I am currently collecting data from a power meter Keysight N7744A to be exact. The issue is that over the course around every 5 minutes (after collecting an hour of data) the data fluctuate over 20%. My goal is to take a single measurement and being able to guarantee that it is within 5% (>0.25dB) of the true value which can be obtained by averaging over the period of 5 minutes. However, this will impact performance by too much... A measurement is collected in 400ms.
Any thoughts on how I can cancel this extra low frequency but high amplitude noise signal? Thanks!
I have attached the data just in case I couldn't explain myself. It has 10k data points collected over 1+hours where each measurements takes ~400ms. data.dat
Perhaps a high pass filter would work.
Related
I have a quick question on sensor data decimation, which I'm sure is pretty easy but thought I'd check. I have a sensor that is sampling at 25Hz and the data is being sent across a serial RS232 connection to an external data logger, which is logging the data at 10Hz.
I think if I want to recover a true 10Hz signal, I should I pass the original 25 Hz signal through a decimation process (i.e. filtering followed by down sampling). Is this correct?
If it is correct, I was thinking that I should decimate the original 25Hz signal by passing it through a low pass filter with a cutoff frequency of ~10 Hz, to remove the higher frequency components. The filtered signal would then be down sampled to produce a final signal. This down sampling would be achieved by extracting a value every 2.5 samples from the filtered signal.
So in other words, the 1st value of the final signal would be the first sample of the filtered signal. The second value of the final signal would be the average of samples 2 & 3 from the filtered signal. Then the third value of the final signal would be sample 5 from the filtered signal, and the fourth sample would be an average between samples 7 & 8 etc.....
Hopefully that makes sense. I think that would provide me with a clean 10Hz signal.
Many thanks for your time and efforts on this, they are very much appreciated
Cheers
The type of filtering you should use will depend in part on what you are using this signal for and how noisy the captured data is.
In general, you should not change the sampling frequency of the filter constantly, this could introduce artificial periodic noise in the captured data. My guess is that for this process you are sampling something that doesn't change rapidly. You might want to just take a rolling average of the last 3 samples, even though some of the data averaged into each logged sample will overlap.
I have a 10 Hz time series measured by a fast instrument and a 1 minute time series measured by a slow reference instrument. The data consists of a fluctuating meteorological parameter. The slow reference instrument is used to calibrate the fast instrument measurements. Both time series are synchronised.
My idea:
Average the 10 Hz data into 1 minute blocks.
Take 5 one minute block from each time series and calculate the linear regression equations.
Use the regression equations to calibrate the 10 Hz data in 5 minute blocks (3000 data points).
What would be the best way to match (calibrate) the high frequency data using the low frequency data? I use MATLAB.
More background: The fast instrument outputs a fluctuating voltage signal while the slow instrument outputs the true value of a trace gas concentration in ppb (parts per billion). The slow instrument samples every ten seconds and outputs the average every one minute.
In short I would like to have my fast signal also in ppb but without losing it's integrity (I need the turbulent fluctuations to remain unfiltered), hence the need to use a linear fit.
Here's my approach and the results I got...
I modelled the problem as there being
a real (unmeasured by instruments) signal.
Let's call this real.
a slow signal - which is just the real signal sampled once a minute.
Let's call this lf (short for low frequency).
a fast signal - real signal + noise + signal drift.
Let's call this hf (short for high frequency).
The task was to take the slow and fast signals and try to reconstruct the real signal.
(Using least squares as a scoring metric)
Strategy:
Define a "piecewise linear filter" - this takes a signal, and returns a piecewise version of it. (With each piecewise part occurring where the slow signal is measured.)
NOTE: The slow signal is considered piecewise anyway.
Define a forwards-backwards low pass filter.
Define "uncertainty" to be 0 at the points where the low frequency signal is measured. It linearly increases to 1 when the timestamp is halfway between low frequency signal measurements.
Now, take your high frequency signal and filter it with the low pass filter.
Let's call this hf_lp
Take hf_lp and apply the "piecewise linear filter" to it.
Let's call this hf_lp_pl
Subtract the last two from each other.
I.e. hf_diff = hf_lp - hf_lp_pl.
You now want to find some function that estimates how by how much hf_diff should be added to the low frequency signal (lf) such that the squared error between real_estimated and real is minimized.
I fitted a function along the lines of real_estimated = lf + diff.*(a1*uncertainty + a2*uncertainty.^2 + a3*uncertainty.^3)
Use fminsearch or other optimization techniques to get a1, a2, a3...
Here is a sample plot of my results - you can see that real_estimated is much closer to real than the slow signal lf.
Closing thoughts...
The fast signal contains too much very low frequency (drift) and too much
very high frequency (noise) components.
But it has valuable medium frequency info.
The slow signal has perfect low frequency information, but no medium frequency info.
The strategy above is really just one way of extracting the medium frequencies from the fast signal and adding it to the low frequency signal.
This way, we get the best of all worlds: low frequencies, medium frequencies and low noise.
I use Matlab to calculate the fft result of a time series data. The signal has an unknown fundamental frequency (~80 MHz in this case), together with several high order harmonics (1-20th order). However, due to finite sampling frequency (500 MHz in this case), I always get the mixing frequencies from high order frequency (7-20), e.g. 7th with a peak at abs(2*500-80*7)=440 MHz, 8th with frequency 360 MHz and 13th with a peak at abs(13*80-2*500)=40 MHz. Does anyone know how to get rid of these artificial mixing frequencies? One possible way is to increase the sampling frequency to sufficient large value. However, my data set has fixed number of data and time range. So the sampling frequency is actually determined by the property of the data set. Any solutions to this problem?
(I have image for this problem but I don't have enough reputation to post a image. Sorry for bring inconvenience for understanding this question)
You are hitting on a fundamental property of sampling - when you sample data at a fixed frequency fs, you cannot tell the difference between two signals with the same amplitude but different frequencies, where one has f1=fs/2 - d and the other has f2=f2/2 + d. This effect is frequently used to advantage - for example in mixers - but at other times, it's an inconvenience.
Unless you are looking for this mixing effect (done, for example, at the digital receiver in a modern MRI scanner), you need to apply a "brick wall filter" with a cutoff frequency of fs/2. It is not uncommon to have filters with a roll-off of 24 dB / octave or higher - in other words, they let "everything through" below the cutoff, and "stop everything" above it.
Data acquisition vendors will often supply filtering solutions with their ADC boards for exactly this reason.
Long way to say: "That's how digitization works". But it's true - that is how digitization works.
Typically, one low-pass filters the signal to below half the sample rate before sampling. Otherwise, after sampling, there is usually no way to separate any aliased high frequency noise (your high order harmonics) from the more useful spectrum below (Nyquist) half the sample rate.
If you don't filter the signal before sampling it, the defect is inherent in the sample vector, not the FFT.
I'm a neuroscientist, and not a very good one. My colleague has kindly provided me with a noisy voltage measurements of the PY neuron of the Stomatogastric Ganglion of the lobster.
The activity of this neuron is characterised by a slow depolarised plateaux with fast spikes on top (a burst).
Both idealised and noisy versions are presented here for you to peruse at your leisure.
It's my job to extract the spike times from the noisy signal but this is so far beyond my experience level I have no idea where to begin. Fortunately, I am a total ninja at Matlab.
Could someone kindly provide me with the name of the procedure, filter or smoothing function which is best suited for this task. Or even the appropriate forum to ask such an asinine question.
Presumably, it needs to increase the signal to noise ratio? The problem here seems to be determining the difference between noise and a bona fide spike as the margin between the two is quite small.
UPDATE: 02/07/2013
I have tried the following filters in Matlab with mixed results. It's still very hard to say what is noise and what is a spike.
Lowpass Butterworth filter,
median filter,
gaussian,
moving weighted window,
moving average filter,
smooth,
sgolay filter.
This may not be an adequate response for stackoverflow - but one way of increasing a signal to noise ratio in your case is to average parts of the signal.
low pass your signal to remove noise (and spikes), and find the minima of the filtered signal (from your image, one minimum every 600 data points). Keep the indexes of each minimum,
on the noisy signal, for each minimum index, select the consecutive 700 data points. If you have 50 minima, you should have a 50 by 700 matrix,
average your matrix. You should have a 1 by 700 vector.
By averaging parts of the signal (minimum-locked potentials), you will take advantage of two properties: noise is zero-mean (well, it should be), and the signal of interest is repetitive. The first will therefore decrease as you pile up potentials, and the second will increase. With this process however, you will lose the spike times for each slow wave figure, but at least have them for blocks of 50 minima.
This technique is known in neuroscience as event-related potential (http://en.wikipedia.org/wiki/Event-related_potential). It may not fit perfectly your signal, or the result may not give nice spikes, but you may extract the spike times for some periods of interest (given the nature of your signal, I would say that you would need 5 or 10 potentials to see an emerging mean activity).
There are some toolboxes that do part of the job (but I would program it myself given the complexity of the task). These are eeglab or fieldtrip. They have a bunch of filter/decomposition options too, as well as some statistical features.
I am using NSTimer to update peak power from iphone. From monitoring, it does not update very fast. I need high frequency of updating peak power in order of 100 micro second (100us). I also try with usleep(100) to update every 100us. Still very slow. Can someone help me to point out how to achieve this? I am thinking I need to use this code to measure distance. Thank you.
you capture the audio (record, input, or file), access its samples from the pcm cbr (uncompressed, with a fixed sampling rate) stream, and read the samples of the range you are interested in. considering the high frequency, you will only have to analyze a small number of samples (2-5, depending on the sampling rate). you may need to interpolate to improve accuracy with so few samples.