I have some code that block processes the xcorr command with parallel computing too. I want to test how robust cross correlation is with data that has lower S/N.
The only problem is I don't quite know how to apply this. I have an audio file with animal calls. It is mostly noise with intermittent calls. all the calls have different S/N. If you look at the Short Term Fourier Transform spectrogram of the animal call, you will see a blob with a distribution of different intensities.
I want to lower the S/N of these calls so that the shape of the distribution of intensities is still the same, it's just that they are smaller in intensity.
To successfully lower the S/N of the audio, I'm assuming I don't want to change the background noise values either, so only the calls themselves are lowering in amplitude but not the noise.
I don't quite know how I can program this, can I get some help please?
I think you can safely just add extra noise to the whole sample, this is common when testing robustness: if your original sample has say 50 units** of signal and 50 units of noise (SNR of 50/50) then adding say 100 units of noise will lead to a SNR or 50/150, which is lower.
**subject to discussion of what constitutes a unit - power vs voltage, dBs or whatever, it's just for the sake of an example.
If it's important what type of noise you add then perhaps you could copy some from the sections without samples in - doing this manually is usually efficient enough when creating test cases. Alternatively rand will give you random numbers and rng will let you control the distribution.
An alternative method might be to apply a compression function to the spectrograph and then apply the inverse transform to bring it back to the time domain. Beware of using modified versions of your training data to test the algorithm, if you have sufficient data you'd be best to reserve some for testing.
To do this with a sound file editor (plus a file full of noise of your desired distribution and type), first turn down the level of the original file until the signal is at your desired lower level, then mix in the noise file to bring the noise back up to the original level (by setting the appropriate mixer parameters). The resulting mix will have a lower S/N.
Related
Review for removing periodicsI have a dataset that contains hourly wind speed data for 7 seven. I am trying to implement a forecasting model to the data and the review paper states that trimming of diurnal, weekly, monthly, and annual patterns in data significantly enhances estimation accuracy. They then follow along by using the fourier series to remove the periodic components as seen in the image. Any ideas on how i model this in matlab?
I am afraid this topic is not explained "urgently". What you need is a filter for the respective frequencies and a certain number of their harmonics. You can implement such a filter with an fft or directly with a IIR/FIR-formula.
FFT is faster than a IIR/FIR-implementation, but requires some care with respect to window function. Even if you do a "continuous" DFT, you will have a window function (like exponential or gaussian). The window function determines the bandwidth. The wider the window, the smaller the bandwidth. With an IIR/FIR-filter the bandwidth is encoded in the recursive parameters.
For suppressing single frequencies (like the 24hr weather signal) you need a notch-filter. This also requires you to specify a bandwidth, as you can see in the linked article. The smaller the bandwidth, the longer it will take (in time) until the filter has evolved to the frequency to suppress it. If you want the filter to recognize the amplitude of the 24hr-signal fast, then you need a wider bandwidth. But then however you are going to suppress also more frequencies slightly lower and slightly higher than 1/24hrs. It's a tradeoff.
If you also want to suppress several harmonics (like described in the paper) you have to combine several notch-filters in series. If you want to do it with FFT, you have to model the desired transfer function in the frequency space and since you can do this for all frequencies at once, so it's more efficient.
An easy but approximate way to get something similar to a notch-filter including all harmonics is with a Comb-filter. But it's an approximation, you have no control over the details of the transfer function. You could do that in Matlab by adding to the original a signal that is shifted by 12hrs. This is because a sinusoidal signal will cancel with one that is shifted by pi.
So you see, there's lots of possibilities for what you want.
Is this because it's a complex problem ? I mean to wide and therefore it does not exist a simple / generic solution ?
Because every (almost) software making signal processing (Avisoft, GoldWave, Audacity…) have this function that reduce background noise of a signal. Usually it uses FFT. But I can't find a function (already implemented) in Matlab that allows us to do the same ? Is the right way to make it manually then ?
Thanks.
The common audio noise reduction approaches built-in to things like Audacity are based around spectral subtraction, which estimates the level of steady background noise in the Fourier transform magnitude domain, then removes that much energy from every frame, leaving energy only where the signal "pokes above" this noise floor.
You can find many implementations of spectral subtraction for Matlab; this one is highly rated on Matlab File Exchange:
http://www.mathworks.com/matlabcentral/fileexchange/7675-boll-spectral-subtraction
The question is, what kind of noise reduction are you looking for? There is no one solution that fits all needs. Here are a few approaches:
Low-pass filtering the signal reduces noise but also removes the high-frequency components of the signal. For some applications this is perfectly acceptable. There are lots of low-pass filter functions and Matlab helps you apply plenty of them. Some knowledge of how digital filters work is required. I'm not going into it here; if you want more details consider asking a more focused question.
An approach suitable for many situations is using a noise gate: simply attenuate the signal whenever its RMS level goes below a certain threshold, for instance. In other words, this kills quiet parts of the audio dead. You'll retain the noise in the more active parts of the signal, though, and if you have a lot of dynamics in the actual signal you'll get rid of some signal, too. This tends to work well for, say, slightly noisy speech samples, but not so well for very noisy recordings of classical music. I don't know whether Matlab has a function for this.
Some approaches involve making a "fingerprint" of the noise and then removing that throughout the signal. It tends to make the result sound strange, though, and in any case this is probably sufficiently complex and domain-specific that it belongs in an audio-specific tool and not in a rather general math/DSP system.
Reducing noise requires making some assumptions about the type of noise and the type of signal, and how they are different. Audio processors typically assume (correctly or incorrectly) something like that the audio is speech or music, and that the noise is typical recording session background hiss, A/C power hum, or vinyl record pops.
Matlab is for general use (microwave radio, data comm, subsonic earthquakes, heartbeats, etc.), and thus can make no such assumptions.
matlab is no exactly an audio processor. you have to implement your own filter. you will have to design your filter correctly, according to what you want.
I have FFT outputs that look like this:
At 523 Hz is the maximum value. However, being a messy FFT, there are lots of little peaks that are right near the large peaks. However, they're irrelevant, whereas the peaks shown aren't. Are the any algorithms I can use to extract the maxima of this FFT that matter; I.E., aren't just random peaks cropping up near "real" peaks? Perhaps there is some sort of filter I can apply to this FFT output?
EDIT: The context of this is that I am trying to take one-hit sound samples (like someone pressing a key on a piano) and extract the loudest partials. In the image below, the peaks above 2000 Hz are important, because they are discrete partials of the given sound (which happens to be a sort of bell). However, the peaks that are scattered about right near 523 seem to be just artifacts, and I want to ignore them.
If the peak is broad, it could indicate that the peak frequency is modulated (AM, FM or both), or is actually a composite of several spectral peaks, themselves each potentially modulated.
For instance, a piano note may be the result of the hammer hitting up to 3 strings that are all tuned just a tiny fraction differently, and they all can modulate as they exchange energy between strings though the piano frame. Guitar strings can change frequency as the pluck shape distortion smooths out and decays. Bells change shape after they are hit, which can modulate their spectrum. Etc.
If the sound itself is "messy" then you need a good definition of what you mean by the "real" peak, before applying any sort of smoothing or side-band rejection filter. e.g. All that "messiness" may be part of what makes a bell sound like a real bell instead of an electronic sinewave generator.
Try convolving your FFT (treating it as a signal) with a rectangular pulse( pulse = ones(1:20)/20; ). This might get rid of some of them. Your maxima will be shifted by 10 frequency bins to teh right, to take that into account. You would basically be integrating your signal. Similar techniques are used in Pan-Tompkins algorithm for heart beat identification.
I worked on a similar problem once, and choosed to use savitsky-golay filters for smoothing the spectrum data. I could get some significant peaks, and it didn't messed too much with the overall spectrum.
But I Had a problem with what hotpaw2 is alerting you, I have lost important characteristics along with the lost of "messiness", so I truly recommend you hear him. But, if you think you won't have a problem with that, I think savitsky-golay can help.
There are non-FFT methods for creating a frequency domain representation of time domain data which are better for noisy data sets, like Max-ent recontruction.
For noisy time-series data, a max-ent reconstruction will be capable of distinguising true peaks from noise very effectively (without adding any artifacts or other modifications to suppress noise).
Max ent works by "guessing" an FFT for a time domain specturm, and then doing an IFT, and comparing the results with the "actual" time-series data, iteratively. The final output of maxent is a frequency domain spectrum (like the one you show above).
There are implementations in java i believe for 1-d spectra, but I have never used one.
I'm trying to write a simple tuner (no, not to make yet another tuner app), and am looking at the AurioTouch sample source (has anyone tried to comment this code??).
My worry is that aurioTouch doesn't seem to actually work very well when looking at the frequency domain graph. I play a single note on an instrument and I don't see a nicely ordered, small, set of frequencies with one string peak at the appropriate frequency of the note.
Has anyone used aurioTouch enough to know whether the underlying code is functional or whether it is just a crude sample?
Other options I have are to use FFTW or KISS FFT. Anyone have any experience with those?
Thanks.
You're expecting the wrong thing!!
Not the library's fault
Whether the library produces it properly or not, you're looking for a pattern that rarely actually exists in real-life sounds. Only a perfect sine wave, electronically generated, will cause an even partway discrete appearing 'spike' in the freq. graph. If you don't believe it try firing up a 'spectrum analyzer' visualization in winamp or media player. It's not so much the PC's fault.
Real sound waves are complicated animals
Picture a sawtooth or sqaure wave in your mind's eye. those sharp turnaround - corners or points on the wave, look like tons of higher harmonics to the FFT or even a real fourier. And if you've ever seen a real 'sqaure wave/sawtooth' on a scope, or even a 'sine wave' produced by an instrument that is supposed to produce a sinewave, take a look at all the sharp nooks and crannies in just ONE note (if you don't have a scope just zoom way in on the wave in audacity - the more you zoom, the higher notes you're looking at). Yep, those deviations all count as frequencies.
It's hard to tell the difference between one note and a whole orchestra sometimes in a spectrum analysis.
But I hear single notes!
So how does the ear do it? It considers the entire waveform. Then your lower brain lies to your upper brain about what the input is: one note, not a mess of overtones.
You can't do it as fully, but you can approximate it via 'training.'
Approximation: building some smarts
PLAY the note on the instrument and 'save' the frequency graph. Do this for notes in several frequency ranges, or better yet all notes.
Then interpolate the notes to fill in gaps (by 1/2 or 1/4 steps) by multiplying the saved graphs for that instrument by 2^(1/12) (or 1/24 for 1/4 steps, etc).
Figure out how to store them in a quickly-searchable data structure like a BST or trie. Only it would have to return a 'how close is this' score. It would have to identify the match via proportions of frequencies as well, in case it came in different volumes.
Using the smarts
Next time you're looking for a note from that instrument, just take the 'heard' freq graph and find it in that data structure. You can record several instruments that make different waveforms and search for them too. If there are background sounds or multiple notes, take the closest match. Then if you want to identify other notes, 'subtract' the found frequency pattern from the sampled one, and rinse, lather repeat.
It won't work by your voice...
If you ever tried to tune yourself by singing into a guitar tuner, you'll know that tuners arent that clever. Of course some instruments (voice esp) really float around the pitch and generate an ever-evolving waveform (even without somebody singing).
What are you trying to accomplish?
You would not have to totally get this fancy for a 'simple' tuner app, but if you're not making just another tuner app them I'm guessing you actually want to identify notes (e.g., maybe you want to autogenerate midi files from songs on the radio ;-)
Good luck. I hope you find a library that does all this junk instead of having to roll your own.
Edit 2017
Note this webpage: http://www.feilding.net/sfuad/musi3012-01/html/lectures/015_instruments_II.htm
Well down the page, there are spectrum analyses of various organ pipes. There are many, many overtones. These are possible to detect - with enough work - if you 'train' your app with them first (just like telling a kid, 'this is what a clarinet sounds like...')
aurioTouch looks weird because the frequency axis is on a linear scale. It's very difficult to interpret FFT output when the x-axis is anything other than a logarithmic scale (traditionally log2).
If you can't use aurioTouch's integer-FFT, check out my library:
http://github.com/alexbw/iPhoneFFT
It uses double-precision, has support for multiple window types, and implements Welch's method (which should give you more stable spectra when viewed over time).
#zaph, the FFT does compute a true Discrete Fourier Transform. It is simply an efficient algorithm that takes advantage of the bit-wise representation of digital signals.
FFTs use frequency bins and the bin frequency width is based on the FFT parameters. To find a frequency you will need to record it sampled at a rate at least twice the highest frequency present in the sample. Then find the time between the cycles. If it is not a pure frequency this will of course be harder.
I am using Ooura FFT to compute the FFT of acceleromter data. I do not always obtain the correct spectrum. For some reason, Ooura FFT produces completely wrong results with spectral magnitudes of the order 10^200 across all frequencies.
I'm trying to write a simple tuner (no, not to make yet another tuner app), and am looking at the AurioTouch sample source (has anyone tried to comment this code??).
My worry is that aurioTouch doesn't seem to actually work very well when looking at the frequency domain graph. I play a single note on an instrument and I don't see a nicely ordered, small, set of frequencies with one string peak at the appropriate frequency of the note.
Has anyone used aurioTouch enough to know whether the underlying code is functional or whether it is just a crude sample?
Other options I have are to use FFTW or KISS FFT. Anyone have any experience with those?
Thanks.
You're expecting the wrong thing!!
Not the library's fault
Whether the library produces it properly or not, you're looking for a pattern that rarely actually exists in real-life sounds. Only a perfect sine wave, electronically generated, will cause an even partway discrete appearing 'spike' in the freq. graph. If you don't believe it try firing up a 'spectrum analyzer' visualization in winamp or media player. It's not so much the PC's fault.
Real sound waves are complicated animals
Picture a sawtooth or sqaure wave in your mind's eye. those sharp turnaround - corners or points on the wave, look like tons of higher harmonics to the FFT or even a real fourier. And if you've ever seen a real 'sqaure wave/sawtooth' on a scope, or even a 'sine wave' produced by an instrument that is supposed to produce a sinewave, take a look at all the sharp nooks and crannies in just ONE note (if you don't have a scope just zoom way in on the wave in audacity - the more you zoom, the higher notes you're looking at). Yep, those deviations all count as frequencies.
It's hard to tell the difference between one note and a whole orchestra sometimes in a spectrum analysis.
But I hear single notes!
So how does the ear do it? It considers the entire waveform. Then your lower brain lies to your upper brain about what the input is: one note, not a mess of overtones.
You can't do it as fully, but you can approximate it via 'training.'
Approximation: building some smarts
PLAY the note on the instrument and 'save' the frequency graph. Do this for notes in several frequency ranges, or better yet all notes.
Then interpolate the notes to fill in gaps (by 1/2 or 1/4 steps) by multiplying the saved graphs for that instrument by 2^(1/12) (or 1/24 for 1/4 steps, etc).
Figure out how to store them in a quickly-searchable data structure like a BST or trie. Only it would have to return a 'how close is this' score. It would have to identify the match via proportions of frequencies as well, in case it came in different volumes.
Using the smarts
Next time you're looking for a note from that instrument, just take the 'heard' freq graph and find it in that data structure. You can record several instruments that make different waveforms and search for them too. If there are background sounds or multiple notes, take the closest match. Then if you want to identify other notes, 'subtract' the found frequency pattern from the sampled one, and rinse, lather repeat.
It won't work by your voice...
If you ever tried to tune yourself by singing into a guitar tuner, you'll know that tuners arent that clever. Of course some instruments (voice esp) really float around the pitch and generate an ever-evolving waveform (even without somebody singing).
What are you trying to accomplish?
You would not have to totally get this fancy for a 'simple' tuner app, but if you're not making just another tuner app them I'm guessing you actually want to identify notes (e.g., maybe you want to autogenerate midi files from songs on the radio ;-)
Good luck. I hope you find a library that does all this junk instead of having to roll your own.
Edit 2017
Note this webpage: http://www.feilding.net/sfuad/musi3012-01/html/lectures/015_instruments_II.htm
Well down the page, there are spectrum analyses of various organ pipes. There are many, many overtones. These are possible to detect - with enough work - if you 'train' your app with them first (just like telling a kid, 'this is what a clarinet sounds like...')
aurioTouch looks weird because the frequency axis is on a linear scale. It's very difficult to interpret FFT output when the x-axis is anything other than a logarithmic scale (traditionally log2).
If you can't use aurioTouch's integer-FFT, check out my library:
http://github.com/alexbw/iPhoneFFT
It uses double-precision, has support for multiple window types, and implements Welch's method (which should give you more stable spectra when viewed over time).
#zaph, the FFT does compute a true Discrete Fourier Transform. It is simply an efficient algorithm that takes advantage of the bit-wise representation of digital signals.
FFTs use frequency bins and the bin frequency width is based on the FFT parameters. To find a frequency you will need to record it sampled at a rate at least twice the highest frequency present in the sample. Then find the time between the cycles. If it is not a pure frequency this will of course be harder.
I am using Ooura FFT to compute the FFT of acceleromter data. I do not always obtain the correct spectrum. For some reason, Ooura FFT produces completely wrong results with spectral magnitudes of the order 10^200 across all frequencies.