A typical choice of characteristic frequency is the sampling rate (fs) that is used to create the digital signal from a continuous one. The normalized quantity, f′ = f / fs, has the unit cycle per sample regardless of whether the original signal is a function of time or space. For example, when f is expressed in Hz (cycles per second), fs is expressed in samples per second. This allows us to present concepts that are universal to all sample rates in a way that is independent of the sample rate. 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. The resultant set of filter coefficients provides that bandwidth ratio for any sample-rate.[1]
Some programs (such as MATLAB toolboxes) that design filters with real-valued coefficients prefer the Nyquist frequency (fs/2) as the characteristic frequency, which changes the numeric range that represents frequencies of interest from [0, 1/2]cycle/sample to [0, 1]half-cycle/sample.
Angular frequency, denoted by ω and with the unit radians per second, can be similarly normalized. When ω is normalized with reference to the sampling rate as ω′ = ω / fs, the normalized Nyquist angular frequency is π radians/sample.
The following table shows examples of normalized frequencies for a 1 kHz signal (or filter bandwidth), a sampling rate fs = 44100 samples/second (often denoted by 44.1 kHz), and 3 normalization options.
normalized, frequency, signal, processing, digital, signal, processing, normalized, frequency, quantity, that, equal, ratio, frequency, characteristic, frequency, system, typical, choice, characteristic, frequency, sampling, rate, that, used, create, digital, . In digital signal processing DSP a normalized frequency is a quantity that is equal to the ratio of a frequency and a characteristic frequency of a system A typical choice of characteristic frequency is the sampling rate fs that is used to create the digital signal from a continuous one The normalized quantity f f fs has the unit cycle per sample regardless of whether the original signal is a function of time or space For example when f is expressed in Hz cycles per second fs is expressed in samples per second This allows us to present concepts that are universal to all sample rates in a way that is independent of the sample rate 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 The resultant set of filter coefficients provides that bandwidth ratio for any sample rate 1 Some programs such as MATLAB toolboxes that design filters with real valued coefficients prefer the Nyquist frequency fs 2 as the characteristic frequency which changes the numeric range that represents frequencies of interest from 0 1 2 cycle sample to 0 1 half cycle sample Angular frequency denoted by w and with the unit radians per second can be similarly normalized When w is normalized with reference to the sampling rate as w w fs the normalized Nyquist angular frequency is p radians sample The following table shows examples of normalized frequencies for a 1 kHz signal or filter bandwidth a sampling rate fs 44100 samples second often denoted by 44 1 kHz and 3 normalization options Quantity Numeric range Computation Valuef fs 0 1 2 1000 cycles second 44100 samples second 0 02268 cycle samplef fs 2 2f fs 0 1 2000 half cycles second 44100 samples second 0 04535 half cycle samplew fs 0 p 1000 cycles second 2p radians cycle 44100 samples second 0 14250 radian sampleSee also EditPrototype filterCitations Edit Carlson Gordon E 1992 Signal and Linear System Analysis Boston MA c Houghton Mifflin Co pp 469 490 ISBN 8170232384 Retrieved from https en wikipedia org w index php title Normalized frequency signal processing amp oldid 1134589378, wikipedia, wiki, book, books, library,
