Homework Question:
Consider a signal $x[n]=\alpha e^{j \omega_{0} n}+\beta e^{j \omega_{1} n}+\gamma e^{j \omega_{2} n} .$ What is the length of impulse response $h[n]$ of a system (non-trivial) such that $x[n] * h[n]=0$ ?
I have written the form in frequency domain in terms of system function as $$H(\omega)\big(\alpha \delta\left(w-w_{0}\right)+\beta \delta\left(w-w_{1}\right)+\gamma \delta\left(w-w_{2}\right)\big)=0$$
Thus $H(\omega)$ must have zeroes at $\omega$ = $\omega_0,\omega_1,\omega_2$
I am not sure about the meaning of impulse response length and also how to proceed to find the same from here.