# Converting frequency from 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 Hz, into the required radians-per-sample for MATLAB?

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

## 1 Answer

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.

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This worked as expected...thanks –  gpuguy Feb 26 '13 at 13:31