Consider an FIR filter having a unit-sample response, *h*[*n*], that extends for *N _{R}* samples. Such a filter’s output,

**20.1**

where *x*[*k*] is the input sequence. In order to produce a block of *N*_{B} output samples, *y*[0] through *y*[*N*_{B} – 1], Eq. (20.1) must process a block of *N*_{B} + *N*_{R} – 1 input samples from *x*[–*N*_{R} + 1] through *x*[N_{B} – 1]. Assuming that *x*[*k*] is valid only for *k* ≥ 0, the first *N*_{R} – 1 samples of the output will not be valid because computation of these values depends on samples of *x*[*k*] before *k* = 0. To produce a second block of *N*_{B} output samples, *y*[*N*_{B}] through ...

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