signal flowgraphs

taps

tapped delay line

Auto-Regressive Moving

values of the input are read with the three preceding values of the index. At

every sample instant, the four indexes are incremented by one, with the trick of

beginning from location 0 whenever we exceed the length M of the buffer (this

ensures the circularity of the buffer). The counterclockwise arrow indicates the

direction taken by the indexes, while the clockwise arrow indicates the movement

that should be done by the data if the indexes would stay in a fixed position.

In fig. 13 we use small triangles to indicate the multiplications by the filter

coefficients. This is a notation commonly used for multiplications within the

signal flowgraphs that represent digital filters. As a matter of fact, an FIR filter

contains a delay line since it stores N consecutive samples of the input sequence

and uses each of them with a delay of N samples at most. The points where the

circular buffer is read are called taps and the whole structure is called a tapped

delay line.

the output signal at a given instant is obtained as a linear combination of

samples of the input and output signals at previous time instants. Moreover,

an instantaneous dependency of the output on the input is also usually included

in the IIR filter. The difference equation that represents an IIR filter is

While the impulse response of FIR filters has a finite time extension, the impulse

response of IIR filters has, in general, an infinite extension. The transfer function

is obtained by application of the Z transform to the sequence (24). In virtue

of the shift theorem, the Z transform is a mere operatorial substitution of each

translation by m samples with a multiplication by z

the input:

can be conceived: the one-pole filter having coefficients a

2

2

2

2