Just to note, I have the vowel already recorded at 2 seconds and a sampling rate of 10000. I've also been given more information, but I still don't know exactly what to do: I need to synthesize the vowel using the equation: A sin(2*pi*f0t)+ A1 sin(2*pi*2f0t)... etc.
Then, I need to write a function that synthesizes a vowel sound of pitch f0 for a duration of D seconds from a smoothed spectrum S.