A linear time-invariant system has finite impulse response when its impulse response is nonzero at only finitely many indices. For a causal filter supported at indices ,This is a finite discrete convolution. The coefficients specify the complete operation; they need not be positive or equal. Such a filter has a simple bounded-input estimate, , so bounded inputs remain bounded. The moving average chooses .
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Finite Impulse Response (FIR) refers to a type of digital filter used in signal processing. The defining characteristic of FIR filters is that their impulse response— the output of the filter when presented with an impulse input— is finite in duration. This means that the filter responds to an input signal and then settles to zero after a certain number of discrete time steps. ### Key Characteristics of FIR Filters: 1. **Finite Duration**: The output only relies on a finite number of input samples.