Fixed-point design
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Fixed Point Design - Multimedia Signal Processing - Lecture Slides, Slides of Electrical Engineering
These are the Lecture Slides of Multimedia Signal Processing which includes Numeric Representation, Simulation Methods, Floating, Fixed Point, Conversion, Analytical Methods, Lower Area, Lower Power, Production Cost etc. Key important points are: Fixed Point Design, Numeric Representation, Simulation Methods, Floating, Fixed Point, Conversion, Analytical Methods, Lower Area, Lower Power, Production Cost
Typology: Slides
2012/2013
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Fixed-point design
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Overview
• Introduction
• Numeric representation
• Simulation methods for floating to fixed point
conversion
• Analytical methods
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Fixed-Point Design
• Float-to-fixed point conversion required to target
- ASIC and fixed-point digital signal processor core
- FPGA and fixed-point microprocessor core
• All variables have to be annotated manually
- Avoid overflow
- Minimize quantization effects
- Find optimum wordlength
• Manual process supported by simulation
- Time-consuming
- Error prone
Copyright Kyungtae Han [2] Docsity.com
Fixed-Point Representation
- Fixed point type
- Wordlength
- Integer wordlength
- Quantization modes
- Round
- Truncation
- Overflow modes
- Saturation
- Saturation to zero
- Wrap-around
S X X X X X
Wordlength
Integer wordlength
SystemC format www.systemc.org
X X X X X
Wordlength
Integer wordlength = 2
Back
Copyright Kyungtae Han [2] Docsity.com
Optimum Wordlength
- Longer wordlength
- May improve application performance
- Increases hardware cost
- Shorter wordlength
- May increase quantization errors and overflows
- Reduces hardware cost
- Optimum wordlength
- Maximize application performance or minimize quantization error
- Minimize hardware cost Wordlength ( w )
Distortion d ( w ) Cost c ( w ) [1/performance]
Optimum wordlength
Copyright Kyungtae Han [2] Docsity.com
Wordlength Optimization Approach
- Analytical approach
- Quantization error model
- For feedback systems, instability and limit cycles can occur
- Difficult to develop analytical quantization error model of adaptive or non-linear systems
- Simulation-based approach
- Wordlengths chosen while observing error criteria
- Repeated until wordlengths converge
- Long simulation time
Copyright Kyungtae Han [2] Docsity.com
Number representation
Matlab examples
• Numeric circle
• fi Basics
• fi Binary Point Scaling
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Fi type
www.mathworks.com Docsity.com
Fi Object
- Notation
- Multiplication
- Multiplication with KeepMSB Mode
- Addition
- Addition with KeepLsb Mode
- Numerictype
- fimath
www.mathworks.com Docsity.com
Overview
• Introduction
• Numeric representation
• Simulation methods for floating to fixed
point conversion
• Analytical methods
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Data-range propagation
Disadvantages
• Provide larger bounds on signal values than
necessary
Solution
• Simulation-based range estimation
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Development of fixed point programs
- Toolbox gFix
[Sung95] Docsity.com
Implementation – range estimation
[Sung95] Docsity.com
Implementation – range estimation
[Sung95] Docsity.com