A comprehensive (2+ hour!) yet accessible in scope look at Digital Filtering. Introduction to digital filtering as a prelude to DAC architecture (in the next video) - topics discussed include the basic theory of a digital filter, especially an FIR Filter. Benefits of digital filtering are discussed, followed by a look at the duality between the time and frequency domains (basic explanation of Discrete Fourier Transform), low-pass filtering for FIR filter construction, linear time invariant (LTI) systems, the theory of how impulse response fully characterizes such a system, followed by FIR design (general N-tap structure) and implications, interpolation and its effect on the filter response with Nyquist parameters, and the interpolation filter design. Basic hand derivation from delta-summed unit impulses to our discrete FIR filter equation to showcase the importance of LTI impulse-characterization (while keeping it accessible and the math reasonable) with examples along the way.
The general FIR coefficient calculation is explained from the impulse response theory as well. Computational efficiency is briefly discussed. Windowed-sinc method of FIR design heavily discussed: general overview of the method followed by a brief window function overview and a more in-depth look at the Kaiser window for our example. The theory is put to work with two interpolation (4x and 8x from 44.1 kHz fundamental) low-pass filters based on the Kaiser window with an emphasis on the audio band (passband DC-20kHz). Overview of the filter, its characterization as well as measurements with detailed graphs of magnitude response, quantized impulse response, phase shift, phase delay, group delay (& its derivation from phase delay), passband ripple, etc. Finally, we take a look at the filter output with Gaussian white noise applied on the spectrum analyzer to verify performance in a real scenario.
The goal is to have a basic understanding of digital filtering as a prelude to DAC architecture (next video), as filtering is key to modern DAC's and makes up a significant portion of the design of a full DAC.
Analog Devices Digital Filtering "Minibook" (great resource): http://www.analog.com/media/en/training-seminars/design-handbooks/MixedSignal_Sect6.pdf
LTI System Theory (good info): https://en.wikipedia.org/wiki/LTI_system_theory
(specifically in relation to this video - on this page re: discrete, a more complete theory/proof of our equations can be found in the subsection https://en.wikipedia.org/wiki/LTI_system_theory#Impulse_response_and_convolution_2)
Group/Phase Delay in more detail:
Stanford outline on Fractional Delay Interpolators (the polynomial-based / Farrow / Lagrange etc. variable delay filter methods are of interest) - more advanced but a great read:
General resources: Google is your friend with respect to Fourier Transforms/Series, further intuition like z-transforms or deeper/complete proofs.