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Equation 3 · Part 1 · What a Neural Recording Actually Records

Symbol y

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)
yy

What this part means

linear.

Its job in the formula

y is part of the quantity the equation computes from the expression on the right.

Where the article explains it

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.

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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See this notation across published equations →

Sources cited in the article section

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