This is from the mathworks documentation on cheby2
For digital filters, the stopband edge frequencies must lie between 0 and 1, where 1 corresponds to the Nyquist rate—half the sample rate or $\pi$ rad/sample.
For discrete-time signals, we use the normalized frequency $\omega$ in radians (per sample), defined as
$$\omega=\frac{2\pi f}{f_s}\tag{1}$$
where $f$ is the actual frequency in Hertz, and $f_s$ is the sampling frequency.
Matlab uses $(1)$ normalized by $\pi$, i.e., edge frequencies etc. are defined by W
$=2f/f_s$. The value W
$=1$ corresponds to $f=f_s/2$, which is the Nyquist frequency.
Example: The cut-off frequency is $f_c=500$ Hz and the sampling frequency is $f_s=2000$ Hz (samples/second). According to $(1)$, the corresponding normalized frequency in radians (per sample) is
$$\omega_c=\frac{2\pi f_c}{f_s}=\frac{\pi}{2}\tag{2}$$
Consequently, when calling a Matlab routine you would use Wc
$=\omega_c/\pi=\frac12$.