I'm developing a software to input a monotonic .wav clip (piano) and show the piano notes which are played in that clip. I'm using FFT to calculate the frequencies but they are giving me values such as 22360 Hz and so on where I want to get around 260 to 600 Hz.
Can someone please help me with this?
Pianos put out a lot of powerful high harmonics or overtones, and thus an FFT should show amplitude in many high frequency bins. Perhaps you should use a pitch detection or estimation algorithm instead of just an FFT?
I think your problem is that you don't have enough samples, so the frequency resolution is poor. All you need to do is to have more samples or just zero-padding. See here and here. That may help.
Hotpaw2 makes an important point about overtone content.
However another thing you will require is a window function to prevent frequency domain artifacts of the sampling interval from contaminating your result. The window function applied to the data before the FFT essentially fades the signal in and out smoothly to avoid this.
Related
How can I make server-side game run the same on every machine, because when I use server's delta time it works different on every computer/phone.
Would something called 'fixed timestep' help me ?
Yes fixed timestep can help you. But also simple movement with a delta can help you.
Fixed timestep commonly using with a physics because sometimes physics needs to be update more often (120-200hz)than game's render method.
However you can still use fixed timestep without physic.
You just need to interpolate your game objects with
lerp(oldValue, newValue, accumulator / timestep);
In your case probably small frame rate differences causes unexpected results.
To avoid that you should use movement depends delta.
player.x+=5*60*delta;//I assume your game is 60 fps
Instead of
player.x+=5;
So last delta will be only difference between machines.And its negligible since delta difference between 60 and 58 fps is only ~0.0005 secs
I want to fit a curve to data obtained from an FFT. While working on this, I remembered that an FFT gives binned data, and therefore I wondered if I should treat this differently with curve-fitting.
If the bins are narrow compared to the structure, I think it should not be necessary to treat the data differently, but for me that is not the case.
I expect the right way to fit binned data is by minimizing not the difference between values of the bin and fit, but between bin area and the area beneath the fitted curve, for each bin, such that the energy in each bin matches the energy in the range of the bin as signified by the curve.
So my question is: am I thinking correctly about this? If not, how should I go about it?
Also, when looking around for information about this subject, I encountered the "Maximum log likelihood" for example, but did not find enough information about it to understand if and how it applied to my situation.
PS: I have no clue if this is the right site for this question, please let me know if there is a better place.
For an unwindowed FFT, the correct interpolation between bins is by using a Sinc (sin(x)/x) or periodic Sinc (Dirichlet) interpolation kernel. For an FFT of samples of a band-limited signal, thus will reconstruct the continuous spectrum.
A very simple and effective way of interpolating the spectrum (from an FFT) is to use zero-padding. It works both with and without windowing prior to the FFT.
Take your input vector of length N and extend it to length M*N, where M is an integer
Set all values beyond the original N values to zeros
Perform an FFT of length (N*M)
Calculate the magnitude of the ouput bins
What you get is the interpolated spectrum.
Best regards,
Jens
This can be done by using maximum log likelihood estimation. This is a method that finds the set of parameters that is most likely to have yielded the measured data - the technique originates in statistics.
I have finally found an understandable source for how to apply this to binned data. Sadly I cannot enter formulas here, so I refer to that source for a full explanation: slide 4 of this slide show.
EDIT:
For noisier signals this method did not seem to work very well. A method that was a bit more robust is a least squares fit, where the difference between the area is minimized, as suggested in the question.
I have not found any literature to defend this method, but it is similar to what happens in the maximum log likelihood estimation, and yields very similar results for noiseless test cases.
I've been playing around with Web Audio some. I have a simple oscillator node playing at a frequency of context.sampleRate / analyzerNode.fftSize * 5 (107.666015625 in this case). When I call analyzer.getByteFrequencyData I would expect it to have a value in the 5th bin, and no where else. What I actually see is [0,0,0,240,255,255,255,240,0,0...]
Why am I getting values in multiple bins?
The webaudio AnalyserNode applies a Blackman window before computing the FFT. This windowing function will smear the single tone.
That has to do that your sequence is finite and therefore your signal is supposed to last for a finite amount of time. Surely you are calculating the FFT with a rectangular window, i.e. your signal is consider to last for the amount of generated samples only and that "discontinuity" (i.e. the fact that the signal has a finite number of samples) creates the spectral leakage. To minimise this effect, you could try several windows functions that when applied to your data prior the FFT calculation, reduces this effect.
It looks like you might be clipping somewhere in your computation by using a test signal too large for your data or arithmetic format. Try again using a floating point format.
I have a series of data and need to detect peak values in the series within a certain number of readings (window size) and excluding a certain level of background "noise." I also need to capture the starting and stopping points of the appreciable curves (ie, when it starts ticking up and then when it stops ticking down).
The data are high precision floats.
Here's a quick sketch that captures the most common scenarios that I'm up against visually:
One method I attempted was to pass a window of size X along the curve going backwards to detect the peaks. It started off working well, but I missed a lot of conditions initially not anticipated. Another method I started to work out was a growing window that would discover the longer duration curves. Yet another approach used a more calculus based approach that watches for some velocity / gradient aspects. None seemed to hit the sweet spot, probably due to my lack of experience in statistical analysis.
Perhaps I need to use some kind of a statistical analysis package to cover my bases vs writing my own algorithm? Or would there be an efficient method for tackling this directly with SQL with some kind of local max techniques? I'm simply not sure how to approach this efficiently. Each method I try it seems that I keep missing various thresholds, detecting too many peak values or not capturing entire events (reporting a peak datapoint too early in the reading process).
Ultimately this is implemented in Ruby and so if you could advise as to the most efficient and correct way to approach this problem with Ruby that would be appreciated, however I'm open to a language agnostic algorithmic approach as well. Or is there a certain library that would address the various issues I'm up against in this scenario of detecting the maximum peaks?
my idea is simple, after get your windows of interest you will need find all the peaks in this window, you can just compare the last value with the next , after this you will have where the peaks occur and you can decide where are the best peak.
I wrote one simple source in matlab to show my idea!
My example are in wave from audio file :-)
waveFile='Chick_eco.wav';
[y, fs, nbits]=wavread(waveFile);
subplot(2,2,1); plot(y); legend('Original signal');
startIndex=15000;
WindowSize=100;
endIndex=startIndex+WindowSize-1;
frame = y(startIndex:endIndex);
nframe=length(frame)
%find the peaks
peaks = zeros(nframe,1);
k=3;
while(k <= nframe - 1)
y1 = frame(k - 1);
y2 = frame(k);
y3 = frame(k + 1);
if (y2 > 0)
if (y2 > y1 && y2 >= y3)
peaks(k)=frame(k);
end
end
k=k+1;
end
peaks2=peaks;
peaks2(peaks2<=0)=nan;
subplot(2,2,2); plot(frame); legend('Get Window Length = 100');
subplot(2,2,3); plot(peaks); legend('Where are the PEAKS');
subplot(2,2,4); plot(frame); legend('Peaks in the Window');
hold on; plot(peaks2, '*');
for j = 1 : nframe
if (peaks(j) > 0)
fprintf('Local=%i\n', j);
fprintf('Value=%i\n', peaks(j));
end
end
%Where the Local Maxima occur
[maxivalue, maxi]=max(peaks)
you can see all the peaks and where it occurs
Local=37
Value=3.266296e-001
Local=51
Value=4.333496e-002
Local=65
Value=5.049438e-001
Local=80
Value=4.286804e-001
Local=84
Value=3.110046e-001
I'll propose a couple of different ideas. One is to use discrete wavelets, the other is to use the geographer's concept of prominence.
Wavelets: Apply some sort of wavelet decomposition to your data. There are multiple choices, with Daubechies wavelets being the most widely used. You want the low frequency peaks. Zero out the high frequency wavelet elements, reconstruct your data, and look for local extrema.
Prominence: Those noisy peaks and valleys are of key interest to geographers. They want to know exactly which of a mountain's multiple little peaks is tallest, the exact location of the lowest point in the valley. Find the local minima and maxima in your data set. You should have a sequence of min/max/min/max/.../min. (You might want to add an arbitrary end points that are lower than your global minimum.) Consider a min/max/min sequence. Classify each of these triples per the difference between the max and the larger of the two minima. Make a reduced sequence that replaces the smallest of these triples with the smaller of the two minima. Iterate until you get down to a single min/max/min triple. In your example, you want the next layer down, the min/max/min/max/min sequence.
Note: I'm going to describe the algorithmic steps as if each pass were distinct. Obviously, in a specific implementation, you can combine steps where it makes sense for your application. For the purposes of my explanation, it makes the text a little more clear.
I'm going to make some assumptions about your problem:
The windows of interest (the signals that you are looking for) cover a fraction of the entire data space (i.e., it's not one long signal).
The windows have significant scope (i.e., they aren't one pixel wide on your picture).
The windows have a minimum peak of interest (i.e., even if the signal exceeds the background noise, the peak must have an additional signal excess of the background).
The windows will never overlap (i.e., each can be examined as a distinct sub-problem out of context of the rest of the signal).
Given those, you can first look through your data stream for a set of windows of interest. You can do this by making a first pass through the data: moving from left to right, look for noise threshold crossing points. If the signal was below the noise floor and exceeds it on the next sample, that's a candidate starting point for a window (vice versa for the candidate end point).
Now make a pass through your candidate windows: compare the scope and contents of each window with the values defined above. To use your picture as an example, the small peaks on the left of the image barely exceed the noise floor and do so for too short a time. However, the window in the center of the screen clearly has a wide time extent and a significant max value. Keep the windows that meet your minimum criteria, discard those that are trivial.
Now to examine your remaining windows in detail (remember, they can be treated individually). The peak is easy to find: pass through the window and keep the local max. With respect to the leading and trailing edges of the signal, you can see n the picture that you have a window that's slightly larger than the actual point at which the signal exceeds the noise floor. In this case, you can use a finite difference approximation to calculate the first derivative of the signal. You know that the leading edge will be somewhat to the left of the window on the chart: look for a point at which the first derivative exceeds a positive noise floor of its own (the slope turns upwards sharply). Do the same for the trailing edge (which will always be to the right of the window).
Result: a set of time windows, the leading and trailing edges of the signals and the peak that occured in that window.
It looks like the definition of a window is the range of x over which y is above the threshold. So use that to determine the size of the window. Within that, locate the largest value, thus finding the peak.
If that fails, then what additional criteria do you have for defining a region of interest? You may need to nail down your implicit assumptions to more than 'that looks like a peak to me'.
I am a programmer and not a good mathematician so FFT is like some black box to me, I would like t throw some data into some FFT library and get out a plottable AFR (amplitude-frequency response) data, like some software like Rightmark audio does:
http://www.ixbt.com/proaudio/behringer/3031a/fr-hf.png
Now I have a system which plays back a logarithmic swept sine (with short fade-in/fade-out to avoid sharp edges) and records the response from the audio system.
As far as I understand, I need to pad the input with zeros to 2^n, use audio samples as a real part of a complex numbers, set imaginary=0, and I'll get back from FFT the frequency bins array whith half length of input data.
But if I do not need as big frequency resolution as some seconds audio buffer give to me, then what is the right way to make, lets say, 1024 size FFT window, feed chunks of audio and get back 512 frequency points which take into account all the data I passed in? Or maybe it is not possible and I need to feed entire swept sine at once to get back all the AFR data I need?
Also is there any smoothing needed? I have seen that the raw output from FFT may be really noisy. What is the right way to avoid the noise as early as possible, so I see the noise only as it comes from the AFR itself and not from FFT calculations (like the image in the link I have given - it seems pretty smooth)?
I am a C++/C# programmer. I would be grateful for any examples which show how to process chunks of swept sine end get back AFR data. For now I have found only examples which process data in small chunks in realtime, and that is not what I need.
Window function should help you reducing the noise
All you need to do is multiply your input data by w(n) :