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Lesson 5 Discrete Filters

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Lesson 5. Discrete Filters. Lesson 2 Recap. Lesson 3 and 4 Recap. I nput. Transfer function. O utput. Transfer function. y [n] = 0.5 y[n-1] + x[n] y [n] = (x[n-1]+x[n]+x[n+1])/3. Transfer function. y[n] = 0.5 y[n-1] + x[n]. Transfer function. y[n] = (x[n-1]+x[n]+x[n+1])/3. - PowerPoint PPT Presentation

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Page 1: Lesson 5

Lesson 5Discrete Filters

Page 2: Lesson 5

Lesson 2 Recap

Page 3: Lesson 5

Lesson 3 and 4 Recap

Transfer functionInputOutput

Page 4: Lesson 5

Transfer function

y[n] = 0.5 y[n-1] + x[n] y[n] = (x[n-1]+x[n]+x[n+1])/3

Page 5: Lesson 5

Transfer function y[n] = 0.5 y[n-1] + x[n]

Page 6: Lesson 5

Transfer function

y[n] = (x[n-1]+x[n]+x[n+1])/3

Page 7: Lesson 5

IIR and FIR

Infinite Impulse Response (IIR)

Finite Impulse Response (FIR)recursive

Page 8: Lesson 5

Linear Phase

Time shifting

Page 9: Lesson 5

Linear Phase

Example

Page 10: Lesson 5

Inverse Filter

How to remove the effect of a filter with transfer function H(z)?

Page 11: Lesson 5

Frequency Scales

0.5 fsfst fp0

0

0

0

Ωp Ωst 0.5Ωs

f(Hz)

Ω=2πf (rad/sec)

ωp ωst π ω=ΩTs (rad)

ωp/π ωst/π 1 ω/π

Page 12: Lesson 5

Loss Function

Page 13: Lesson 5

Loss Function

Example

Page 14: Lesson 5

Advantages of FIR

Stability (BIBO: Bounded Input Bounded Output) Possible linear phase Efficient implementation (convolution sum via FFT) Minor disadvantage compared with IIR: a larger

number of coefficients results in slightly larger storage

Page 15: Lesson 5

FIR Filter Design

Page 16: Lesson 5

FIR Filter Design

Windowing

Page 17: Lesson 5

FIR Filter Design

The effect of windowing

Page 18: Lesson 5

FIR Filter Design

Shifting

Page 19: Lesson 5

FIR Filter Design

The effect of shifting

Linear Phase

Page 20: Lesson 5

FIR Filter Design

Different Window Functions Rectangular Triangular or Bartlett Hamming Kaiser Etc.

Page 21: Lesson 5

FIR Filter Design

Example

Page 22: Lesson 5
Page 23: Lesson 5

FIR Filter Design

High-pass filter

Page 24: Lesson 5

Properties of DTFT

Frequency shifting

Page 25: Lesson 5

FIR Filter Design

High-pass filter

Page 26: Lesson 5

FIR Filter Design

Example

Design a high-pass filter of order 14 and a cut-off frequency 0.2π using the Kaiser window.