I have been reading up on FFT and Pitch Detection for a while now, but I'm having trouble piecing it all together.
I have worked out that the Accelerate framework is probably the best way to go with this, and I have read the example code from apple to see how to use it for FFTs. What is the input data for the FFT if I wanted to be running the pitch detection in real time? Do I just pass in the audio stream from the microphone? How would I do this?
Also, after I get the FFT output, how can I get the frequency from that? I have been reading everywhere, and can't find any examples or explanations of this?
Thanks for any help.
Frequency and pitch are not the same thing - frequency is a physical quantity, pitch is a psychological percept - they are similar, but there are important differences, which may or may not matter to you, depending on the type of instrument for which you are trying to measure pitch.
You need to read up a little on the various pitch detection algorithms (and on the meaning of pitch itself), decide what algorithm you want to use and only then set about implementing it. See this Wikipedia page for a good overview of pitch and pitch detection (note that you can use FFT for the autocorrelation-based and frequency domain methods).
As for using the FFT to identify peaks in a spectrum and their associated frequencies, there are many questions and answers related to this on SO already, see for example: How do I obtain the frequencies of each value in an FFT?
I have an example implementation of an Autocorrelation function available online for ios 5.1. Look at this post for a link to the implementation AND functions on how to find the nearest note and how to create a string representing the pitch (A, A#, B, B#, etc...)
While the FFT is very useful in many applications, it might not be the most accurate if you're trying to do simple pitch detection. (It can be as accurate, but you have to deal with complex numbers to do a lot of phase calculations)
Related
I'm trying to figure out how to correct drift errors introduced by a SLAM method using GPS measurements, I have two point sets in euclidian 3d space taken at fixed moments in time:
The red dataset is introduced by GPS and contains no drift errors, while blue dataset is based on SLAM algorithm, it drifts over time.
The idea is that SLAM is accurate on short distances but eventually drifts, while GPS is accurate on long distances and inaccurate on short ones. So I would like to figure out how to fuse SLAM data with GPS in such way that will take best accuracy of both measurements. At least how to approach this problem?
Since your GPS looks like it is very locally biased, I'm assuming it is low-cost and doesn't use any correction techniques, e.g. that it is not differential. As you probably are aware, GPS errors are not Gaussian. The guys in this paper show that a good way to model GPS noise is as v+eps where v is a locally constant "bias" vector (it is usually constant for a few metters, and then changes more or less smoothly or abruptly) and eps is Gaussian noise.
Given this information, one option would be to use Kalman-based fusion, e.g. you add the GPS noise and bias to the state vector, and define your transition equations appropriately and proceed as you would with an ordinary EKF. Note that if we ignore the prediction step of the Kalman, this is roughly equivalent to minimizing an error function of the form
measurement_constraints + some_weight * GPS_constraints
and that gives you a more straigh-forward, second option. For example, if your SLAM is visual, you can just use the sum of squared reprojection errors (i.e. the bundle adjustment error) as the measurment constraints, and define your GPS constraints as ||x- x_{gps}|| where the x are 2d or 3d GPS positions (you might want to ignore the altitude with low-cost GPS).
If your SLAM is visual and feature-point based (you didn't really say what type of SLAM you were using so I assume the most widespread type), then fusion with any of the methods above can lead to "inlier loss". You make a sudden, violent correction, and augment the reprojection errors. This means that you lose inliers in SLAM's tracking. So you have to re-triangulate points, and so on. Plus, note that even though the paper I linked to above presents a model of the GPS errors, it is not a very accurate model, and assuming that the distribution of GPS errors is unimodal (necessary for the EKF) seems a bit adventurous to me.
So, I think a good option is to use barrier-term optimization. Basically, the idea is this: since you don't really know how to model GPS errors, assume that you have more confidance in SLAM locally, and minimize a function S(x) that captures the quality of your SLAM reconstruction. Note x_opt the minimizer of S. Then, fuse with GPS data as long as it does not deteriorate S(x_opt) more than a given threshold. Mathematically, you'd want to minimize
some_coef/(thresh - S(X)) + ||x-x_{gps}||
and you'd initialize the minimization with x_opt. A good choice for S is the bundle adjustment error, since by not degrading it, you prevent inlier loss. There are other choices of S in the litterature, but they are usually meant to reduce computational time and add little in terms of accuracy.
This, unlike the EKF, does not have a nice probabilistic interpretation, but produces very nice results in practice (I have used it for fusion with other things than GPS too, and it works well). You can for example see this excellent paper that explains how to implement this thoroughly, how to set the threshold, etc.
Hope this helps. Please don't hesitate to tell me if you find inaccuracies/errors in my answer.
I'm writing a program that has, as one facet, a wave filtration/resolution routine. The more data I collect, the bigger the files stored to the device get. I'm collecting data at discrete time steps, and in the interest of accuracy I'm doing this pretty frequently. However, I noticed that the overall wave form tends to be wide enough that I could be collecting data at about half the rate I am and still be able to draw an accurate-enough-for-my-purposes waveform over the data.
So the question: is there a way to, from this data, create a continuous mathematic description of the curve? I haven't been able to find anything. My data is float inside of NSNumbers contained by an NSArray.
The two things I would like to be able to do are get intersections points for a threshold and find local maximums. The ability to do either one of these would be sufficient.
-EDIT-
If anyone knows a good objective-c FFT method for 1-dimensional real arrays I would love to hear it.
Apple includes an FFT in the Accelerate framework.
Using Fourier Transforms
Example: FFT Sample
Also: Using the Apple FFT and Accelerate Framework
I want to get the pitch of a song at any point. I plan on storing the pitches later. How can I read say... an mp3 file or wav file to get the pitch played at a certain point?
Here is a visual example:
Say I wanted to get the pitch that is here at ^this point of the song.
Thanks if you can!
The matter is a tad more complicated than you may be anticipating.
While time-domain approaches exist (that is, approaches which work with the PCM data directly), frequency-domain pitch detection is going to be more accurate. You can read a very simplified overview here.
What you probably want is a Fourier Transform, which can be used to transform blocks of your signal from time-domain to frequency-domain (that is, a distribution of frequency content over a given span of the signal). From there, you would need to analyze the frequency spectrum within that block. The problem becomes even harder still, because there is no best way to deduce pitch from a sampled frequency spectrum in the general case. The aforementioned Wikipedia article should give you a foundation for looking into those algorithms.
Finally, it's worth noting that this is really a language-agnostic question, unless your primary interest is in reading a WAV file specifically using VB.NET.
I am writing an audio visualizing application which will detect the low, mid and high frequencies of a song. I have looked endlessly on google and can't seem to find anything and the Apple developer documents all seem to show audio uses in standard ways.
Ideally, I'm just looking for an objective-C function.
I was also looking for something to filter out frequencies and I could not find anything pre-made. So I started to create my own. I am using a window-sinc filter based off this code.
Check it out!
http://logix4u.net/DSP/Digital_Filters/Windowed_sinc_filter.html
You can use a simple FFT routine, such as KissFFT, with a fairly small window size (e.g. 256). Then just sum the magnitudes of the bins of interest for each of the three ranges.
I am new to CoreAudio, and I would like to output a simple sine wave and square wave with a given frequency and amplitude through the speakers using CA. I don't want to use sound files as I want to synthesize the sound.
What do I need to do this? And can you give me an example or tutorial? Thanks.
There are a number of errors in the previous answer. I, the legendary :-) James McCartney, not James Harkins wrote the sinewavedemo, I also wrote SuperCollider which is what the audiosynth.com website is about. I also now work at Apple on CoreAudio. The sinewavedemo DOES use CoreAudio, since it uses AudioHardware.h from CoreAudio.framework as its way to play the sound.
You should not use the sinewavedemo. It is very old code and it makes dangerous assumptions about the buffer layout of the audio hardware. The easiest way nowadays to play a sound that you are generating is to use the AudioQueue, or to use an output audio unit with a render callback set.
The best and easiest way to do that without files is to prepare a single cycle buffer, containing one cycle of the wave (this is called technically a wavetable)
In the playback function called by CoreAudio thread, fill the output buffer with samples read from the wave buffer.
Note however that you will face two problems very quickly :
- for the sine wave, if the playback frequency is not an integer multiple of the desired sine frequency, you will probably need to implement an interpolator if you want to have a good quality. Using only integer pointers will generate a significant level of harmonic noise.
for the square wave, avoid to just program an array with +1 / -1 values. Such a signal is not bandlimited and will alias a lot. Do not forget that the spectrum of a square wave is virtually infinite!
To get good algorithms for signal generation, take a look to musicdsp.org, that's probably one of the best resource for that
Are you new to audio programming in general? As a starting point i would check out
http://www.audiosynth.com/sinewavedemo.html
This is a minimum osx sinewave implementation by the legendary James Harkins. Note, it doesn't use CoreAudio at all.
If you specifically want to use CoreAudio for your sinewave you need to create an output unit (RemoteIO on the iphone, AUHAL on osx) and supply an input callback, where you can pretty much use the code from the above example. Check out
http://developer.apple.com/mac/library/technotes/tn2002/tn2091.html
The benefits of CoreAudio are chiefly, chain other effects with your sinewave, write plugins for hosts like Logic & provide the interfaces for them, write a host (like Logic) for plugins that can be chained together.
If you don't wont to write a plugin, or host plugins then CoreAudio might not actually be for you. But one of the best things about using CoreAudio is that once you get your sinewave callback working it is easy to add effects, or mix multiple sines together
To do this you need to put your output unit in a graph, to which you can effects, mixers, etc.
Here is some help on setting up graphs http://timbolstad.com/2010/03/16/core-audio-getting-started-pt2/
It isn't as difficult as it looks. Apple provides C++ helper classes for many things (/Developer/Examples/CoreAudio/PublicUtility) and even if you don't want to use C++ (you don't have to!) they can be a useful guide to the CoreAudio API.
If you are not doing this realtime, using the sin() function from math.h is not a bad idea. Just fill however many samples you need with sin() beforehand when it is time to play it, just send it to the audio buffer. sin() can be quite slow to call once every sample if you are doing this realtime, using an interpolated wavetable lookup method is much faster, but the resulting sound will not be as spectrally pure.
There is a good and well documented sine wave player code example in Chapter 7 of the Adamson/Avila "Learning Core Audio" book, published by Addison-Wesley Professional (ISBN-10: 0-321-63684-8 ):
http://www.informit.com/store/learning-core-audio-a-hands-on-guide-to-audio-programming-9780321636843
It is a rather new publication (2012) and addresses precisely the issue of this question. It's only a starting point, but it's a valuable starting point.
BTW. Don't jump to graphs before having this basic lesson (which involves some math) behind.
Concerning example code, a quick and efficient method I often use deals with a pre-filled sinewave lookup table which has as many members as sample rate, for 44100 Hz the table has size of 44100. In other words, cycle length equals sample rate. This gives an acceptable trade-off between speed and quality in many cases. You can initialize it with the program.
If you generate floating point samples (which is default in OSX), and use math functions, use sinf() rather than (float)sin(). Promotions in inner loop cycles of a render callback are always resource-expensive. So are repetitive multiplications of constants, such as 2.0*M_PI, which can too often be found in code examples.