The LoRa modulation scheme is arousing a growing interest in the Internet of Things community as it is adopted by the emerging LoRaWAN technology. In this paper, we firstly analyse the baseband processing for the generation of LoRa signals at the transmitter side, providing a simple algorithm that leverages digital signal processing techniques to reduce the modulator complexity. Secondly, we analytically investigate the signal demodulation technique. Quite surprisingly, we found that its effectiveness depends on the particular choice of the sampling frequency at the receiver side, which purposely does not meet the sampling theorem requirement. Finally, we consider the actual architecture of digital receivers investigating the trade-off between the selectivity of receive digital filters, which impacts on the required computational effort and power consumption, and the receiver performance.