# Why sampling rate is not an option with normalized frequency in Matlab Filter Designer

My Matlab version is 2017b. When I use Filter designer with normalized frequency specifications, I cannot set the sampling rate. May you tell me why the sampling frequency cannot be specified? As I know, the normalized frequency mapped $[0,\pi]$ to $[0,1]$, so the sampling rate is not dropped out. ...the normalized frequency mapped $[0,\pi]$ to $[0,1]$...

The normalized frequency $F$ is defined as $f/f_s$ where $f$ is the "real" frequency (i.e. not the normalized one) and $f_s$ is the sampling frequency. The map is thus from $[0, f_s]$ to $[0, 1]$ (or to $[0, 2\pi]$ in normalized pulsation $\Omega = 2\pi F$). When using normalized frequency $F$, you thus specify frequencies as a percentage of the sampling frequency. Hence, the sampling frequency itself is not directly needed.

• Yes, but it worries me that the screenshot shows the (greyed out) sampling rate as 10 and the magnitude plot goes from 0 to 5. :-)
– Peter K.
May 23, 2017 at 18:25
• @PeterK. Sorry I am new to DSP. Is this setting a big error? I am also wondering wheter 0.5*pi is a legitimate option. May 23, 2017 at 18:30
• @PeterK: if the interface of the "Filter Design & Analysis Tool" didn't change compared to my MATLAB R2014a version, the interface only refreshes the plot after clicking the "Design Filter" button. After this refresh, the plot goes from 0 to $\pi$. May 23, 2017 at 18:32

The point of "normalized frequency" is exactly that, it is normalized to the sampling rate.

• Thank you. Does it normalized to sampling rate or half of the sampling rate? May 23, 2017 at 18:15
• I'm pretty sure fs/2 is normalized to 1, you cannot display a frequency higher than fs/2
– Ben
May 23, 2017 at 18:28