In the first incident, a 40-year-old woman bravely fought off a knife attacker when he tried to snatch her handbag in New Street just after 11am on Thursday February 15. The man fled empty-handed.
The second attack happened at about 1am on Sunday February 18 when a knifeman stabbed a 17-year-old boy and demanded his phone in an attack in Rushams Road at its junction with Victory Road.
The teenager was later treated for two stab wounds – one to his back and one to his arm.
Police say that an 18-year-old man from Horsham, arrested on suspicion of robbery and attempted robbery, has been released under investigation as enquiries continue.
But they say they are still appealing for witnesses to either incident – or anyone who recognises the man in the e-fit image – to come forward.
Said a spokesman: “Anyone with any information is asked to report it online or call 101 quoting serial 766 of 15/02 for the New Street incident, or serial 99 of 18/02 for the Rushams Road incident.
“Alternatively, you can visit the Crimestoppers website or contact the independent charity anonymously on 0800 555 111.”