低通 FIR 滤波器 - 无延迟
我正在使用 FIR 滤波器对音频进行过采样。这是一个简单的典型加窗 sinc，即截断并加窗的 sinc 函数。像往常一样，它需要过去和“未来”的样本才能工作。实际上，这意味着音频输出被延迟。 sinc 函数是理想的低通滤波器。我的问题是，除了不需要“未来”样本之外，等效的是什么。我猜这个函数与砖墙 IIR 滤波器的脉冲响应相同。它将具有完美的砖墙截止，但不会具有完美的相位响应。
I'm using a FIR filter to oversample audio. It's a simple typical windowed sinc, i.e. a sinc function truncated and windowed. As usual it requires past and 'future' samples to work. in practical terms this means the audio output is delayed.
The sinc function is an ideal low pass filter. My question what is the equivalent, except with no 'future' samples required. I guess this function is the same as the impulse response of a brick wall IIR filter. It will have a perfect brick-wall cuttoff, but will not have perfect phase response.
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如果您想要特定的频率响应，那么最小相位滤波器将提供具有该响应的 IIR 或 FIR 滤波器的最低“延迟”或延迟。所有极点和零点都位于单位圆内的 IIR 滤波器将是最小相位滤波器。最小相位滤波器也不是线性相位，因此您必须释放该约束以减少延迟。 FIR 滤波器可以通过倒数技术近似转换为最小相位（请参阅Oppenheim & Schafer< /a>），或者通过数值求解具有足够相似频率响应的 IIR 滤波器，翻转内部的所有极点和零点，并将适当加窗的脉冲响应转换回 FIR 滤波器。
尝试获得小于最小相位延迟将使滤波器的过渡带变平，直到在“零”延迟时，滤波器要么必须拒绝任何内容，要么拒绝所有内容，从而变得无用。
If you want a particular frequency response, then a minimum phase filter would provide the lowest "delay" or latency of IIR or FIR filter with that response. An IIR filter with all its poles and zeros inside the unit circle would be a minimum phase filter. A minimum phase filter is also not linear phase, so you'll have to release that constraint to reduce latency. A FIR filter can be approximately converted to minimum phase either by cepstum techniques (see Oppenheim & Schafer), or by numerically solving for an IIR filter with a similar enough frequency response, flipping all the poles and zeros inside, and converting a suitably windowed impulse response back to a FIR filter.
Trying to get any less than minimum phase delay will flatten a filter's transition band(s) until, at "zero" delay, the filter would either have to reject nothing or reject everything, and thus become useless.