So if the simplest equation for a sound wave at a given frequency and for a given sample rate is s i n 2 p x f s a m p l e r a t e where f is frequency is there a similar equation for the sound that a piano makes. F frequency the cycles in a unit of time. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence.
Im not looking for anything too complicated here just a wave that approximates this estimation.
Remember over here we wanted to show that the beat frequency formula looked like this and it does. In the article Derivation of Frequency Modulation Equation you will learn mathematical derivation of FM equation waveform of frequency modulated voltage with solved example. So if the simplest equation for a sound wave at a given frequency and for a given sample rate is s i n 2 p x f s a m p l e r a t e where f is frequency is there a similar equation for the sound that a piano makes. The operational properties of the Fourier transformation that are relevant to this equation are that it takes differentiation in x to multiplication by 2piks and differentiation with respect to t to multiplication by 2pif where f is the frequency.