Spinodal decomposition both complete one cycle per second—but they represent different frequencies in the Fourier transform. Hence, frequency no longer measures the number of cycles per unit time, but is closely related.) If A(β) is the amplitude of a Fourier component of wavelength λ and wavenumber β = 2π/λ the spatial variation in composition can be expressed by the Fourier integral: in which the coefficients are defined by the inverse relationship: Substituting, we obtain on equating coefficients: This is an ordinary differential equation that has the solution: in which "A(β)" is the initial amplitude of the Fourier component of wave wavenumber β
Cycles per instruction instructions in the five pipeline stages at once (one instruction per stage), a different instruction would complete stage 5 in every clock cycle and on average the number of clock cycles it takes to execute an instruction is 1 (CPI = 1). In this case, the processor is said to be "scalar". With a single-execution-unit processor, the best CPI attainable is 1. However, with a multiple-execution-unit processor, one may achieve even better CPI values (CPI < 1). In this case, the processor is said to be "superscalar". To get better CPI values without pipelining, the number of execution units must