It's a lot easier to begin by analysing a half wave rectifier and resistive load: -
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/exUZU.png)
Is the smoothed waveform basically DC or is there more to it?
Then if you add a smoothing capacitor, can you see that the output waveform becomes like this (my addition in red): -
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/FEPYd.png)
So, when the input voltage is positive, it both supplies the resistor load and, charges up the capacitor. Then, when the input voltage is falling from the positive peak, the diode becomes reverse biased and no longer supplies current to the capacitor and load resistor.
So, the capacitor slightly discharges due to the resistor taking current directly from the capacitor.
If you understand this, the full wave rectifier is a relatively short leap in understanding.
Since it's not a completely straight DC signal what am I missing.
You might be missing that the diode becomes reverse biased and the resistive load discharges the capacitor a little until the AC voltage waveform becomes positive again and recharges the capacitor close to the top of the waveform.
abs(sin(t))
thing) is considered DC. \$\endgroup\$