Direct Form 2 is noisy in the first test. This is the one similar to Matt's in his presentation. Input signal was a sine wave at 1 Hz with small amplitude white noise x[n] = sin(2*pi*1*t[n]) + 1e-10 * random( [-1, 1] ). It was filtered with a notch filter: f=1Hz, Q=100, depth=210dB. SOS representation was calculated in Foton. Sampling frequency is 16kHz.

DF2 output noise level is the same if I change white noise amplitude while DF1, BQF, LNF can follow it. Time series show quantization noise of DF2. I've plotted coherence of the signals relative to DF1, because non of the signals will be coherent to it at low frequencies due to fft calculations.  

In the second test the input was white noise  x[n] = random( [-1, 1] ) It was filtered with a 2 order low-pass butterworth filter with cut-off frequency f = 0.25 Hz. SOS representation was calculated in Python. Sampling frequency is 16kHz.

In this test all implementations work fine. I guess dtt works with single precision and for that reason we see disturbance in coherence when we do the same test online.