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Define FIR (Finite Impulse Response) filter h(n) with N number of samples:

(Matlab Simulink file)

Define IIR (Infinite Impulse Response) filter with of N number of numerator coefficients and M number of denominator coefficients:

(a0 = 1)

Direct form 2 is a second alternative to implementing IIR filter implementation. The theory is based on splitting the system is into separate blocks: