# Converting frequency from $\textrm{Hz}$ to radians-per-sample

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 $\textrm{Hz}$, into the required radians-per-sample for MATLAB?

• Do you know the sample rate? – hotpaw2 Feb 20 '13 at 9:46
• yes, lets say Fs – gpuguy Feb 20 '13 at 9:55

$$f_{[\rm rad/samples]} = f_{[\rm cycles/sec]}\cdot \frac{\text{sec}}{\text{samples}}\cdot \frac{\text{rad}}{\text{cycle}}$$
$$f_{[\rm rad/samples]} = f_{[\rm cycles/sec]}\cdot \frac{2\pi}{f_s}$$
where $f_s$ is the sample rate in $\textrm{Hz}$.