Digital Signal Processing and Digital Filters Practice Sheet 07Python

Java Python Digital Signal Processing and Digital Filters

Practice Sheet 07

1)  The Direct Form. I and Direct Form. II of digital filters are depicted in the diagrams below.

Let the input initial conditions be x[0] = −1 and x[1] = 2. Find y0 , y1 , t0 , t1  such that, if yI [i] = yII [i] = yi and t [i] = ti, i = 0, 1,  then the two forms are equivalent, i.e., yI [n] = yII  [n] , ∀n ∈ Z.

2)  Le Digital Signal Processing and Digital Filters Practice Sheet 07Python t y [n] be the output of a linear system as depicted below

(a)  Convert the block diagram into an equivalent transposed form,

(b)  Derive the transfer function of the original block diagram and compute the values of b [i] , i = 0, 1, 2 and a [i] , i = 0, 1 from its Direct Form I/II representation as shown in the diagram of Question 1.

3)  Let a linear system be described by

(a)  Calculate the zeros and poles of the system.

(b)  Write the system as the product of two biquads such that ensure a low peak gain