ASK demodulation using DSP
In general, a receiver would consist of these blocks:


An analog band-pass filter centered around the carrier frequency.
A low-noise amplifier to bring the signal above the receiver's sensitivity.
Optionally, an analog intermediate frequency stage.
A sampler. You can do bandpass sampling if the carrier frequency is too large for the ADC.
In a DSP, implement:


Final downconversion if needed.
Downsampling to reduce the sampling rate
Carrier, frame and symbol synchronization
Matched filtering to recover the bits with optimum BER (in the case of ASK with rectangular pulse shaping, the matched filter is just an integrate &amp; dump filter)



I highly recommend that you get and read Telecommunications Breakdown, by Johnson and Sethares, which is available for free (as a draft) from the authors' website here.