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音频采样率超过 40 kHz 的意义

2019-08-30

奈奎斯特采样定理看,48 kHz 绝对是够了。但是,更高的采样率也不是完全没有效果:

让我们来读一下维基百科的 Oversampling(过采样) 词条,只看重点

过采样有两个作用:

首先,是抗混叠。

Oversampling can make it easier to realize analog anti-aliasing filters.

采样率提高之后,设计滤波器会更加游刃有余。如果学过 DSP,这个应该很好理解。不过这里 48 kHz 应该也勉强够用。

此外,还能减少量化噪声。

In practice, oversampling is implemented in order to reduce cost and improve performance of an analog-to-digital converter (ADC) or digital-to-analog converter (DAC). When oversampling by a factor of N, the dynamic range also increases a factor of N because there are N times as many possible values for the sum. However, the signal-to-noise ratio (SNR) increases by [公式] , because summing up uncorrelated noise increases its amplitude by [公式] , while summing up a coherent signal increases its average by N. As a result, the SNR increases by [公式]

在提高采样率的同时,0-20 kHz 频段信号的离散时间傅里叶变换频谱看上去是被压缩了,与此同时,量化噪声的频谱却没有发生变化。也就是说,采样率提升n倍,我们所需要的 0-20kHz 频段内的量化噪声就减少了n倍。就信号质量而言,如果采样率提高了 4 倍,等价于采样精度提高了 1 位。虽然这种改善很玄学,但总是有的。

Certain kinds of ADCs known as delta-sigma converters produce disproportionately more quantization noise at higher frequencies. By running these converters at some multiple of the target sampling rate, and low-pass filtering the oversampled signal down to half the target sampling rate, a final result with less noise (over the entire band of the converter) can be obtained. Delta-sigma converters use a technique called noise shaping to move the quantization noise to the higher frequencies.

对于某些类型的 ADC,改善会更大。Σ-Δ型 AD 转换器会在高频产生更高的量化噪声,此时,过采样是很有必要的,我们可以把噪声移到没用的高频段,然后用低通滤波器把它过滤掉。

当然,人耳能不能听到这些区别,又是另一回事了。不过,既然我们不差这点计算资源,那么自然是:韩信点兵,多多益善。


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