Normalized Frequency?归一化

Normalized&nbsp;Frequency?归一化<br /><br />If&nbsp;you&nbsp;start&nbsp;reading&nbsp;books&nbsp;about&nbsp;DSP,&nbsp;you'll&nbsp;notice&nbsp;that&nbsp;they&nbsp;use&nbsp;a&nbsp;strange&nbsp;way&nbsp;of&nbsp;labeling&nbsp;the&nbsp;frequency&nbsp;of&nbsp;a&nbsp;signal.&nbsp;Instead&nbsp;of&nbsp;seeing&nbsp;graphs&nbsp;with&nbsp;frequency&nbsp;ranges&nbsp;of&nbsp;20&nbsp;Hz&nbsp;to&nbsp;20&nbsp;kHz,&nbsp;you'll&nbsp;usually&nbsp;see&nbsp;something&nbsp;called&nbsp;a&nbsp;normalized&nbsp;frequency&nbsp;ranging&nbsp;from&nbsp;0&nbsp;to&nbsp;0.5&nbsp;and&nbsp;no&nbsp;unit&nbsp;attached&nbsp;(it's&nbsp;not&nbsp;0&nbsp;to&nbsp;0.5&nbsp;Hz).?<br />如果你开始学习dsp，你将发现他们会用一种奇怪的方法标注信号的频率。通常你会看到一种叫归一化的频率，范围从0到0.5，并且没有单位，而不是20Hx到20KHz的频率图。<br />What&nbsp;does&nbsp;this&nbsp;mean?&nbsp;Well,&nbsp;think&nbsp;about&nbsp;a&nbsp;digital&nbsp;audio&nbsp;signal.&nbsp;If&nbsp;we&nbsp;record&nbsp;a&nbsp;signal&nbsp;with&nbsp;a&nbsp;48&nbsp;kHz&nbsp;sample&nbsp;rate&nbsp;and&nbsp;play&nbsp;it&nbsp;back&nbsp;with&nbsp;a&nbsp;48&nbsp;kHz&nbsp;sampling&nbsp;rate,&nbsp;then&nbsp;the&nbsp;frequency&nbsp;of&nbsp;the&nbsp;signal&nbsp;that&nbsp;went&nbsp;in&nbsp;is&nbsp;the&nbsp;same&nbsp;as&nbsp;the&nbsp;frequency&nbsp;of&nbsp;the&nbsp;signal&nbsp;that&nbsp;comes&nbsp;out.&nbsp;However,&nbsp;if&nbsp;we&nbsp;play&nbsp;back&nbsp;the&nbsp;signal&nbsp;with&nbsp;a&nbsp;24&nbsp;kHz&nbsp;sampling&nbsp;rate&nbsp;instead,&nbsp;then&nbsp;the&nbsp;frequency&nbsp;of&nbsp;the&nbsp;signal&nbsp;that&nbsp;comes&nbsp;out&nbsp;will&nbsp;be&nbsp;one&nbsp;half&nbsp;that&nbsp;of&nbsp;the&nbsp;recorded&nbsp;signal.&nbsp;<br />这有什么含义呢？好吧，先想想数字音频。如果我们用48kHz的频率采样和播放，那么采样的和播放的是一样的。但是，如果我们用24kHz的频率播放采集到的声音，那么播放的声音频率是采样的一半。<br />The&nbsp;ratio&nbsp;of&nbsp;the&nbsp;input&nbsp;frequency&nbsp;to&nbsp;the&nbsp;output&nbsp;frequency&nbsp;of&nbsp;the&nbsp;signal&nbsp;is&nbsp;the&nbsp;same&nbsp;as&nbsp;the&nbsp;ratio&nbsp;of&nbsp;the&nbsp;recording&nbsp;sampling&nbsp;rate&nbsp;to&nbsp;the&nbsp;playback&nbsp;sampling&nbsp;rate.&nbsp;<br />信号的输出频率与输入频率的比值，和播放采样率与纪录采样率是一样的。<br />This&nbsp;probably&nbsp;doesn't&nbsp;come&nbsp;as&nbsp;a&nbsp;surprise.&nbsp;(Remember&nbsp;as&nbsp;well&nbsp;that&nbsp;since&nbsp;a&nbsp;change&nbsp;in&nbsp;sampling&nbsp;rate&nbsp;will&nbsp;change&nbsp;the&nbsp;sampling&nbsp;period&nbsp;-&nbsp;the&nbsp;time&nbsp;it&nbsp;takes&nbsp;to&nbsp;play&nbsp;one&nbsp;sample&nbsp;-&nbsp;then&nbsp;a&nbsp;delay&nbsp;composed&nbsp;of&nbsp;an&nbsp;integer&nbsp;number&nbsp;of&nbsp;samples&nbsp;will&nbsp;also&nbsp;change&nbsp;its&nbsp;length&nbsp;in&nbsp;time.)?<br />这一点也不奇怪。<br />What&nbsp;happens&nbsp;if&nbsp;you&nbsp;really&nbsp;don't&nbsp;know&nbsp;the&nbsp;sampling&nbsp;rate?&nbsp;<br />如果你不知道采样率会发生什么呢。<br />You&nbsp;just&nbsp;have&nbsp;a&nbsp;bunch&nbsp;of&nbsp;samples&nbsp;that&nbsp;represent&nbsp;a&nbsp;time-varying&nbsp;signal.&nbsp;<br />你会得到一堆时变的信号。<br />You&nbsp;know&nbsp;that&nbsp;the&nbsp;sampling&nbsp;rate&nbsp;is&nbsp;constant,&nbsp;you&nbsp;just&nbsp;don't&nbsp;know&nbsp;its&nbsp;frequency.&nbsp;<br />你知道采样率是恒定的，你只是不知道频率。<br />This&nbsp;is&nbsp;the&nbsp;what&nbsp;a&nbsp;DSP&nbsp;processor&nbsp;``knows.''<br />这也是dsp知道的<br />&nbsp;So,&nbsp;all&nbsp;you&nbsp;know&nbsp;is&nbsp;what&nbsp;the&nbsp;frequency&nbsp;of&nbsp;the&nbsp;signal&nbsp;is&nbsp;relative&nbsp;to&nbsp;the&nbsp;sampling&nbsp;rate.<br />那么，现在你能知道的所有情况是，信号的频率与采样率的比值<br />&nbsp;If&nbsp;the&nbsp;samples&nbsp;all&nbsp;have&nbsp;the&nbsp;same&nbsp;value,&nbsp;then&nbsp;the&nbsp;signal&nbsp;must&nbsp;have&nbsp;a&nbsp;frequency&nbsp;of&nbsp;0&nbsp;(the&nbsp;DSP&nbsp;assumes&nbsp;that&nbsp;you've&nbsp;done&nbsp;your&nbsp;anti-aliasing&nbsp;properly...).&nbsp;<br />如果它们是相同的，那么信号的频率是0<br />If&nbsp;the&nbsp;signal&nbsp;bounces&nbsp;back&nbsp;between&nbsp;positive&nbsp;and&nbsp;negative&nbsp;on&nbsp;every&nbsp;sample,&nbsp;then&nbsp;its&nbsp;frequency&nbsp;must&nbsp;be&nbsp;the&nbsp;Nyquist&nbsp;Frequency&nbsp;-&nbsp;one&nbsp;half&nbsp;of&nbsp;the&nbsp;sampling&nbsp;rate.?<br />如果信号的频率位于每个采样的正负之间，那么他的频率必须是奈奎斯特，采样频率的一半<br />So,&nbsp;according&nbsp;to&nbsp;the&nbsp;DSP&nbsp;processor,&nbsp;the&nbsp;sampling&nbsp;rate&nbsp;has&nbsp;a&nbsp;frequency&nbsp;of&nbsp;``1''&nbsp;and&nbsp;your&nbsp;signal&nbsp;will&nbsp;have&nbsp;a&nbsp;frequency&nbsp;that&nbsp;can&nbsp;range&nbsp;from&nbsp;0&nbsp;to&nbsp;0.5.&nbsp;This&nbsp;is&nbsp;called&nbsp;the&nbsp;normalized&nbsp;frequency&nbsp;of&nbsp;the&nbsp;signal.?<br /><br />There's&nbsp;an&nbsp;important&nbsp;thing&nbsp;to&nbsp;remember&nbsp;here.&nbsp;Usually&nbsp;people&nbsp;use&nbsp;the&nbsp;word&nbsp;``normalize''&nbsp;to&nbsp;mean&nbsp;that&nbsp;something&nbsp;is&nbsp;changed&nbsp;(you&nbsp;normalize&nbsp;a&nbsp;mixing&nbsp;console&nbsp;by&nbsp;returning&nbsp;all&nbsp;the&nbsp;knobs&nbsp;to&nbsp;a&nbsp;default&nbsp;setting,&nbsp;for&nbsp;example).&nbsp;With&nbsp;normalized&nbsp;frequency,&nbsp;nothing&nbsp;is&nbsp;changed&nbsp;-&nbsp;it's&nbsp;just&nbsp;a&nbsp;way&nbsp;of&nbsp;describing&nbsp;the&nbsp;frequency&nbsp;of&nbsp;the&nbsp;signal.

通常一个50Hz的信号，最少我们要用50×2的采样频率采集，这个是奈奎斯特频率。但是，实际上我们用1000Hz的采样频率采集信号时，500Hz才是奈奎斯特频率。奈奎斯特频率是由采样频率决定的，只是它不能小于2倍的被采样频率。