PSDIntegralPhonon¶
This class calculates the power of phonon signals in frequency bands 4-60, 10-20, 20-30, 30-50, 50-70, and 70-100kHz and returns RQs 'P#intPSD460', 'P#intPSD1020', 'P#intPSD2030', 'P#intPSD3050', 'P#intPSD5070', 'P#intPSD70100', where # is one of 'A', 'B', 'C', and 'D'.
Theory¶
Suppose a pulse in time domain is represented by the time series x_{k}=x(k\Delta T),k=0,\cdots,N-1, then its discrete Fourier transform (DFT) is:
X_{n}=\frac{1}{N}\sum_{k=0}^{N-1}x_{k}e^{-2\pi ink/N}=\frac{1}{N}\sum_{k=0}^{N-1}x_{k}e^{-2\pi i(n\Delta f)k\Delta T}=\frac{1}{N}\sum_{k=0}^{N-1}x_{k}e^{-2\pi if_{n}k\Delta T}
where f_{n}=n\Delta f and \Delta f\Delta T=1/N.
The power in the frequency band w:f_{l}\leq f_{n} \leq f_{u} is:
P_{w}=\sum_{f_{l}\leq f_{n} \leq f_{u}}|X_{n}|^{2}