1. Today's lecture LTI Systems characteristics Cascade LTI Systems
Graphical convolution

2. Cascade Systems

3. Cascade Equivalent

4. Example 5.3: Given two Systems
h1[n] =u[n] – u[n- 4] and h2[n] =u[n -1] – u[n-4]
h[n] = h1[n] * h2[n]
h [n] = ∑ bkδ[n-k] = [ ]
System can be implemented as a single difference equation or by a pair of difference equations
y [n] = ∑ bk x[n-k]
w[n] = ∑ x[n-k] y [n] = ∑ w[n-k] 6
K = 0 6
K = 0 3 3
K = 0
K = 1

5. Graphical Convolution
Perform graphical convolution of h1[n] * h2[n]

6. Hardware Requirements
y [n] = ∑ bk x[n-k] with bk = [ ]
Five adders and four multipliers
w[n] = ∑ x[n-k] y [n] = ∑ w[n-k]
Five adders only, no multipliers needed! 6
K = 0 3 3
K = 0
K = 1