tight frame for $\mathbb{C}^N$

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I have a question to ask

Prove that if $K\in\mathbb{Z}-\{0\}$, then $\{\phi_p[n]=\exp(i2\pi pn/(KN))\}_{0\leq p<KN}$ is a tight frame of $\mathbb{C}^N$, i.e.

$\sum_{k}|\langle f,\phi_p\rangle |^2= A||f||^2$ for some constant $A$.

I only know that $\{e_k[n]=\frac{1}{\sqrt{N}}\exp{\frac{i2k\pi n}{N}}\}_{0\leq k<N}$ forms an orthonormal basis for $\mathbb{C}^N$, but how do I extend it to the above question?