The article, "Let’s build an MP3-decoder!" describes quantization noise in the time domain:
[masking] This property is very useful: not only can the nearby masked signals be removed; the audible signal can also be compressed further as the noise introduced by heavy compression will be masked too.
This means that if we take a pure sine wave, say at 440 Hz, and quantize it, the quantization error will manifest itself as new frequency components in the signal. This makes sense – the quantized sine is not really a pure sine, so there must be something else in the signal. These new frequencies will be all over the spectra, and is noise
And this is where we can thank evolution our ear is not perfect: If there’s a strong signal within a critical band, the noise due to quantization errors will be masked, up to the threshold. The encoder can thus throw away as much information as possible from the samples within the critical band, up to the point were discarding more information would result in noise passing the audible threshold. This is the key insight of lossy audio encoding.
But the article then describes how the MP3 format quantizes in the frequency domain. I'd like someone to discuss the ramifications of quantization noise in the frequency domain. Because there seems to be a disconnect between the article's description of quantization noise, and how the MP3 format utilizes quantization and masking. First of all, if the frequency 7123 Hz is quantized to 7200 Hz, all you have is a slightly different frequency. Not noise "all over the spectra", after converting back to the time domain. And this completely defeats the "key insight of lossy audio encoding". Because while a 7123 Hz frequency quantized in the time domain will mask the weaker quantization noise in its critical band, a single 7200 Hz frequency quantized in the frequency domain will have nothing to mask.