The defendant, Richard Gulley, appeals the district court’s denial of his motion for a downward departure based upon his alleged diminished mental capacity, pursuant to U.S.S.G. § 5K2.13. The record demonstrates that the district court was fully aware of its authority to grant a downward departure but determined that the defendant had not established that a departure was warranted under the applicable guideline. Because denials of motions for downward departure are reviewable only where the district court fails to recognize its authority to depart downward under the guidelines, the judgment below must be affirmed.
FACTUAL AND PROCEDURAL BACKGROUND
Gulley and a co-defendant were indicted for the manufacture and possession of methamphetamine with the intent to distribute, in violation of 21 U.S.C. § 841(a)(1). When a question arose about Gulley’s competence to enter a guilty plea, the district court ordered a psychological evaluation. After examining Gulley, Dr. David Solovey concluded that he was competent to enter a plea. However, Dr. Solovey also reported that Gulley “has suffered from [bjrain injury as a result of several minor head injuries and a severe one from a motorcycle accident in 1993.” He further noted that Gulley was manic depressive and “taking medications to maintain emotional and mental stability.” Intelligence testing revealed that Gulley’s intellectual capacity was in the “very low” range, with an IQ of 79.
After Gulley’s counsel provided Dr. Solovey’s report to the government and the court. Gulley pleaded guilty to the sole count of the indictment. Prior to the sentencing hearing three months later, Gulley filed with the district court a sentencing memorandum and motion for downward departure, citing several grounds that he believed supported a downward departure. The most significant among them, and the only one at issue here, was Gulley’s limited mental capacity. Gulley relied on Dr. So-lovey’s findings regarding his brain injury and limited intelligence in arguing that his “significantly reduced mental capacity” *230qualified him for a departure pursuant to U.S.S.G. § 5K2.13.
At Gulley’s sentencing hearing, his lawyer explained to the court that her client’s “diminished capacity” was the “strongest basis” for a downward departure. The district court directed Gulley’s counsel’s attention to the application note to U.S.S.G. § 5K2.13, which requires that a defendant seeking a downward departure under that guideline have “a significantly impaired ability to (A) understand the wrongfulness of the behavior comprising the offense or to exercise the power of reason; or (B) control behavior that the defendant knows is wrongful.” U.S.S.G. § 5K2.13, cmt. (n.l). The court asked Gulley’s lawyer “to speak to those two items.” After Gulley’s counsel was heard, the court made the following observations:
From this doctor’s report and from what you’ve indicated, I don’t think there’s any question but that Mr. Gulley has a diminished mental capacity, both in terms of how he compares with the general population and also how he compares with himself at some former time. The application note indicates that the reduced mental capacity has to be significant, and it says that there has to be an “impaired ability to understand the wrongfulness of the behavior or (2) an impaired ability to control behavior that the defendant knows is wrongful.” I don’t see that much in the report, other than what we’ve already talked about that really helps the Court on those two scores, but I don’t think there is any issue that Mr. Gulley has a diminished capacity. I think my question here is whether it meets the two criteria set forth in the application note.
In response, Gulley’s counsel suggested that Dr. Solovey’s report “demonstrates that Mr. Gully does have problems with controlling behavior, making good judgments.” The court responded by noting that such problems are common to criminal defendants, and that the language of the guideline suggested that something more was needed:
I wouldn’t speak in terms of percentages, but many of the offenders that we see commit what we would consider almost irrational crimes. They’re impulsive, they have difficulty controlling their impulses, and they exercise poor judgment. That’s a characteristic of their lives. So I don’t think that that in and of itself must be what the authors of the guidelines are talking about .... I think that what they’re getting at is something less than the old definition of insanity but something that is out of the ordinary, something that is — I won’t say “unique,” but at least is rare, separating people that would fall within this guideline from the large category of defendants that we see who repeatedly commit crimes ....
The court went on to note that of the two defendants charged in the indictment, it was Gulley who was the “leader” in the methamphetamine-manufacturing operation. Referring back to the application note, the court denied the motion for downward departure, concluding that it “cannot make a finding that Mr. Gulley suffered from a significantly reduced mental capacity, although, as the Court stated, it is convinced that he does suffer from a reduced mental capacity.” Ultimately, the court sentenced Gulley to a term of 33 months imprisonment, the low end of the applicable guideline range of 33-41 months. Gulley appeals from this sentence, arguing that the district court erred in refusing to grant a downward departure.1
*231 DISCUSSION
It is now well-settled under Sixth Circuit precedent that “the refusal of a district judge to make a downward departure is not ordinarily appealable.” United States v. Byrd, 53 F.3d 144, 145 (6th Cir.1995). In fact, we “may review a denial of a downward departure only if the district court incorrectly believed that it lacked the authority to grant such a departure as a matter of law.” United States v. Owusu, 199 F.3d 329, 349 (6th Cir.2000). Moreover, the district judge is not under an obligation to state affirmatively that he knows he has the power to make a down-
ward departure but declines to do so. See Byrd, 53 F.3d at 145. And, the reviewing court “should be reluctant to ‘treat as ambiguous’ a ruling which does not affirmatively state that the judge knew he could depart downward but failed to do so,” but should instead assume that the district court, “ ‘in the exercise of its discretion, found downward departure unwarranted.’ ” See id. (quoting United States v. Barrera-Baron, 996 F.2d 244, 245-46 (10th Cir. 1993)).
It is plain from the record that the district court was aware of its authority to *232issue a sentence below the applicable guideline range upon a determination that the Gulley’s mental condition met the requirements of U.S.S.G. § 5K2.13. Not only did the court entertain oral argument on Gulley’s written motion seeking a downward departure under that provision, but the district court made several statements regarding its applicability during the sentencing hearing. The court made clear that it was not convinced that Gulley suffered from a “significantly reduced mental capacity,” as contemplated by the guideline. Further, the court invited Gulley’s counsel to explain how Gulley met the definition set forth in the guideline’s application note for “significantly reduced mental capacity.” The court’s pointed statements and questions of counsel demonstrate that it was fully aware of its authority but concluded that Gulley’s mental limitations were not severe enough to warrant a downward departure. See, e.g., United States v. Shabazz, 263 F.3d 603, 611 (6th Cir.2001) (“Unless Shabazz would have us believe that the district court heard arguments on a motion that it thought it lacked the legal authority to grant, only an affirmative statement could more directly reflect the district court’s knowledge of its discretion to depart.”). Accordingly, the district court’s decision is not reviewable.
Notwithstanding the district court’s acknowledgment of its authority, Gulley argues that our intervening holding in United States v. Sadolsky, 234 F.3d 938 (6th Cir.2000), changed the law with respect to the application of section 5K2.13. After a review of that opinion, we conclude that Sadolsky is not applicable to this case.
CONCLUSION
For the reasons set out above, we AFFIRM the judgment of the district court.
. Although not raised by the parties on appeal, we note a problem with the notice of *231appeal in this case. The judgment and commitment order was signed on September 21, 2000, and entered by the district cotut on October 3, 2000. Thus, pursuant to Federal Rule of Appellate Procedure 4(b)(1)(A), Gulley’s notice of appeal was due to be filed on or before October 13, 2000. On November 2, 2000, Gulley moved unopposed under Fed. R.App. P. 4(b)(4) for an enlargement of time in which to file a notice of appeal. The district court granted the motion on November 7, 2000, stating that Gulley "shall have an additional 30 days from November 2, 2000 within which to file an appeal in this matter.” Gulley filed his notice of appeal on November 20, 2000.
Notwithstanding the language of the district court's November 7 order, Gulley’s notice of appeal was not timely filed. Rule 4(b)(4) provides that "[ujpon a finding of excusable neglect or good cause, the district court may— before or after the time has expired, with or without motion or notice — extend the time to file a notice of appeal for a period not to exceed 30 days from the expiration of the time otherwise prescribed by this Rule 4(b).” Fed. R.App. P. 4(b)(4) (emphasis added). Accordingly, the district court was authorized to enlarge the time for Gulley to file his notice of appeal until no later than November 13, 2000, which is 30 days from the expiration of the time prescribed by Rule 4(b)(1)(A).
Given that the notice of appeal of November 20 was filed one week late, the question becomes whether Gulley’s motion to enlarge the time in which to appeal, filed on November 7, can be deemed the "functional equivalent” of a notice of appeal. See Smith v. Barry, 502 U.S. 244, 248, 112 S.Ct. 678, 116 L.Ed.2d 678 (1992). In Smith, the Supreme Court held that a filing not meeting the formal requirements of a notice of appeal may be treated as a proper notice where "the filing is timely under Rule 4 and conveys the information required by Rule 3(c)." Id. at 249. In United States v. Christoph, 904 F.2d 1036, 1040 (6th Cir.1990), this court treated a motion for enlargement of time as a notice of appeal where the motion met the requirements of Rule 3(c).
We conclude that Gulley’s motion can be treated as the functional equivalent of a notice of appeal. The information contained in the motion satisfies the requirements of Federal Rule of Appellate Procedure 3(c), in that it specifies the party taking the appeal and the judgment being appealed. Although the motion does not specify the court to which the appeal was being taken as required by Rule 3(c)(1)(C), this court held in Dillon v. United States, 184 F.3d 556, (6th Cir.1999) (en banc) that "where only one avenue of appeal exists, Rule 3(c)(1)(C) is satisfied even if the notice of appeal does not name the appellate court.” The motion was filed on November 7, 2000, making it timely given the district court’s order extending the time in which to appeal and Rule 4(b)(4). There can be no question that the government was not prejudiced by Gulley’s technical failures — the government did not oppose the motion to enlarge time and has raised no jurisdictional objections to this appeal. As such, this court has jurisdiction and should address the merits of Gulley’s appeal.