Presentation on theme: "Sensorimotor Transformations Maurice J. Chacron and Kathleen E. Cullen."— Presentation transcript:
Sensorimotor Transformations Maurice J. Chacron and Kathleen E. Cullen
Outline Lecture 1: - Introduction to sensorimotor transformations - The case of “linear” sensorimotor transformations: refuge tracking in electric fish - introduction to linear systems identification techniques - Example of sensorimotor transformations: Vestibular processing, the vestibulo-occular reflex (VOR).
Lecture 1 Sensorimotor transformation: if we denote the sensory input as a vector S and the motor command as M, a sensorimotor transformation is a mapping from S to M : M =f(S) Where f is typically a nonlinear function
Examples of sensorimotor transformations -Vestibulo-occular reflex -Reaching towards a visual target, etc…
Example: Refuge tracking in weakly electric fish
Results (Cowan and Fortune, 2007) -Tracking performance is best when the refuge moves slowly -Tracking performance degrades when the refuge moves at higher speeds -There is a linear relationship between sensory input and motor output
Linear functions What is a linear function? So, a linear system must obey the following definition:
Linear functions (continued) This implies the following: a stimulus at frequency f 1 can only cause a response at frequency f 1
Linear transformations assume output is a convolution of the input with a kernel T(t) with additive noise. We’ll also assume that all terms are zero mean. -Convolution is the most general linear transformation that can be done to a signal
An example of linear coding: Rate modulated Poisson process time time dependent firing rate
Linear Coding: Example: Recording from a P-type Electroreceptor afferent. There is a linear relationship between Input and output Gussin et al. 2007 J. Neurophysiol.
Fourier decomposition and transfer functions - Fourier Theorem: Any “smooth” signal can be decomposed as a sum of sinewaves -Since we are dealing with linear transformations, it is sufficient to understand the nature of linear transformations for a sinewave
Linear transformations of a sinewave Scaling (i.e. multiplying by a non-zero constant) Shifting in time (i.e. adding a phase)
Cross-Correlation Function For stationary processes: In general,
Cross-Spectrum Fourier Transform of the Cross-correlation function Complex number in general a: real part b: imaginary part
Representing the cross-spectrum: : amplitude : phase
Transfer functions (Linear Systems Identification) assume output is a convolution of the input with a kernel T(t) with additive noise. We’ll also assume that all terms are zero mean. Transfer function
Calculating the transfer function multiply by: and average over noise realizations =0
Summary Some sensorimotor transformations can be described by linear systems identification techniques. These techniques have limits (i.e. they do not take variability into account) on top of assuming linearity.