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Matrix Interpretation of Convolution

Module by: Richard Baraniuk

Summary: In this section, you will learn about Matrix Interpretation of Convolution.

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C^N Case

Figure 1
Figure 1 (fig1.png)
Figure 2
Figure 2 (fig4.png)
Figure 3
Figure 3 (fig2.png)
y=Hx y H x (1)
yn=∑k=0N−1hn−kmodNxk y n k 0 N 1 h n k N x k (2)

0≤n≤N−1 0 n N 1

∞-length Case

Figure 4
Figure 4 (fig3.png)
yn=∑k=-∞∞hn−kxk y n k h n k x k (3)

Write as a matrix multiply.

y= H ∞ x y H ∞ x (4)

Exercise 1

What is the structure of H ∞ H ∞ ?

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