How have the courts dealt with a motion to suppress a defendant's Miranda waiver?

At the suppression hearing, defense counsel informed the trial court that the "general nature" of the motion to suppress was "on the issue of voluntariness." Counsel claimed that defendant's Miranda waiver (Miranda v. Arizona (1966) 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694) was invalid because he did not specifically waive his rights to remain silent and obtain counsel. The trial court rejected the claim, finding that defendant was adequately advised of and validly waived his Miranda rights. The court then asked defense counsel about the previous "general objection" on the voluntariness issue, inquiring whether he wanted to make an objection for the record. Defense counsel declined and merely submitted the issue. The court ruled as follows: