Find filter's frequency characteristics from its impulse response
How can I approach this problem?


Here's a useful identity:

\$sin(x)cos(y)=​\frac{1}{2}(sin(x+y)+sin(x−y))\$



\$ \begin{align}  \end{align} \$

\$ 
\begin{align}
h(n) &amp;= sin(\pi\frac{1}{100}n)cos(2\pi\frac{12}{100}n) \\\\
&amp; =\frac{1}{2}(sin(\pi\frac{1}{100}n+2\pi\frac{12}{100}n)+sin(\pi\frac{1}{100}n-2\pi\frac{12}{100}n))\\\\
&amp; =\frac{1}{2}(sin(\pi\frac{25}{100}n)+sin(\pi\frac{-23}{100}n)) 
\end{align} \$

This together with the hints  from Peter K should get you sorted. 



I'm copy pasting Peter K's comment so it's gathered in one spot. 


  Hint 1: an input signal convolved with the impulse response of the filter gives its output response. Hint 2: the Fourier transform of the impulse response gives the frequency response. – Peter K