Multi-Tap Delay Line Example

Multi-Tapped delay lines efficiently simulate multiple echoes from the same source signal.

Figure 4: A multi-tapped delay with length $M_3$.

In the above figure, the total delay line length is $M_3$ samples, and the internal taps are located at delays of $M_1$ and $M_2$ samples, respectively.

The output signal is a linear combination of the input signal $x(n)$, the delay-line output $x(n-M_3)$, and the two tap signals $x(n-M_1)$ and $x(n-M_2)$.

The difference equation is given by

$$y(n) = b_0x(n)+b_1x(n-M_1)+b_2x(n-M_2)+b_3x(n-M_3)$$

Convolution is equivalent to tapping a delay line every sample and multiplying the output of each tap by the value of the impulse response for that time.