Python

Multiplying the i th term in the partial sum i=0n2i+1sin((2i+1)x) by the Lanczos sigma factor sinc(4n(2i+1)) gives a new function \[ \text { lanczos_partial_sum }(x, n)=\sum_{i=0}^{n} \operatorname{sinc}\left(\frac{(2 i+1) \pi}{4 n} ight) \frac{\sin ((2 i+1) x)}{2 i+1} \text {. } \] On the same axes, plot lanczos_partial_sum (x,100), square_wave (x) The function square_wave (x) is defined by \[ \text { square_wave }(x)=\left\{\begin{array}{ll} -\pi / 4 & x2 \pi \end{array} ight. \]