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Equation 3 · Part 14 · What a Neural Recording Actually Records

Ending index or upper bound: infty

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)
∞\infty

What this part means

This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.

Its job in the formula

infty appears in the bound of this integral. The bound states where the repeated operation starts, ends, or which values it includes.

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

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

Open the illustrated sums and products: repeat an operation over an index guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.