the same size, that contains a 1 if a note onset is detected, and a 0 if not. So basically, the distance between each 1 will be used to determine the duration.
How can I do this? I know that I have to use the Sample Rate and other attributes of the audio data, but is there a particular formula that I can use?
Thank you!
So you are starting with a list of ONSETS, what you are really looking for is a list of OFFSETS.
There are many methods for onset detection (here is a paper on it) https://adamhess.github.io/Onset_Detection_Nov302011.pdf
many of the same methods can be applied to Offset Detection:
Since the onset is marked by an INCREASE in spectral content you can measure a decrease in Spectral content.
take a reasonable time window before and after your onset. (.25-.5s)
Chop up the window into smaller segments and take 50% overlapping Fourier transforms.
compute the difference between the fourier co-efficient between two successive windows decreases and only allow negative changes in SD.
multiple your results by -1.
pick the peaks off of the results
Voila, offsets.
(look at page 7 of the paper listed above for more detail about spectrial difference function, you can apply a modified (as above) version of it_
Well, if your samplerate in Hz is fs, then the time between two nodes is equal to
1/fs * <number of zeros between the two node-ones>
Very simple :-)
Regards