原创 Normalized Frequency?归一化

If you start reading books about DSP, you'll notice that they use a strange way of labeling the frequency of a signal. Instead of seeing graphs with frequency ranges of 20 Hz to 20 kHz, you'll usually see something called a normalized frequency ranging from 0 to 0.5 and no unit attached (it's not 0 to 0.5 Hz).?
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。
What does this mean? Well, think about a digital audio signal. If we record a signal with a 48 kHz sample rate and play it back with a 48 kHz sampling rate, then the frequency of the signal that went in is the same as the frequency of the signal that comes out. However, if we play back the signal with a 24 kHz sampling rate instead, then the frequency of the signal that comes out will be one half that of the recorded signal.?
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。
The ratio of the input frequency to the output frequency of the signal is the same as the ratio of the recording sampling rate to the playback sampling rate.?
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。
This probably doesn't come as a surprise. (Remember as well that since a change in sampling rate will change the sampling period - the time it takes to play one sample - then a delay composed of an integer number of samples will also change its length in time.)?
这一点也不奇怪。
What happens if you really don't know the sampling rate??
如果你不知道采样率会发生什么呢。
You just have a bunch of samples that represent a time-varying signal.?
你会得到一堆时变的信号。
You know that the sampling rate is constant, you just don't know its frequency.?
你知道采样率是恒定的，你只是不知道频率。
This is the what a DSP processor ``knows.''
这也是dsp知道的
So, all you know is what the frequency of the signal is relative to the sampling rate.
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
If the samples all have the same value, then the signal must have a frequency of 0 (the DSP assumes that you've done your anti-aliasing properly...).?
如果它们是相同的，那么信号的频率是0
If the signal bounces back between positive and negative on every sample, then its frequency must be the Nyquist Frequency - one half of the sampling rate.?
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
So, according to the DSP processor, the sampling rate has a frequency of ``1'' and your signal will have a frequency that can range from 0 to 0.5. This is called the normalized frequency of the signal.?

There's an important thing to remember here. Usually people use the word ``normalize'' to mean that something is changed (you normalize a mixing console by returning all the knobs to a default setting, for example). With normalized frequency, nothing is changed - it's just a way of describing the frequency of the signal.

奈奎斯特

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。