fft based FIR filter design (windowing and phase issues) 

Yes it is frequency sampling method. In a lot of texts you will also see an approach which starts with a mathematical description of an 'ideal brick wall' frequency response, then the inverse fourier transform is a sinc function, and the sinc function is sampled to obtain the b coefficients. www.allaboutcircuits.com/technical-articles/design-of-fir-filters-using-frequency-sampling-method/ also goes through some details on the various approaches.

The phase spectrum calculation is shown at the very end of the video where some matlab code is provided. I haven't investigated the impact of increasing the steepness of the line so can't comment at this point in time. In theory, it is possible to achieve any frequency response but the trade off is an infinite number of filter coefficients, which isn't practical!

okay, let me follow that then and ill try some experiments of my own. thank you!

i did some learning, and i found out that the negative of the slope of the phase spectrum (unwrapped) corresponds to the group delay introduced into the signal. in other words, the steeper down the (unwrapped) phase shift will be, the further back in time the peak will be. Wikipedia has an article on phase delay and group delay. i confirmed this using libreoffice calc; i just applied it in practice. and it works!

@@daa2622 Ah yes! That makes perfect sense. I did a video on linear phase filters that might be of interest ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-xPTe7ZWLVhQ.htmlsi=WiqiA7-z8QENey7K

No

@@ddorran Ah, sorry, meant like: is there a similar way to design IIR filters from an arbitrary/given frequency response? Thank you!

@@autumnfox3619 There are, but it's not something I know a lot about. Having said that, an approach using pole zero placement (see ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-m5TP2uG_O2M.html) might give you some intuition on how to tackle the problem. You can meet an arbitrary frequency response by moving poles and zeros around the z-plane. Then you can use the poles and zeros to get the system coefficients. You can do this by hand using the zpgui tool (by Tom Krauss of Perdue). Mathematical approaches would seek to position poles and zeros to minimise the error between the desired frequency response and the response resulting from pole zero placement. Hope this helps.