X-Nico

Clenshaw–Curtis quadrature

Unlike computation of arbitrary integrals, however, Fourier-series integrations for periodic functions (like $f(\backslash cos\backslash theta)$, by construction), up to the Nyquist frequency $k=N$, are accurately computed by the $N+1$ equally spaced and equally weighted points $\backslash theta\; n\; =\; n\; \backslash pi\; /\; N$ for $n\; =\; 0,\backslash ldots,N$ (except the endpoints are weighted by 1/2, to avoid double-counting, equivalent to the trapezoidal rule or the Euler–Maclaurin formula).

Aliasing

The bandlimited sawtooths are synthesized from the sawtooth waveform's Fourier series such that no harmonics above the Nyquist frequency are present.

see also