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?

  • $\begingroup$ Do you know the sample rate? $\endgroup$
    – hotpaw2
    Feb 20, 2013 at 9:46
  • $\begingroup$ yes, lets say Fs $\endgroup$
    – gpuguy
    Feb 20, 2013 at 9:55

1 Answer 1


Problems like these are best attacked using some dimensional analysis:

$$f_{[\rm rad/samples]} = f_{[\rm cycles/sec]}\cdot \frac{\text{sec}}{\text{samples}}\cdot \frac{\text{rad}}{\text{cycle}}$$

$$f_{[\rm rad/samples]} = f_{[\rm cycles/sec]}\cdot \frac{2\pi}{f_s}$$

where $f_s$ is the sample rate in $\textrm{Hz}$.


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