数字信号处理(第二版)(英文版) (8)
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➢Step 4.The desired Laplace output equation is the inverse Laplace transformed to yield the desired time-domain output function’s equation
Understanding DSP, Second Edition
Understanding DSP, Second Edition
8
§8.2 The Laplace Transform
The Laplace transform is a mathematical method of solving linear differential equations that has proved very useful in the fields of engineering and physics. The fundamental process ➢ Step 1.A time-domain differential equation is written that describes the input/output relationship of a physical system ➢ Step 2.The differential equation is Laplace transformed, converting it to an algebraic equation
ห้องสมุดไป่ตู้
Understanding DSP, Second Edition
2
§8.1 An Introduction to Infinite Impulse Response Filters
Infinite impulse response(IIR) digital filters are feedback system.
10
The Laplace transform of a continuous timedomain function f(t), where f(t) is defined only for positive time(t>0), is expressed mathematically as
F (s) f (t )estdt 0
7
These design methods use a discrete sequence, mathematical transformation process known as the z-transform whose origin is the Laplace transform traditionally used in the analyzing of continuous systems.
IIR filter output sample depends on previous input samples and previous filter output samples.
The characteristic of IIR filters:
1)More complicated structures
2)Harder to design and analyze
3)Do not have linear phase responses
Understanding DSP, Second Edition
3
IIR filters are very efficient
Understanding DSP, Second Edition
4
FIR digital filter structures
(a)Traditional FIR filter structure;
(b)Rearranged, but equivalent, FIR filter structure.
Understanding DSP, Second Edition
Chapter 8 Infinite Impulse Response Filters
Understanding DSP, Second Edition
Outline
§8.1 An Introduction to Infinite Impulse Response Filters
§8.2 The Laplace Transform §8.3 Analog Low-Pass Filters §8.4 Impulse Invariance IIR Filter Design Method §8.5 Bilinear Transform IIR Filter Design Method §8.6 Low-Pass IIR Filter Design §8.7 Other Types IIR Filter Design
Understanding DSP, Second Edition
9
➢Step 3.Standard algebraic techniques are used to determine the desired output function’s equation in the Laplace domain
1)the impulse invariance
2)bilinear transform
3)optimization methods
Understanding DSP, Second Edition
6
IIR digital filter structures
Understanding DSP, Second Edition
5
IIR digital filter structures
IIR filters’s previous output samples are used to calculate the current output sample.
Standard IIR filter design techniques fall into three basic classes:
Understanding DSP, Second Edition
Understanding DSP, Second Edition
8
§8.2 The Laplace Transform
The Laplace transform is a mathematical method of solving linear differential equations that has proved very useful in the fields of engineering and physics. The fundamental process ➢ Step 1.A time-domain differential equation is written that describes the input/output relationship of a physical system ➢ Step 2.The differential equation is Laplace transformed, converting it to an algebraic equation
ห้องสมุดไป่ตู้
Understanding DSP, Second Edition
2
§8.1 An Introduction to Infinite Impulse Response Filters
Infinite impulse response(IIR) digital filters are feedback system.
10
The Laplace transform of a continuous timedomain function f(t), where f(t) is defined only for positive time(t>0), is expressed mathematically as
F (s) f (t )estdt 0
7
These design methods use a discrete sequence, mathematical transformation process known as the z-transform whose origin is the Laplace transform traditionally used in the analyzing of continuous systems.
IIR filter output sample depends on previous input samples and previous filter output samples.
The characteristic of IIR filters:
1)More complicated structures
2)Harder to design and analyze
3)Do not have linear phase responses
Understanding DSP, Second Edition
3
IIR filters are very efficient
Understanding DSP, Second Edition
4
FIR digital filter structures
(a)Traditional FIR filter structure;
(b)Rearranged, but equivalent, FIR filter structure.
Understanding DSP, Second Edition
Chapter 8 Infinite Impulse Response Filters
Understanding DSP, Second Edition
Outline
§8.1 An Introduction to Infinite Impulse Response Filters
§8.2 The Laplace Transform §8.3 Analog Low-Pass Filters §8.4 Impulse Invariance IIR Filter Design Method §8.5 Bilinear Transform IIR Filter Design Method §8.6 Low-Pass IIR Filter Design §8.7 Other Types IIR Filter Design
Understanding DSP, Second Edition
9
➢Step 3.Standard algebraic techniques are used to determine the desired output function’s equation in the Laplace domain
1)the impulse invariance
2)bilinear transform
3)optimization methods
Understanding DSP, Second Edition
6
IIR digital filter structures
Understanding DSP, Second Edition
5
IIR digital filter structures
IIR filters’s previous output samples are used to calculate the current output sample.
Standard IIR filter design techniques fall into three basic classes: