d-blaise non-heuristic equations that represent my signal flow from audio in to digital out on a Bela Mini.
The audio CODEC inner operations are TI's proprietary information. You have to rely on empirical data and reverse engineering. It uses a delta-sigma converter, which has its own frequency response, and I don't recall that TI publishes the order of the delta-sigma converter, but you can infer this based upon the 16-bit resolution and audio clock generation information.
Following the delta-sigma is an FIR decimation filter. There is some information that gives you a chance at designing a filter that meets TI's specification (reverse engineering). You could empirically verify your guess by measuring the system response with a Vector Network Analyzer.
The device datasheet for the audio CODEC is going to be the best information available to you:
http://www.ti.com/lit/ds/symlink/tlv320aic3104.pdf
Questions to ask yourself: What order delta-sigma does TI use? How many FIR filter taps? What type of windowing on the FIR filter? If you engineer a system to meet TI's specs, then it has to be fairly close to what TI is using, but you will really never know exactly how the system was implemented.
The things you CAN know come from the datasheet, a few examples:
The TLV320AIC3104 includes a stereo audio ADC, which uses a delta-sigma modulator with 128-times oversampling in single-rate mode, followed by a digital decimation filter."
and,
The integrated digital decimation filter removes high-frequency content and downsamples the audio data from an initial sampling rate of 128 f S to the final output sampling rate of f S . The decimation filter provides a linear phase output response with a group delay of 17/f S . The –3-dB bandwidth of the decimation filter extends to 0.45 f S and scales with the sample rate (f S ). The filter has minimum 75-dB attenuation over the stop band from 0.55 f S to 64 f S . Independent digital high-pass filters are also included with each ADC channel, with a corner frequency that can be independently set.
There is also information about the DAC oversampling and reconstruction filter (which is stated to be a second-order analog filter). The DAC reconstruction filter states -20 dB at 1MHz, second-order, so you can infer the cut-off from that based on -40 dB/decade (-12 dB/octave), which puts the cut-off roughly in the area of 250 kHz. The type of filter is not specified, but you can make reasonable guesses based upon the system requirements. Butterworth is maximmally flat, or Bessel because the designer thought linear phase is more important. At the same time it may simply be two cascaded RC filters because performance near 250 kHz is irrelevant and it's cheaper and simpler to fabricate this on silicon and with lower noise than some sort of active filter circuit.
The more complex system is in the ADC FIR decimation filter, and the FIR filter shape has more meaning at audible frequencies. This significance of filter responses above the Nyquist frequency is related to the amount of noise mirrored back into the band from 0 Hz to (fs/2) Hz.
