This paper deals with the influence of a wideband signal key parameters on its spectrum reconstruction, for Internet-of-Things (IoT) applications. The impact of the frequency resolution , the bandwidths of the sensed transmitters, and the frequency spacing between their subbands are thoroughly analyzed. The spectrum detection of LoRaWAN EU868, one of the IoT standards , is simulated and examined. In the framework of cognitive networks or spectrum sensing, an input wideband signal, whose bandwidth is exceptionally large (resulting in an extremely high Nyquist rate), can be sampled at a much lower rate than the Nyquist limit. Under the hypothesis of Compressed Sensing, this paper deploys a sub-Nyquist sampling scheme, called Modulated Wideband Converter (MWC). The spectrum reconstruction is carried out from the sub-Nyquist samples, and then evaluated based on the correct reconstruction and false alarm rates.