FiniteImpulseResponse

The Finite Impulse Response (FIR) operator implements a classical FIR filter, computing the weighted sum of a sliding window of input values.

Buffer Size

The buffer size equals the length of the coefficient vector. For N coefficients, the operator maintains an N-sample buffer.

Output Computation

For input sequence x[n] and coefficients b[k], the output y[n] is computed as:

$y[n] = \sum_{k=0}^{N-1} b[k] \cdot x[n-k]$

Example Operation

Time series showing input values and corresponding outputs for coefficients [0.5, 0.3, 0.2]:

Time	Input	Output	Notes
1	1.0	-	Buffering
2	2.0	-	Buffering
3	3.0	1.6	3.0×0.5 + 2.0×0.3 + 1.0×0.2
5	4.0	2.4	4.0×0.5 + 3.0×0.3 + 2.0×0.2
6	5.0	3.2	5.0×0.5 + 4.0×0.3 + 3.0×0.2

Note how output starts after buffer fills and continues with constant throughput.

Error Handling

Throws std::runtime_error if:

• Coefficient vector is empty
• Input message has invalid type