Question about high and lowpass filters and noise removal

Do the highpass filters in the Nyquist library preserve the amplitudes of frequencies below the cutoff, but change phases slightly?

Dual question for lowpass.

I tried using a highpass filter and then computing the difference between the result and the original. That operation seems to preserve low frequency components, subjectively and in spectrogram view. I thought that might mean there is some attenuation of the lower frequencies, but then I thought again, maybe not, phase shift might explain that.

It seems too that noise removal with the “isolate” choice gives some of the non-noise signal, enough that I have been hesitant to use it. But could that be explained by slight phase shifting too?

You’ve not written which highpass type you mean.
HP is totally different from HighPass2 - 8.
All Biquad filters introduce a phase shift, in general 90 degrees at the cut off point (depending on the filter order).
You can also create these lp/hp effects by substraction with help of “allpass2”.

The built in HP and Highpass2 to 8 filters are close approximations to ideal Butterworth filters 1st order to 8th order respectively. There is significant phase shift in the stopband and much less in the passband.

HPand LP are differently implemented. They are based on the four functions snd-atone, snd-atonev, snd-tone and snd-tonev. Those are derivates of the csound tone unit generator.
In this original, there are higher order implementations available. They are mainly interesting because the hz and Q-factors can be sounds and because one is always the complement of the other.

So, I gather that listening to the difference between the original and high or lowpass filtered signals will not give a clear idea of what frequency components are subtracted, because there is indeed phase shift in the passband that I can see with a zoomed in view of the waveform.

And what about the Noise Removal tool? I do not see such obvious phase shift but I do hear some of the original sound, enough that words are recognizable.

About time I give myself a bit of proper education in DSP… I’m not math averse, just lazy. Is there a good textbook in eBook form that is also inexpensive?

I don’t understand where you are going with this. Assuming good hearing, the ability to identify highpass or lowpass filtered signals is a question of “ear training” rather than phase shift. I don’t see how phase shift relates to what you are saying.

Noise Removal is a sophisticated “gate” effect. See here for a little more description:
Depending on how aggressive the settings are and how bad the noise is, some of the “non-noise” sound may “slip through” the gate. This is normal when aggressively suppressing noise. The Noise Removal effect works best for reducing low level, constant noise. Ironically, the lower the original noise level, the better the effect works.

There are frequently posts on the forum asking how to dig an audio recording out of a sea of noise - basically, it can’t be done, and certainly not with standard audio processing tools (the CIA may have better software for this type of job).
On the other hand, if you have a good, clear recording, and there is a low level hiss, say around -50 dB, then the Audacity Noise Removal tool can do an excellent job at reducing the noise floor further, with virtually no impact on the retained audio.

Excessive Noise Removal damages the retained audio. It’s important not to overdo Noise Removal. Personally I would have preferred the effect to be called “Noise Reduction”, so as to avoid unrealistic expectations.

From a programming perspective, there is an excellent eBook, and it gets better - it’s free: