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Equation 3 · Part 5 · What a Neural Recording Actually Records

Symbol n

y(t)=∫0∞h(τ) n(t−τ) dτ+ε(t)y(t) = \int_{0}^{\infty} h(\tau)\, n(t-\tau)\, d\tau + \varepsilon(t)
nn

What this part means

n is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

n is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

Nearly all standard analysis assumes that neural activity and the measured signal are related by a linear time-invariant system, so that the measured time course is a convolution of an underlying activity time course with a canonical response function plus noise: y(t)=∫0∞h(τ) n(t−τ) dτ+ε(t)y(t) = \int_{0}^{\infty} h(\tau)\, n(t-\tau)\, d\tau + \varepsilon(t). Writing it this way exposes what is being assumed rather than measured: that h is known, that it is the same across regions, subjects and states, and that the mapping from n to y is linear. Each of those is an approximation with documented exceptions.

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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