In this chapter we introduced a class of digital audio effects based on frequency-warping techniques of recent interest in musical applications. The deformation of the frequency axis, whether static or dynamic, introduces a new point of view and new tools for processing sounds. This transformation allows us to insert or edit vibrato, trill, Flatterzunge and glissando, adding controlled expression to static sounds. Harmonic sounds can be mapped into inharmonic sounds, introducing fine partial detuning to color them. Frequency warping also provides a concerned or model-based method for pitch-shifting inherently inharmonic sounds such as piano and drums sounds. Mixing independent time-varying warping channels achieves interesting generalizations of flanging, chorusing and phasing effects. An efficient algorithm based on the short-time Laguerre transform makes frequency warping computable in real-time. Since frequency warping is at present fairly unexploited in musical contexts we encourage musicians and sound engineers to experiment with this appealing technique.
1 The function lugtun is the same as lagt reported in Section 11.2.3, except that the line yy = filter(sqrt(1-b 
2),[1,b],x); is replaced by the line yy = x; in order to compute the non-normalized Laguerre transform.