"Turbocharging" - BMW accelerates after a while - what is it and how should it work?

The problem is that after pressing the accelerator pedal, the car "wonders" whether it should go and only after two or three seconds it starts to accelerate. I observed the phenomenon at speeds from 80 km/h upwards. I have replaced the filters and catalytic converter. What could be the cause, maybe

"Turbocharging" - BMW accelerates after a while - what is it and how should it work?
BMW 740i L6 silnik i turbina

BMW driver question

The problem is that after pressing the accelerator pedal, the car is "wondering" if it should go and only after two or three seconds it starts to accelerate. I observed the phenomenon at speeds from 80 km/h upwards. I have replaced the filters and catalytic converter. What could be the cause, maybe the flow meter?

The problem was with the BMW 530d, but also occurs in other models.

turbodziura bmw
BMW 5 E60 | By Matthias (Self-photographed) [Attribution], via Wikimedia Commons

Response from BM Cars service

In BMW cars equipped with a turbocharger, e.g. 530d, at the moment of rapid acceleration at engine speed around 1800 rpm, the air supercharger should turn on.

The moment of activation of the supercharging - after pressing the accelerator pedal is controlled by an electro-valve that transmits a signal to the turbocharger. With a well-functioning intake system, the delay of the so-called turbocharger can last around 1-2 seconds. A longer delay may indicate improper operation or damage to the control solenoid valve or damage to the turbocharger.

He suggests performing a full diagnostics related to the turbocharger and its control.

turbodziura bmw
TwinPower turbo engine in BMW 740i | By 根川孝太郎 (Own work)[CC BY-SA 4.0], via Wikimedia Commons
turbodziura bmw
BMW 5 E60 | By OSX (Own work) [Public domain], via Wikimedia Commons

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BMW M Power Twin Turbo Engine | By Thesupermat (Own work)[CC BY-SA 3.0], via Wikimedia Commons