# Most appropriate spectral analysis method for a recording of a saxophone note?

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.

• 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. – Jazzmaniac Nov 1 '16 at 8:36
• My ultimate goal is to identify at what frequencies the harmonics of the fundamental are located at for each note. – LPC16 Nov 2 '16 at 9:06
• 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? – Jazzmaniac Nov 2 '16 at 11:08
• @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 ? – Arpit Jain Nov 2 '16 at 13:56
• Your question title is misleading. It should be about formant analysis, which is more commonly used in speech vowel recognition. – hotpaw2 Nov 2 '16 at 16:46