A speaker verification system should include effective precautions against malicious spoofing attacks, and although some initial countermeasures have been recently proposed, this remains a challenging research problem. This paper investigates discrimination between spoofed and genuine speech, as a function of frequency bands, across the speech bandwidth. Findings from our investigation inform some proposed filter bank design approaches for discrimination of spoofed speech. Experiments are conducted on the Spoofing and Anti-Spoofing (SAS) corpus using the proposed frequency-selective approach demonstrates an 11% relative improvement in terms of equal error rate compared with a conventional mel filter bank.