So basically, my problem is that I have a speech signal in .wav format that is corrupted by a harmonic noise source at some frequency. My goal is to identify the frequency at which this noise occurs, and use a notch filter to remove said noise. So far, I have read the speech signal into matlab using:
[data, Fs] = wavread('signal.wav');
My question is how can I identify the frequency at which the harmonic noise is occurring, and once I've done that, how can I go about implementing a notch filter at that frequency?
NOTE: I do not have access to the iirnotch() command or fdesign.notch() due to the version of MATLAB I am currently using (2010).
The general procedure would be to analyse the spectrum, to identify the frequency in question, then design a filter around that frequency. For most real applications it's all a bit woolly: the frequencies move around and there's no easy way to distinguish noise from signal, so you have to use clever techniques and a bit of guesswork. However if you know you have a monotonic corruption then, yes, an FFT and a notch filter will probably do the trick.
You can analyse the signal with fft and design a filter with, among others, fir1, which I believe is part of the signal processing toolbox. If you don't have the signal processing toolbox you can do it 'by hand', as in transform to the frequency domain, remove the frequency(ies) you don't want (by zeroing the relevant elements of the frequency vector) and transform back to time domain. There's a tutorial on exactly that here.
The fft and fir1 functions are well documented: search the Mathworks site to get code examples to get you up and running.
To add to/ammend xenoclast's answer, filtering in the frequency domain may or may not work for you. There are many thorny issues with filtering in the frequency domain, some of which are covered here: http://blog.bjornroche.com/2012/08/why-eq-is-done-in-time-domain.html
One additional issue is that if you try to process your entire file at once, the "width" or Q of the filters will depend on the length of your file. This might work out for you, or it might not. If you have many files of different lengths, don't expect similar results this way.
To design your own IIR notch filter, you could use the RBJ audio filter cookbook. If you need help, I wrote up a tutorial here:
http://blog.bjornroche.com/2012/08/basic-audio-eqs.html
My tutorial uses bell/peaking filter, but it's easy to follow that and then replace it with a notch filter from RBJ.
One final note: assuming this is actually an audio signal in your .wav file, you can also use your ears to find and fix the problem frequencies:
Open the file in an audio editing program that lets you adjust filter settings in real-time (I am not sure if audacity lets you do this, but probably).
Use a "boost" or "parametric" filter set to a high gain and sweep the frequency setting until you hear the noise accentuated the most.
replace the boost filter with a notch filter of the same frequency. You may need to tweak the width to trade off noise elimination vs. signal preservation.
repete as needed (due to the many harmonics).
save the resulting file.
Of course, some audio editing apps have built-in harmonic noise reduction features that work especially well for 50/60 Hz noise.
Related
I am currently analyzing sensor signals in MATLAB.
As you see FFT is done for the raw and filtered signal.
This is just an exemplary filter, which I need to adjust.
However, I am having trouble deciding which signal frequencies are relevant and which should be filtered out.
I do know that the highest peaks in frequency spectrum depict the most important, however they are not always a clearly visible as on the screenshot which I sent you.
Do you know any methods of determining the most relevant frequencies or maybe you could recommend some articles/literature which would explain it ?
We can't tell you what the important frequencies are, that's for you to decide. Why are you doing an FFT? There must be something you're trying to evaluate. Whatever is driving you to run an FFT should give you hints about what frequencies to look at.
You could look for fundamental frequencies, but that's just a guess. The harmonics and their relative magnitudes are just as important - they determine the timbre of the sound. A saxophone, a clarinet, a trumpet, and a flute may all play the same fundamental frequency/note, but they sound different because their harmonics generate different timbres.
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 two wave files, one is normal version, another one is distorted version. In distorted version, I hear a long beep like sound. Here are the frequency domain plots of normal and distorted version sounds. First one is normal, second one is distorted. notice the scales.
How do I go about this?
It's a bit hard to tell without using a marker or zooming in, but it seems you have a sinusoid inserted to your signal, which would explain the continuous beep you hear and the delta like function you have in the spectrum. Try to locate the noise frequency using the marker and filtering it using the filter design tool (type "fdatool" in the command line). I would go for a notch filter at the frequency of the noise, and if this doesn't work a high (~1000) order high pass FIR filter.
Good luck
Since you have the signal in frequency domain, you can also remove the noise there (with a simple threshold) and then you take inverse Fourier transform and you get the noise free signal in time domain.
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.