← All parts of this equation

Equation 3 · Part 9 · What a Neural Recording Actually Records

addition

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)
addition

What this part means

Add the term after the plus sign to the term or group before it.

Its job in the formula

Add the term after the plus sign to the term or group before it.

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.

Read this part in the article →

Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

Open the illustrated addition and subtraction in an equation guide →

Sources cited in the article section

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