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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Normalized frequency (digital signal processing) ： ウィキペディア英語版 Normalized frequency (unit) Normalized frequency is a unit of measurement of frequency equivalent to ''cycles/sample''. In digital signal processing (DSP), the continuous time variable, t, with units of ''seconds'', is replaced by the discrete integer variable, n, with units of ''samples''. More precisely, the time variable, in ''seconds'', has been normalized (divided) by the sampling interval, T (''seconds/sample''), which causes time to have convenient integer values at the moments of sampling. This practice is analogous to the concept of Natural units, meaning that the natural unit of time in a DSP system is ''samples''. The normalized value of a frequency variable, $\backslash textstyle\; f$ (''cycles/sec''), is $\backslash textstyle\; f/f\_s,$  where $\backslash textstyle\; f\_s\; =\; 1/T$  is the sampling rate in ''samples/sec''.  The maximum frequency that can be unambiguously represented by ''digital'' data is $\backslash textstyle\; f\_s/2$  (known as Nyquist frequency) when the samples are real numbers, and $\backslash textstyle\; f\_s$  when the samples are complex numbers.〔See Aliasing〕  The normalized values of these limits are respectively 0.5 and 1.0 ''cycles/sample''. This has the advantage of simplicity, but (similar to natural units) there is a potential disadvantage in terms of loss of clarity and understanding, as these constants $\backslash textstyle\; T$ and $\backslash textstyle\; f\_s$ are then omitted from mathematical expressions of physical laws. The simplicity offered by normalized units is favored in textbooks, where space is limited and where real units are incidental to the point of a theorem or its proof. But there is another advantage in the DSP realm (compared to physics), because $\backslash textstyle\; T$ and $\backslash textstyle\; f\_s$ are not "universal physical constants". The use of normalized frequency allows us to present concepts that are universal to all sample rates in a way that is independent of sample rate. An example of such a concept is a digital filter design whose bandwidth is specified not in hertz, but as a percentage of the sample rate of the data passing through it. Formulas expressed in terms of $\backslash textstyle\; f\_s$  and/or $\backslash textstyle\; T$  are readily converted to normalized frequency by setting those parameters to 1. The inverse operation is usually accomplished by replacing instances of the frequency parameter, $\backslash textstyle\; f\; ,$  with $\backslash textstyle\; f/f\_s$  or  $\backslash textstyle\; f\backslash cdot\; T.$ == Alternative normalizations == Some programs (such as MATLAB) that design filters with real-valued coefficients use the Nyquist frequency ($\backslash textstyle\; f\_s/2$) as the normalization constant. The resultant normalized frequency has units of ''half-cycles/sample'' or equivalently ''cycles per 2 samples''. Sometimes, the unnormalized frequency is represented in units of ''radians/second'' (angular frequency), and denoted by $\backslash textstyle\; \backslash omega.$  When $\backslash textstyle\; \backslash omega$ is normalized by the sample-rate (''samples/sec''), the resulting units are ''radians/sample''. The normalized Nyquist frequency is π ''radians/sample'', and the normalized sample-rate is 2π ''radians/sample''. The following table shows examples of normalized frequencies for a 1 kHz signal, a sample rate $\backslash textstyle\; f\_\backslash mathrm$ = 44.1 kHz, and 3 different choices of normalized units. Also shown is the frequency region containing one cycle of the discrete-time Fourier transform, which is always a periodic function. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Normalized frequency (unit)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.