The impulse response of a LTI discrete system is $h[n]=\big(\frac{1}{3}\big)^n u[n]$. Find the response of this system to the input $x[n]= e^{jnπ/4}$

Hi I'm trying to solve the problem when studying for an upcoming test.

The given solution is $$1.2503 e^{jnπ/4 -0.2991}$$, and is found by computing $$H(Ω)$$ and evaluating this at $$Ω=π/4$$. when I try this I get $$H(π/4)=(1/3)^8=0.000152$$ and therefore the convolution is $$0.000152e^{jnπ/4}$$.

I'm not sure where I'm going wrong so any help would be appreciated so much!

• You should first find the DTFT $H(\omega)$ of $h[n]$, then evaluate $H(\pi/4)$... – Fat32 Oct 31 '20 at 19:05
• You should really explain how you evaluated $H(\pi/4)$ ... – Matt L. Nov 1 '20 at 8:41