A reliable voice anti-spoofing countermeasure system needs to robustly protect automatic speaker verification (ASV) systems in various kinds of spoofing scenarios. However, the performance of countermeasure systems could be degraded by channel effects and codecs. In this paper, we show that using the low-frequency subbands of signals as input can mitigate the negative impact introduced by codecs on the countermeasure systems. To validate this, two types of low-pass filters with different cut-off frequencies are applied to countermeasure systems, and the equal error rate (EER) is reduced by up to 25% relatively. In addition, we propose a deep learning based bandwidth extension approach to further improve the detection accuracy. Recent studies show that the error rate of countermeasure systems increase dramatically when the silence part is removed by Voice Activity Detection (VAD), our experimental results show that the filtering and bandwidth extension approaches are also effective under the codec condition when VAD is applied.