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## freqz frequency units

**From**: |
Shaun Jackman |

**Subject**: |
freqz frequency units |

**Date**: |
Wed, 29 Nov 2006 16:04:36 -0700 |

What is the frequency unit of the plot shown by the freqz function?
The scale is from 0 to 1. I'm unsure if this is normalized to the
sampling frequency or the Nyquist frequency.
To give a concrete example:
[b a] = butter(1, 0.1)
freqz(b, a)
The plot clearly shows the -3 dB point at 0.1. If the sampling
frequency is 1 kHZ, is the cutoff frequency 0.1 times the sampling
frequency (1 kHz) so 100 Hz, or 0.1 times the Nyquist frequency (500
Hz) so 50 Hz? I tried to answer this question as follows:
octave:104> [H, W] = freqz(b, a);
octave:105> H = abs(H);
octave:106> find(min(H - 10^(-3/20), 0))(1)
ans = 54
octave:107> H(54)
ans = 0.70386
octave:108> W(54)
ans = 0.32520
octave:109> W(54)/(2*pi)
ans = 0.051758
octave:112> W(54)/(2*pi)*1000
ans = 51.758
Giving that the cutoff frequency is 50 Hz. Is this correct? Thanks!
Many thanks,
Shaun

**freqz frequency units**,
*Shaun Jackman* **<=**