DSP lesson 4

1
DSP lesson 4

• Total square error (TSE)
• Orthogonality
• Discrete Fourier Series (DFS)

2
Total Square Error
3
Total Square Error

• M terms in the least-squares polynomial
• So, what is the order of the polynomial?
• Is there an advantage to low-order least-squares
  polynomials?
• Is there an advantage to high-order least-squares
  polynomials?

4
Total Square Error
5
Orthogonality

• But why do we need the transpose?

6
Discrete Fourier Series

• But what is M?
• Is this analysis or synthesis?

7
Discrete Fourier Series

• Is this analysis or synthesis?
• What is a0?
• Isnt a0 improperly scaled by a factor of 2?

8
Discrete Fourier Series

• Convert between the rectangular and complex
  Fourier series coefficients using Table 2.1 (pg
  28)?

9
Homework Assignment

• Implement equation 2.31 (page 30)
• For very large M
• What is the largest value of M that you could
  use?
• Plot the results of your synthesis