Discrete-Time Linear Systems and Signal-Flow Graphs

CSC3313 Signals And Systems

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Task

1. Consider the discrete-time system represented by the linear constant-coefficient difference equation below:

a. Draw a block-diagram representation of the system in terms of adders, delays, and coefficient multiplication branches.
b. Draw a linear signal-flow graph representation of the system
c. Apply the transposition theorem to (b) and show the resulting signal flow graph

2. Consider the discrete-time linear causal system defined by the difference equation below:

Draw a signal flow graph to implement this system in each of the following forms:
a. Direct Form I
b. Direct Form II (Transpose of Direct Form I)
c. Cascade
d. Parallel

3. In the figure below, several networks are shown. Determine and draw the transpose of each and verify that in each case the original and transpose networks have the same transfer function.

4. H(z) represents the system function for an FIR linear system, and is given by:

Draw a flow-graph implementation of the system in each of the following forms:
a. Cascade form
b. Direct Form
c. Linear-phase form
d. Frequency-sampling form

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