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?enter image description here

  • $\begingroup$ Hint: there's a composite function involving a fraction and a sine in your table 5.2. $\endgroup$ – Marcus Müller May 9 '20 at 14:17
  • $\begingroup$ 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. $\endgroup$ – Juancho May 9 '20 at 14:17
  • $\begingroup$ @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 $\endgroup$ – keanehui May 9 '20 at 15:40
  • 1
    $\begingroup$ you're on the right path. Combine that with the usual scaling or time-shifting approaches. $\endgroup$ – Marcus Müller May 9 '20 at 17:33

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