Studying signal and noise properties of recorded neural data is critical in developing more efficient algorithms to recover the encoded information. Important issues exist in this research including the variant spectrum spans of neural spikes that make it difficult to choose a global optimal bandpass filter. Also, multiple sources produce aggregated noise that deviates from the conventional white Gaussian noise. In this work, the spectrum variability of spikes is addressed, based on which the concept of adaptive bandpass filter that fits the spectrum of individual spikes is proposed. Multiple noise sources have been studied through analytical models as well as empirical measurements. The dominant noise source is identified as neuron noise followed by interface noise of the electrode. This suggests that major efforts to reduce noise from electronics are not well spent. The measured noise from in vivo experiments shows a family of 1/f^{x} (x=1.5\pm 0.5) spectrum that can be reduced using noise shaping techniques. In summary, the methods of adaptive bandpass filtering and noise shaping together result in several dB signal-to-noise ratio (SNR) enhancement.