Normalized Frequency 正規化頻率

frequency 頻率 unit: number of cycles/second (Hz) - f

normalized frequency 正規化頻率 = frequency (Hz) / sampling frequency (Hz) => fn = f / f_s

Example:

if f = f_s, then f_normalized = f/f_s = f_s/f_s = 1

if f = f_nyquist = f_s/2, then f_normalized = f/f_s = f_nyquist/f_s = (f_s/2)/f_s = 0.5

f_normalized = f/f_s => f = f_normalized × f_s

unnormalized frequency ω unit: radians/second (rad/sec)
normalized frequency ω_normalized = 2πf_normalized => f_normalized = ω_normalized/2π
=> f = f_normalized × f_s = ω_normalized× f_s/2π

其他表示符號(Loizou, 2013)：
 f = F/Fs

where

f = normalized frequency

F = frequency of signal

Fs = sampling frequency

頻率是每秒有幾個週期訊號

正規化頻率每個樣本有幾個週期訊號

例如取樣頻率16000Hz = 16000 samples/second

則8000Hz的正規化頻率是

(8000 cycles/second) / (16000 samples/second) = 0.5 cycles/sample

也就是每個樣本有半個週期

參考資料

What is actually Normalized Frequency?

P. C. Loizou, Speech Enhancement: Theory and Practice, 2nd ed., Boca Raton, FL, USA: CRC Press, pp. 15, 2013.