# How much will a low/high pass filter reintroduce quantization noise into a dithered signal?

For example, most audio signals are dithered prior to distribution. However, if a low or high pass filter is introduced after dithering or during playback, won't that negate some of the benefits of dithering? Is there any way of calculating the magnitude of the effect?

Many lossy audio encoders automatically cut around 16-18kHz. On a 48kHz signal, that's a good ~25% of the bandwidth gone, wouldn't that have a noticeable effect on the dither, and therefore the signal too? especially if there is noise shaping pushing more dither into the high frequencies?

• can you explain why you think that would happen? Of course, a filter has an effect on the signal, but that has little to nothing to do with dithering... Commented Jan 11, 2018 at 23:31
• Dither spreads quantization noise across the spectrum. So by removing part of that spectrum, the effect of dither should be diminished. Intuitively, I would expect it to "push" that noise into other parts of the spectrum, distorting the signal. Playing around with a few audio and image tools somewhat confirms that. I just don't really understand exactly how it affects the rest of the spectrum, what's going on mathematically and at a higher level, and why this does not really seem to cause many problems when low pass filters are commonly applied after dither in audio and image processing tools. Commented Jan 12, 2018 at 6:49
• yes, that's absolutely correct! But: Filtering doesn't introduce new quantization error, typically; if you design your filter implementation sensibly, the filter, in each mathematical operation, preserves the bit width of the input signal. On the very contrary, low-pass filters, often used in conjunction with decimation, are usually bit-widening, i.e. quantization-reversing elements (compare: oversampling), even without dithering. You're right, the filter will shape the dither noise; as the filters we're looking at here are linear, you can just as well first filter the dither noise and add… Commented Jan 12, 2018 at 10:45
• …it to the filtered signal, mathematically. But: filtering dithering noise does not quantize it! Commented Jan 12, 2018 at 10:45
• @goweon please see my comment to the answer provided by damian101. Commented Mar 17, 2023 at 8:14