frequency of th partial. Time-dependent frequencies In the general case, the instantaneous frequency of a sinusoid is the derivative (with respect to time) of the argument of the sine or cosine function. If this frequency is represented in hertz, rather than in angular frequency form, then this derivative is divided by . This is the case whether the partial is harmonic or inharmonic and whether its frequency is constant or time-varying. In the most general form, the frequency of each non-harmonic partial is a non-negative function of time, , yielding Broader definitions Additive synthesis more broadly may mean sound synthesis techniques that sum simple elements to create more complex timbres, even when the elements are not sine waves. For example, F. Richard Moore listed additive synthesis as one of the "four basic categories" of sound synthesis alongside subtractive synthesis, nonlinear synthesis, and physical modeling. In this broad sense, pipe organs, which also have pipes producing non-sinusoidal waveforms, can be considered as a variant form of additive synthesizers. Summation of principal components and Walsh functions have also been classified as additive synthesis. Implementation methods Modern-day implementations of additive synthesis are mainly digital. (See section Discrete-time equations for the underlying discrete-time theory) Oscillator bank synthesis Additive synthesis can be implemented using a bank of sinusoidal oscillators, one for each partial. Wavetable synthesis In the case of harmonic, quasi-periodic musical tones, wavetable synthesis can be as general as time-varying additive synthesis, but requires less computation during synthesis. As a result, an efficient implementation of time-varying additive synthesis of harmonic tones can be accomplished by use of wavetable synthesis. Group additive synthesis Group additive synthesis is a method to group partials into harmonic groups (having different fundamental frequencies) and synthesize each group separately with wavetable synthesis before mixing the results. Inverse FFT synthesis An inverse fast Fourier transform can be used to efficiently synthesize frequencies that evenly divide the transform period or "frame". By careful consideration of the DFT frequency-domain representation it is also possible to efficiently synthesize sinusoids of arbitrary frequencies using a series of overlapping frames and the inverse fast Fourier transform. Additive analysis/resynthesis It is possible to analyze the frequency components of a recorded sound giving a "sum of sinusoids" representation. This representation can be re-synthesized using additive synthesis. One method of decomposing a sound into time varying sinusoidal partials is short-time Fourier transform (STFT)-based McAulay-Quatieri Analysis. By modifying the sum