i have a sinusoidal-like shaped signal,and i would like to compute the frequency.
I tried to implement something but looks very difficult, any idea?
So far i have a vector with timestep and value, how can i get the frequency from this?
thank you
If the input signal is a perfect sinusoid, you can calculate the frequency using the time between positive 0 crossings. Find 2 consecutive instances where the signal goes from negative to positive and measure the time between, then invert this number to convert from period to frequency. Note this is only as accurate as your sample interval and it does not account for any potential aliasing.
You could try auto correlating the signal. An auto correlation can be rapidly calculated by following these steps:
Perform FFT of the audio.
Multiply each complex value with its complex conjugate.
Perform the inverse FFT of the audio.
The left most peak will always be the highest (as the signal always correlates best with itself). The second highest peak, however, can be used to calculate the sinusoid's frequency.
For example if the second peak occurs at an offset (lag) of 50 points and the sample rate is 16kHz and the window is 1 second then the end frequency is 16000 / 50 or 320Hz. You can even use interpolation to get a more accurate estimation of the peak position and thus a more accurate sinusoid frequency. This method is quite intense but is very good for estimating the frequency after significant amounts of noise have been added!
Related
I have a data (file) which contains 2 columns:
Seconds, Volts
0, -0.4238353
2.476346E-08, -0.001119718
4.952693E-08, -0.006520569
(..., thousands of similar entries in file)
4.516856E-05, -0.0002089292
How to calculate the frequency of the highest amplitude wave ? (Each wave is of fixed frequency).
Is there any difference between calculating frequency of seconds and amplitude vs. seconds and volts? Because in Frequency & amplitue there is seconds and amplitude example solved, so it might help in my case.
Your data is in the time domain, the question is about the frequency domain. Your course should have told you how the two are related. In two words: Fourier Transform. In practical programming, we use the FFT: Fast Fourier Tranform. If the input is a fixed frequency sine wave, your FFT output will have one hump. Model that as a parabola and find the peak of the parabola. (Finding the highest amplitude in the FFT is about 10 times less accurate)
The link you give is horrible; I've downvoted the nonsense answer there. In your example, time starts at t=0 and the solution given would do a 1/0.
After applying a Fourier transform to a signal, the energy of a single sine wave is often spread out across multiple bins (aka smearing). Have a look at the right side of the image below for an illustration:
I want to extract a list of peak frequencies. Just finding the highest bin is easy. But after that smearing becomes a problem.
I would like to have a heuristic which tells me if the magnitude of a specific bin is possibly the result of smearing or if there has to be another peak frequency in order to explain the signal. (It is better if I miss some than have false positives)
My naive approach would be to just calculate a few thousand examples and take the maximum of these to get an envelope curve so that any smearing is likely below that envelope.
But is there a better way to do this?
The FFT result of any rectangularly windowed pure unmodulated sinusoid is a Sinc function. This Sinc (sin(pix)/(pix)) function is only zero for all bins except one (at the peak magnitude) when the frequency of the input sinusoid has exactly an integer number of periods in the FFT width.
For all other frequencies that are not at the exact center of an FFT result bin, if you know that exact frequency and magnitude (which won't be in any single FFT bin), you can calculate all the other bins by sampling the Sinc function.
And, of course, if the input sinusoid isn't perfectly pure, but modulated in any way (amplitude, frequency or phase), this modulation will produce various sidebands in the FFT result as well.
I'm using a FFT on audio data to output an analyzer, like you'd see in Winamp or Windows Media Player. However the output doesn't look that great. I'm plotting using a logarithmic scale and I average the linear results from the FFT into the corresponding logarithmic bins. As an example, I'm using bins like:
16k,8k,4k,2k,1k,500,250,125,62,31,15 [hz]
Then I plot the magnitude (dB) against frequency [hz]. The graph definitely 'reacts' to the music, and I can see the response of a drum sample or a high pitched voice. But the graph is very 'saturated' close to the lower frequencies, and overall doesn't look much like what you see in applications, which tend to be more evenly distributed. I feel that apps that display visual output tend to do different things to the data to make it look better.
What things could I do to the data to make it look more like the typical music player app?
Some useful information:
I downsample to single channel, 32kHz, and specify a time window of 35ms. That means the FFT gets ~1100 points. I vary these values to experiment (ie tried 16kHz, and increasing/decreasing interval length) but I get similar results.
With an FFT of 1100 points, you probably aren't able to capture the low frequencies with a lot of frequency resolution.
Think about it, 30 Hz corresponds to a period of 33ms, which at 32kHz is roughly 1000 samples. So you'll only be able to capture about 1 period in this time.
Thus, you'll need a longer FFT window to capture those low frequencies with sharp frequency resolution.
You'll likely need a time window of 4000 samples or more to start getting noticeably more frequency resolution at the low frequencies. This will be fine too, since you'll still get about 8-10 spectrum updates per second.
One option too, if you want very fast updates for the high frequency bins but good frequency resolution at the low frequencies, is to update the high frequency bins more quickly (such as with the windows you're currently using) but compute the low frequency bins less often (and with larger windows necessary for the good freq. resolution.)
I think a lot of these applications have variable FFT bins.
What you could do is start with very wide evenly spaced FFT bins like you have and then keep track of the number of elements that are placed in each FFT bin. If some of the bins are not used significantly at all (usually the higher frequencies) then widen those bins so that they are larger (and thus have more frequency entries) and shring the low frequency bins.
I have worked on projects were we just spend a lot of time tuning bins for specific input sources but it is much nicer to have the software adjust in real time.
A typical visualizer would use constant-Q bandpass filters, not a single FFT.
You could emulate a set of constant-Q bandpass filters by multiplying the FFT results by a set of constant-Q filter responses in the frequency domain, then sum. For low frequencies, you should use an FFT longer than the significant impulse response of the lowest frequency filter. For high frequencies, you can use shorter FFTs for better responsiveness. You can slide any length FFTs along at any desired update rate by overlapping (re-using) data, or you might consider interpolation. You might also want to pre-window each FFT to reduce "spectral leakage" between frequency bands.
100 periods have been collected from a 3 dimensional periodic signal. The wavelength slightly varies. The noise of the wavelength follows Gaussian distribution with zero mean. A good estimate of the wavelength is known, that is not an issue here. The noise of the amplitude may not be Gaussian and may be contaminated with outliers.
How can I compute a single period that approximates 'best' all of the collected 100 periods?
Time-series, ARMA, ARIMA, Kalman Filter, autoregression and autocorrelation seem to be keywords here.
UPDATE 1: I have no idea how time-series models work. Are they prepared for varying wavelengths? Can they handle non-smooth true signals? If a time-series model is fitted, can I compute a 'best estimate' for a single period? How?
UPDATE 2: A related question is this. Speed is not an issue in my case. Processing is done off-line, after all periods have been collected.
Origin of the problem: I am measuring acceleration during human steps at 200 Hz. After that I am trying to double integrate the data to get the vertical displacement of the center of gravity. Of course the noise introduces a HUGE error when you integrate twice. I would like to exploit periodicity to reduce this noise. Here is a crude graph of the actual data (y: acceleration in g, x: time in second) of 6 steps corresponding to 3 periods (1 left and 1 right step is a period):
My interest is now purely theoretical, as http://jap.physiology.org/content/39/1/174.abstract gives a pretty good recipe what to do.
We have used wavelets for noise suppression with similar signal measured from cows during walking.
I'm don't think the noise is so much of a problem here and the biggest peaks represent actual changes in the acceleration during walking.
I suppose that the angle of the leg and thus accelerometer changes during your experiment and you need to account for that in order to calculate the distance i.e you need to know what is the orientation of the accelerometer in each time step. See e.g this technical note for one to account for angle.
If you need get accurate measures of the position the best solution would be to get an accelerometer with a magnetometer, which also measures orientation. Something like this should work: http://www.sparkfun.com/products/10321.
EDIT: I have looked into this a bit more in the last few days because a similar project is in my to do list as well... We have not used gyros in the past, but we are doing so in the next project.
The inaccuracy in the positioning doesn't come from the white noise, but from the inaccuracy and drift of the gyro. And the error then accumulates very quickly due to the double integration. Intersense has a product called Navshoe, that addresses this problem by zeroing the error after each step (see this paper). And this is a good introduction to inertial navigation.
Periodic signal without noise has the following property:
f(a) = f(a+k), where k is the wavelength.
Next bit of information that is needed is that your signal is composed of separate samples. Every bit of information you've collected are based on samples, which are values of f() function. From 100 samples, you can get the mean value:
1/n * sum(s_i), where i is in range [0..n-1] and n = 100.
This needs to be done for every dimension of your data. If you use 3d data, it will be applied 3 times. Result would be (x,y,z) points. You can find value of s_i from the periodic signal equation simply by doing
s_i(a).x = f(a+k*i).x
s_i(a).y = f(a+k*i).y
s_i(a).z = f(a+k*i).z
If the wavelength is not accurate, this will give you additional source of error or you'll need to adjust it to match the real wavelength of each period. Since
k*i = k+k+...+k
if the wavelength varies, you'll need to use
k_1+k_2+k_3+...+k_i
instead of k*i.
Unfortunately with errors in wavelength, there will be big problems keeping this k_1..k_i chain in sync with the actual data. You'd actually need to know how to regognize the starting position of each period from your actual data. Possibly need to mark them by hand.
Now, all the mean values you calculated would be functions like this:
m(a) :: R->(x,y,z)
Now this is a curve in 3d space. More complex error models will be left as an excersize for the reader.
If you have a copy of Curve Fitting Toolbox, localized regression might be a good choice.
Curve Fitting Toolbox supports both lowess and loess localized regression models for curve and curve fitting.
There is an option for robust localized regression
The following blog post shows how to use cross validation to estimate an optimzal spaning parameter for a localized regression model, as well as techniques to estimate confidence intervals using a bootstrap.
http://blogs.mathworks.com/loren/2011/01/13/data-driven-fitting/
gyroscopes which measure rate of rotation of angles when integrated produce angles right?
my question is how do i do this? what im doing so far is just adding all the angles ive detected and that seems to be very wrong
AngleIntegrated = GyroDegPersec * (1/GyroBandWidth);
suggestions are very welcome. thanks
You need to integrate with respect to time. So ideally you should sample the gyroscope at regular (fixed) time intervals, T, and then incorporate that sampling interval, T, into your integral calculation.
Note that T needs to be small enough to satisfy the Nyquist criterion.
You can integrate in discrete domain. Suppose the angular rate is da, it's time integral is a.
k is the discrete step number.
a(k) = a(k-1) + T*0.5*(da(k) + da(k-1))
For example, da(k) is current angular rate reading. da(k-1) is previoud angular rate reading. a(k-1) is the previous step's integration value(rotation angle). T is sampling rate. If the sensor outputs in every 1 millisecond, T becomes 0.001.
You can use this formula when k>0. The initial value, a(0), must be given.
Knowing that of course you can't count on having a correct value in the long run (by integration your error window will always increase over time) what I would do is reading the gyroscope, interpolating the current read and previous few ones to get a smooth curve (e.g. a parabola using current read and previous two) and then computing the integral of that parabola from last read time and current time.