# How to get coefficient of the discrete fourier Series from the fourier transform

Given $$X(v)$$ the Discrete Fourier transform of a discrete periodic signal $$x(n)$$, it's possible to arrive to the $$c_k$$ of the Fourier series $$x(n)=\sum_{k=0}^{n-1} c_k \exp(2\pi i k t)$$ directly?

• um, write down the formula of the IDFT directly below your formula, i.e. how $x(n)$ can be calculated from $X(k)$. What do you notice? – Marcus Müller Nov 27 '20 at 11:01
• what's the IDFT ? @MarcusMüller – Giovanni Cerciello Nov 27 '20 at 17:04
• The inverse discrete Fourier transform; wikipedia! – Marcus Müller Nov 27 '20 at 17:28