The Delay Line

The delay line is an elementary functional unit modeling acoustic propagation delay (e.g. digital waveguide models and delay effects processors).

Figure 11: The $M$-sample delay line.

The delay line introduces a time delay (phase delay of $M$ samples) between input $x(n)$ and output $y(n)$:

$$y(n) = x(n-M), \quad n=0,1,2,\ldots$$

It is linear phase (delay is the same at all frequencies) as can be seen by the symmetry of the impulse response about the $M^{th}$ sample.