Converting frequency from Hz to radians-per-sample

Question

In MATLAB I have to pass cut-off frequency for designing a filter. But this Cut-off frequency is in radians-per-sample. How do I convert my analog Cut off frequency in Hz, into the required radians-per-sample for MATLAB?

Answer 1

Problems like these are best attacked using some dimensional analysis:

$$f|_{rad/samp} = f|_{cycles/sec} * \frac{\text{sec}}{\text{samp}} * \frac{\text{rad}}{\text{cycle}}$$

$$f|_{rad/samp} = f|_{cycles/sec} \frac{2\pi}{f_s}$$

where $f_s$ is the sample rate in Hz.