NEW YORK -- Roger Federer is impressed by Richard Gasquet's recent play, one guy with a sweet one-handed backhand appreciating another.

The 17-time major champion remembers what Gasquet did against Federer's countryman, Stan Wawrinka, in the quarterfinals of the previous major. The Frenchman won the fifth set 11-9 at Wimbledon with the sort of gritty performance he hasn't been known for in his career.

Now he meets Federer in the U.S. Open quarterfinals Wednesday night.

"I'm not sure if I've seen maybe Gasquet play as well as he has right now," Federer said.

At Wimbledon, the Swiss great added, "He had a good attitude. He was fighting. Good shot selection. It was nice. Now he's backing it up."

In last year's Davis Cup final, Federer beat Gasquet in straight sets to clinch the title for Switzerland, part of his 14-2 record against the Frenchman.

"He kind of went away" is how Federer describes his opponent's performance that day. At two straight majors now, the 12th-seeded Gasquet is showing signs that won't happen again.

A one-time teen prodigy who won the U.S. Open junior title at age 16, Gasquet, now 29, is still trying to fulfil that promise.

"I feel like this could be one of the tougher Gasquets I've played in previous years," Federer said, "so I expect it to be difficult."

The winner of their match will face Wawrinka or Kevin Anderson. Wawrinka is a two-time major champion, while Anderson is making his first Grand Slam quarterfinal appearance after stunning Andy Murray on Monday. Yet the big-serving South African is the one who has won their last four meetings.

"I feel like I'm able -- at least I have been in our matches -- to stay with him from the back," Anderson said. "When I've been aggressive, I've been able to keep him at bay."

He hopes the U.S. Open fans will embrace him as one of their own. Anderson is working to become an American citizen, though he doesn't plan to represent the United States in competition. He has lived in the country for a decade -- he played college tennis at Illinois -- and his wife, a former Illini golfer, is American.

At age 29, Anderson has reached a career-high ranking of 14th. His next opponent is the perfect role model for his faith that he can peak in his early 30s. Wawrinka was almost 29 when he won his first major title at the Australian Open last year. Anderson believes the late start to his pro career saved wear and tear on his body.

"He knows what it takes," Anderson said of Wawrinka. "He's been in that position. It's my first time, but I feel like I'm hitting the ball very well."

Wednesday's two women's quarterfinals pit a player who always seems to thrive at the U.S. Open against one who used to wilt in New York's late-summer heat.

Two-time Australian Open champ Victoria Azarenka, whose ranking is down to 20th after two injury-plagued seasons, took Serena Williams to three sets in the 2012 and '13 U.S. Open finals and has been giving some glimpses of that level of play. Her opponent, Simona Halep, may be seeded second, but this is her first quarterfinal at Flushing Meadows.

In the first match, 26th-seeded Flavia Pennetta is in the U.S. Open quarters for the sixth time in seven years. Asked about visiting New York, she said that "for two weeks is perfect. More? No."

"It's too crowded," she explained. "Too much traffic. I am a person for a small city."

Petra Kvitova would agree -- and she has made clear in the past she doesn't even enjoy two weeks in the big city.

Not that she had ever stayed that long. This is the first U.S. Open quarterfinal appearance for the two-time Wimbledon champ.

She didn't expect 2015 would be the year to break the drought after she suffered from mononucleosis this summer. Strangely enough, the illness might have contributed to her breakthrough run: She felt less pressure of expectations and less fatigue because she hasn't been able to practice as much.

And the fifth-seeded Kvitova is working harder to embrace the bustle of the Big Apple. She tweeted a photo Tuesday of herself hailing a cab with the comment: "Do I look like a New Yorker or what?!"