Although Aviva Premiership champions Quins lost their last two league games against Saracens and Exeter, they bounced back with successive Heineken Cup victories over Biarritz and Connacht.
"It will be a tough afternoon," Smith said.
"We can expect a thorough examination in all departments as Harlequins have a strong pack and some extremely dangerous back-line players.
"While we have a healthy respect for our opponents, we have faith in each other and the belief that we can beat any team in this league."
Irish have collected just nine points from their opening six Premiership games - only Sale Sharks' record is worse - but a 37-19 drubbing of league leaders Northampton three weeks ago suggested that 11th could be a false position.
Skipper Declan Danaher will make his 250th appearance for the Exiles and Smith added: "It is a great milestone for one of London Irish's finest warriors.
"It is an incredible feat of endurance and courage."
Quins are again without injured fly-half Nick Evans, although he is on course to return against Gloucester next Saturday, while centre Jordan Turner-Hall rests a knee complaint before linking up with the England squad.
London Welsh, one point above Irish, include new signing Tom Voyce in their line-up to face Wasps at Adams Park, also on Sunday.
Voyce, a former Wasps player, agreed a deal with Welsh this week after impressing during a trial period that saw make several A League appearances.
"I am delighted to be joining London Welsh and excited to be able to contribute to what has been a good start to their season," Voyce said.
"(Coach) Lyn Jones and the players have been great in welcoming me into their culture.
"For me, it is a case of getting my head down and proving a few points. There are some great challenges ahead for us as a team, and that is what rugby is all about."
London Welsh's solid start to their debut Premiership season has not surprised Wasps boss David Young.
The Exiles have collected 10 points from their first six league games and announced themselves as credible top-flight material.
Most pundits had predicted a season-long struggle for Welsh, but victories over Exeter and Sale Sharks mocked that theory.
"London Welsh have surprised a lot of people in the last few months, but they haven't surprised me at all," Young said.
"I always felt with someone like Lyn Jones there that they would be very competitive.
"He is the kind of coach that thrives on leading a team with an underdog status, and he knows how to get the best out of players in that situation.
"We know that if we play to our potential we are a hard team to beat at home, but we need to do that, otherwise we will be punished.
"It is well-known that your home games are vitally important in this league, and this weekend is no different.
"We are coming into this game on the back of three wins, albeit two in a different competition, and this is a chance for us to build further on that."
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