Electronic – Clalculating effective value of square waveform

This is the average value of the current flowing on the power line, isn't it so? However, I need the effective value of the current in order to calculate the power.

Be careful. If the shapes of the currents or voltages are not sinusoidal, knowing the RMS values for them, and the phase difference between them, is not enough. For arbitrary waveforms (as in your figure) for either one of the two (voltage or current), the only way to have an accurate calculation of the power is by integrating the product of the instantaneous voltage and the instantaneous current.

\$P=\dfrac{1}{T}\int v(t)i(t)dt \$

Nowadays, that is usually done in the digital domain. You have two ADCs (or a single ADC with two S/H front-ends). One converts v(t) and the other one converts i(t). In the digital domain, you multiply those two signals, and do the integral.

You can also do it in an analog way, using an analog multiplier and a low pass filter, but analog multipliers are tricky to use.

In summary: the circuit that you posted, that filters the shape of the current, is not valid for computing power, if the current may have the shape that you show in the figure.

USB - Universal Serial Bus - Signaling (WikiPedia)

The real problem with USB is not in the physical signalling. Say you capture a waveform with a scope right after the device is connected. It's likely to be a part of a Setup packet which is a part of a control transfer which is a part of a descriptor request which is a part of device enumeration, and that's only to have your device recognized by the host. Actual data transfer hasn't even started yet, and it will be wrapped inside transfers (of 4 different kinds) to some endpoint belonging to some interface that implements some device class, standard one like HID or completely custom. It's a lot like trying to understand HTTP by looking at Ethernet signal with a scope. In fact, you'd probably have a hard time finding your UART data even in a USB sniffer log (unlike a TCP/IP sniffer, a USB sniffer may well not know the exact protocol that e.g. FTDI uses to transfer data).

Together with the great USB in a Nutshell tutorial (HTML version), I found this book to be an excellent reference if you actually want working knowledge of USB to e.g. create your own USB devices.