# Parseveral Theorem

Theorem 4: Parseval’s theorem

If $f$ is $L_{2}[−τ/2,τ/2]$ and $τ$ periodic function then $τ1 ∫_{−τ/2}∣f(t)∣_{2}dt=∑_{n=−∞}∣c_{n}∣_{2}$

Theorem 5: Parseval’s theorem

If $f$ is a real valued PWC1 and τ periodic function then $1/τ∫_{−τ/2}∣f(t)∣_{2}dt=c_{0}+21 ∑_{n=1}(c_{n}+s_{n})$

where $c_{n}$ and $s_{n}$ are the Fourier cosine and sine coefficients.