# Finding the frequency response $H(\omega)$ of a shifted sinc function

Given $$h[n]=\frac{\sin\left(\frac{\pi}{3}n-\frac{\pi}{3}\right)}{\pi n-\pi}\text,$$ use the table to find the frequency response $$H(\omega)$$.

I don't have any clue that how to deal with the denominator, could anyone help me please?

• Hint: there's a composite function involving a fraction and a sine in your table 5.2. – Marcus Müller May 9 '20 at 14:17
• You have the definition and transform for sinc(), and you have the time-shift property. What are you missing? Try to put the argument of the sin() function in terms of the denominator, so you can use your transform table. – Juancho May 9 '20 at 14:17
• @MarcusMüller Thank you. This is what I got so far: $h[n]=\frac{\sin(\pi (\frac{n}{3}-\frac{1}{3}))}{\pi (n-1)}$, but it still can't fit in $\frac{\sin(Wn)}{\pi n}$, and if I use Juancho's method, the result will be very complex and I can't make $n$ in the denominator disappear – keanehui May 9 '20 at 15:40
• you're on the right path. Combine that with the usual scaling or time-shifting approaches. – Marcus Müller May 9 '20 at 17:33