. 2008 Sep;124(3):1526–1537. doi: 10.1121/1.2950081

Table 1.

Terms that define the time space decomposition of the Hanning-weighted pulse v(t−τ) for transient apodized FNM calculations.

Temporal basis functions g_m(t)
$g_{1} (t) = \frac{1}{2} \sin (2 π f_{0} t)$
$g_{2} (t) = - \frac{1}{2} \cos (2 π f_{0} t)$
$g_{3} (t) = - \frac{1}{2} \cos (\frac{2 π t}{W}) \sin (2 π f_{0} t)$
$g_{4} (t) = \frac{1}{2} \cos (\frac{2 π t}{W}) \cos (2 π f_{0} t)$
$g_{5} (t) = - \frac{1}{2} \sin (\frac{2 π t}{W}) \sin (2 π f_{0} t)$
$g_{6} (t) = \frac{1}{2} \sin (\frac{2 π t}{W}) \cos (2 π f_{0} t)$
Spatial basis functions f_m(τ)
f₁(τ)=cos(2πf₀τ)
f₂(τ)=sin(2πf₀τ)
$f_{3} (τ) = \cos (\frac{2 π τ}{W}) \cos (2 π f_{0} τ)$
$f_{4} (τ) = \cos (\frac{2 π τ}{W}) \sin (2 π f_{0} τ)$
$f_{5} (τ) = \sin (\frac{2 π τ}{W}) \cos (2 π f_{0} τ)$
$f_{6} (τ) = \sin (\frac{2 π τ}{W}) \sin (2 π f_{0} τ)$