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A leaky integrator equation is a differential equation that describes a system that takes the integral of an input, but gradually leaks a small amount of input over time The filter coefficient α controls the leakiness (smaller α means less leakiness (slower decay), larger α means more leakiness (faster decay)). It is used in hydraulics, electronics, and neuroscience to model single or local neurons.

A leaky integrator is a simple smoothing or lowpass function for data that can forget over time Through examples and mathematical derivations, the lecture illustrates the application of the leaky integrator in signal processing. Learn how to calculate its output, transfer function and impulse response using a parameter α and a straight line connection.

The cutoff frequency of the filter is set above the highest frequency you want to keep in your signal

With a leaky integrator, your signal is in the stopband The cutoff frequency of the filter is set below the lowest frequency in your signal A leaky integrator is used to measure the averaged signal magnitude over a period of time The leaky integrator time constant is programmable from a single t4/t8 clock cycle to 2 16 clock cycles.

It's the discrete analogue to the antiderivative operator It amplifies frequencies by a linear gain factor proportional to their wavelength, which means that it's not bibo stable The instructor explains how the leaky integrator works, its impulse response, and why it is named as such due to its ability to prevent signal 'explosion' by retaining only a fraction of the accumulated value

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