In this paper, a narrow band wireless body area network (WBAN) model based on IEEE 802.15.4 standard is employed for transmitting vital biomedical signals such as electrocardiography (ECG) or Fetal ECG. To restrict the sampling rate and energy consumption to minimum, compressed sensing based on exploring the sparsity of structured blocks in the signal is employed. The center frequency of the ZigBee transceiver is 2.4 GHz. At the transmitter, the signal is quantized, coded and modulated using offset quadrature phase shift keying (OQPSK). At the receiver, which is a mirror image of the transmitter, the normalized least mean square (NLMS) adaptive equalizer is added. To improve the quality of the reconstructed signal, the double-density dual tree discrete wavelet transform (DWT) is employed for denoising, and is compared with other denoising methods. The bit error rate is calculated over a range of signal-to-noise ratio values, and the system feasibility is evaluated using efficient metrics. Results indicate that the proposed system can transmit signals with minimum energy consumption, meanwhile reconstructing them with high quality at the receiver.