20Cerebellar granule cells (GCs) making up majority of all the neurons in the 21 vertebrate brain, but heterogeneities among GCs and potential functional 22 consequences are poorly understood. Here, we identified unexpected gradients 23 in the biophysical properties of GCs. GCs closer to the white matter (inner-zone 24 GCs) had higher firing thresholds and could sustain firing with larger current 25 inputs. Dynamic clamp experiments showed that inner-and outer-zone GCs 26 preferentially respond to high-and low-frequency mossy fiber inputs, 27 respectively, enabling to disperse the mossy fiber input into its frequency 28 components as performed by a Fourier transformation. Furthermore, inner-zone 29GCs have faster axonal conduction velocity and elicit faster synaptic potentials in 30 Purkinje cells. Neuronal network modeling revealed that these gradients improve 31 spike-timing precision of Purkinje cells and decrease the number of GCs required 32 to learn spike-sequences. Thus, our study uncovers biophysical gradients in the 33 cerebellar cortex enabling a Fourier-like transformation of mossy fiber inputs. 34Controlling the timing and precision of movements is considered to be one of the 52 main functions of the cerebellum. In the cerebellum, the firing frequency of 53Purkinje cells (PCs) (Heiney et al., 2014;Herzfeld et al., 2015; Hewitt et al., 54 2011;Medina and Lisberger, 2007;Payne et al., 2019; Sarnaik and Raman, 55 2018;Witter et al., 2013) or the timing of spikes (Brown and Raman, 2018; 56 Sarnaik and Raman, 2018) have been shown to be closely related to movement. 57Indeed, cerebellar pathology impairs precision in motor learning tasks (Gibo et 58 al., 2013;Martin et al., 1996) and timing of rhythmic learning tasks (Keele and 59 Ivry, 1990). These functions are executed by a remarkably simple neuronal 60 network architecture. Inputs from mossy fibers (MFs) are processed by GCs and 61 transmitted via their parallel fiber (PF) axons to PCs, which provide the sole 62 output from the cerebellar cortex. GCs represent the first stage in cerebellar 63 processing and have been proposed to provide pattern separation and 64 3 conversion into a sparser representation of the MF input (recently reviewed by 65 (Cayco-Gajic and Silver, 2019). These MF inputs show a wide variety of signaling 66 frequencies, ranging from slow modulating activity to kilohertz bursts of activity 67 (Arenz et al., 2008;Rancz et al., 2007; Ritzau-Jost et al., 2014; van Kan et al., 68 1993). Interestingly, in cellular models of the cerebellum, each MF is considered 69 to be either active or inactive with little consideration for this wide range of 70 frequencies (Albus, 1971;Marr, 1969). Furthermore, in these models, GCs are 71 generally considered as a uniform population of neurons. 72 Here we show that the biophysical properties of GCs differ according to their 73 vertical position in the GC layer. GCs located close to the white matter (inner-74 zone) selectively transmit high-frequency MF inputs, have shorter action 75 poten...