I have an exam tomorrow on Signal Processing and one of the questions can go two ways:
Use a Hamming window to design an Nth th order (N+1 tap) band pass FIR filter with a pass-band between $f_0$-$f_1$ and a sampling frequency of $f_s$Hz
Following the windowing method of FIR filter design, use a Hamming window to design a Nth order (N+1-tap) FIR lowpass filter with a cut-off frequency of $f_0$ Hz and a sampling rate of $f_s$Hz.
Now I have a slight problem with how the questions are answered in Mark Scheme for previous paper. For the band pass he uses this definition of $sinc$: $$sinc(x)=\frac{sin(\pi x)}{\pi x}$$
While for the low pass he uses $$sinc(x)=\frac{sin(x)}{x}$$
Here are the extracts:
Even in the first case he states that
But then his answers for $h[n]$ follow the $\pi x$ version of the sinc. I have a suspicion that he used matlab to evaluate the numbers and matlab in fact is using the $\frac{sin(\pi x)}{\pi x}$. During the lectures the only way we were taught to define sinc was in the "normal version" without $\pi$.
But then again looking at Wiki article about sinc. It states that the version with $\pi$ is commonly used in signal processing. Could someone tell me what to use and when? Thanks.