Cycleaveraged

Cycleaveraged, also written cycle-averaged, refers to the value of a quantity averaged over one cycle of a periodic process. If a quantity A(t) has a period T, its cycle-averaged value is A_c = (1/T) ∫_{t0}^{t0+T} A(t) dt. For strictly periodic signals, this average is independent of the starting time t0, so any complete cycle yields the same result.

The concept is a form of time averaging that isolates the steady, periodic component of a signal or field. It contrasts with averaging over longer intervals that may include transients, and with instantaneous values that fluctuate within the cycle. In Fourier analysis, the cycle average corresponds to the DC or zeroth-frequency component of the signal.

Cycleaveraged measures are widely used in science and engineering to summarize periodic behavior. In fluid mechanics, cycle averaging is applied to pulsatile or oscillatory flows, such as cardiovascular or respiratory flows, to quantify mean flow rates, displacement, transport, or energy flux per cycle. In electrical engineering, the cycle average of a waveform yields its mean (DC) level over a cycle. In mechanical and aerospace engineering, cycleaveraged quantities help assess periodic loads on blades, rotors, or actuators.

Practical use requires consideration of cycle variability and nonstationarity. If cycle shapes drift, or if the process is not truly periodic, the computed cycle average may depend on cycle selection or may obscure important transient features. Numerically, the integral is approximated by summation over sampled data or by averaging over a finite window equal to T.