This is something I do not understand correctly about transistor polarization
If your input voltage goes below that necessary to bias the transistor on, it won't amplify it. This circuit will amplify decently well as long as your signal is positive only, which you can achieve by capacitively coupling your signal into the base node like so:







simulate this circuit &ndash; Schematic created using CircuitLab

Though personally I would highly recommend a design like this, which has improved linearity and is less likely to damage your transistor:







simulate this circuit

The use of the resistor between the emitter and ground allows you to control the gain of your amplifier, so that you don't have to deal with having far too much amplification which would result in signal clipping. It also improves linearity as well. Biasing the base with a resistor divider instead of with a resistor to Vcc also allows better control of the amplifier characteristics, improving linearity.