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I'm currently doing an investigation where I am attempting to resonant frequencies of an Alto Saxophone at various different notes. I have taken audio recordings of the notes with a sample rate of $44100\textrm{ Hz}$, and exported them into CSV files. Now, I am attempting to analyze this data using the signal processing plugin for MATLAB, but I'm feeling a little bit overwhelmed with all the different options, as I'm not sure which spectral analysis method is most suitable for the my task.

In MATLAB, I'm seeing a number of spectral analysis methods including FFT, Burg Method, Welch Method, Multitaper Method, and more - but I'm not sure of their specific applications.

Again, my goal is to clearly identify the major spectral peaks (formants) which correspond to the resonant frequencies of the Saxophone bore. The data was taken with a condenser microphone at a sample rate of $44100\textrm{ Hz}$, with the Saxophone bore exactly 1 meter from the microphone. Ultimately, I'm looking to create a plot similar to the image I have attached.

Please excuse my ignorance on this subject, this is my first time using MATLAB and I am not well-versed in digital signal processing. If anyone could help me with this, I would be extremely grateful.

enter image description here

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    $\begingroup$ What do you need the data for? In other words, what is your ultimate goal or application? Depending on that, different methods may be preferable. $\endgroup$
    – Jazzmaniac
    Commented Nov 1, 2016 at 8:36
  • $\begingroup$ My ultimate goal is to identify at what frequencies the harmonics of the fundamental are located at for each note. $\endgroup$
    – LPC16
    Commented Nov 2, 2016 at 9:06
  • $\begingroup$ Ok, that seems to be a significantly different question. To you have any reason to believe that the overtones are not at integer multiples of a fundamental frequency? Reed instruments usually have a very strict harmonic overtone spectrum, because the reed vibration determines the overtones and the nature of the vibration phase-locks the overtones to be true harmonics. Why do you want to determine the frequencies of the overtones? $\endgroup$
    – Jazzmaniac
    Commented Nov 2, 2016 at 11:08
  • $\begingroup$ @LPC16 The above plot definitely gives you the major frequencies present in a particular note. so log magnitude spectrum plot with its envelope should work out for you, as answered below. Do you have any other requirements/implementation issues ? $\endgroup$
    – Arpit Jain
    Commented Nov 2, 2016 at 13:56
  • $\begingroup$ Your question title is misleading. It should be about formant analysis, which is more commonly used in speech vowel recognition. $\endgroup$
    – hotpaw2
    Commented Nov 2, 2016 at 16:46

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The plot OP shared looks similar to log magnitude spectrum(black line) plotted with its envelope(red line). so from what OP says, OP need to plot log magnitude spectrum of recorded audio/signal. One thing to remember for this analysis is that same note should be played for entire duration of the signal to be analysed. if not, one should use proper windowing methods to ensure that signal remains stationary(in same note) for the entire duration of window under analysis. I am assuming that a note corresponds to a few particular frequencies.

that is the way if you want to plot/analyse a graph similar to the one shared. are you also looking for other methods for determining the peaks corresponding to a particular note at a time?

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  • $\begingroup$ Of course, if your note isn't held stationary for an infinite amount of time, and you therefore use a finite time window, then your FFT must have a finite resolution as well (Gabor limit). $\endgroup$
    – MSalters
    Commented Nov 2, 2016 at 11:00
  • $\begingroup$ The OP seems to want a formant graph (over the instrument's entire pitch range of notes), not just the spectrum of a single note. $\endgroup$
    – hotpaw2
    Commented Nov 2, 2016 at 16:42
  • $\begingroup$ @hotpaw2 from what OP has shared its not very clear he wants analysis for each note individually or for entire pitch range of notes as told by you. OP says "Ultimately, I'm looking to create a plot similar to the image I have attached.", that is clearly a log magnitude spectrum for a single note(assuming a note consists of few major frequencies). even if he wants to analyse all the notes he needs to play them at different time intervals(even in same time series/signal) to see which peaks correspond to which note. and this could be done by windowing which I have mentioned in my answer. $\endgroup$
    – Arpit Jain
    Commented Nov 2, 2016 at 18:25
  • $\begingroup$ @hotpaw2 in comments also OP says "My ultimate goal is to identify at what frequencies the harmonics of the fundamental are located at for each note". am I missing something here.? But I am not clear why downvote for my answer ? $\endgroup$
    – Arpit Jain
    Commented Nov 2, 2016 at 18:26

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