Highly-swept blades are used in automotive cooling systems, in the fans of modern ultra-high bypass ratio engines and in counter-rotating open rotors, in part in order to reduce noise emission. The present work investigates the effect of sweep on the free-field noise emission from the trailing edge of an isolated airfoil analytically, as a first step towards a more complete approach dedicated to rotating blades. Firstly, Amiet-Schwarzschild's technique is extended to the case of a swept airfoil in order to assess the effect of sweep on the sound directivity both by a single three-dimensional gust and by the combined effect of all gusts at a given frequency. It is found that sweep produces a non-symmetric directivity pattern, similar to the effect of a skewed gust. Sweep also affects the wavenumber distribution of the wall-pressure fluctuations beneath a turbulent boundary layer. This effect is studied by means of a generalised Corcos' model, which allows distributing energy in the chordwise and spanwise wavenumber ranges independently. The role of the spanwise-wavenumber distribution of wall-pressure power spectral density in amplifying the radiated noise is investigated and shown to have a limited impact.