Transposed Direct Form Filter Noise Quantization

Continuing our studies on lowering bit precision, we turn our attention to the transposed version of the direct form filter. This is motivated by our desire to understand how different forms of the biquad filter perform under lower bit resolution, with specific attention to the system's response to noise. I have attached the same plot multiple times, each with different bit resolutions toggled off to highlight the behavior of particular curves. These plots are for a low-pass filter with a 10 MHz sampling frequency, a 10 kHz critical frequency, and an input tone of 12 kHz. For 15 to 35 bits, the digitization and readout noise remain unaffected, and there is also a similar overlay between 10 and 15 bits for higher frequencies. The interesting behavior to note is that when we reduce the resolution from 15 to 10 bits, we observe a counterintuitive decrease in noise level. Reasons for this behavior are unclear. However, 15 bits should be sufficient since increasing bit resolution beyond this does not decrease the noise level.