Sound Synthesis

To synthesize a desired sound at base frequency $F$Hz, find the frequencies of the $N$ peaks of the recording with the closest base frequency to $F$. Alternatively, other search methods can be used. For example, find the recording with the closest base frequency to $F$ that is not greater than $F$, if there is such a frequency. Generate sinusoids at these frequencies at desired lengths and sampling frequencies. Apply $F$ to Eq. (1) with output as $P$, and scale (e.g., multiply) each value from the generated sinusoids by $P$. Then simply add the first, second, third, etc. value of each wave together to produce the output wave.