LPF in the stage of IQ demodulator is it a analgor filter or digital filter?

I recently designed the LPF of the IQ demodulator using the Butterworth LPF refering to https://dspillustrations.com/pages/posts/misc/baseband-up-and-downconversion-and-iq-modulation.html. But I have a question. If you look at the block in the picture below, you can see the baseband block after passing the A/D Conversion. I think I applied IIR digital filter, but the composition of the picture below shows that LPF is analog domain. So I'm suddenly very curious. Is this LPF analog filter or a digital filter?

I designed Lowpass filter corresponding to LP block using Butterworth IIR filter design method in the IQ demodulator block diagram above. I first calculated analog butterworth filter coefficient, and then I calculated IIR filter coefficient b,a of z-domain using the bilinear transform. And with this, we calculated the waveform through the lpf using the filter(b,a,x) function of the matlab. So, we got the spectrum for Inphase and Quadrature phase as below. But in this process, I have a question. Obviously, I designed a digital filter of z-domain, and I wonder why digital filter exists in analog domain because it is before ADC in block diagram.

• The filters given by "LP" and $g(t)$ are in the analog domain. The article from that link is just showing you how to simulate it. – Envidia Apr 15 at 16:44
• I designed LPF using the method of Butterworth IIR lowpass filter synthesis. so I consider LPF is digital filter. by the way why digital lowpass filter is in a analog domain? This is my question. – agile Apr 16 at 6:57

The block diagram as shown in the question does not make that clear that $$v(t)$$, $$y(t)$$ and $$\hat d[k]$$ are complex signals (although clearer if you read through the linked reference).