Delay Line as a Digital Filter

Difference Equation

$$y(n) = x(n-M)$$

Transfer Function

$$H(z) = z^{-M}$$

• $M$ poles at $z=0$
• $M$ zeros at $z=\infty$

Frequency Response

$$H(e^{j\omega T}) = e^{-jM\omega T}, \quad \omega T\in [-\pi,\pi)$$

• ``Allpass'' since $\left\vert H(e^{j\omega T})\right\vert=1$
• ``Linear Phase'' since $\angle H(e^{j\omega T}) = -M\omega T = \alpha\omega$