Algorithm Implementation

Algorithm development for fixed-point data

Functions

`bitand`	Bitwise `AND` of two `fi` objects
`bitor`	Bitwise `OR` of two `fi` objects
`bitshift`	Shift bits specified number of places

`cordicabs`	CORDIC-based absolute value
`cordicangle`	CORDIC-based phase angle
`cordicatan2`	CORDIC-based four quadrant inverse tangent
`cordiccart2pol`	CORDIC-based approximation of Cartesian-to-polar conversion
`cordiccexp`	CORDIC-based approximation of complex exponential
`cordiccos`	CORDIC-based approximation of cosine
`cordicpol2cart`	CORDIC-based approximation of polar-to-Cartesian conversion
`cordicrotate`	Rotate input using CORDIC-based approximation
`cordicsin`	CORDIC-based approximation of sine
`cordicsincos`	CORDIC-based approximation of sine and cosine
`cordicsqrt`	CORDIC-based approximation of square root
`cordictanh`	CORDIC-based hyperbolic tangent

`fi`	Construct fixed-point numeric object
`fimath`	Set fixed-point math settings
`filter`	One-dimensional digital filter of `fi` objects
`fipref`	Set fixed-point preferences
`for`	Execute statements specified number of times
`mean`	Average or mean value of fixed-point array
`median`	Median value of fixed-point array
`numerictype`	Construct an `embedded.numerictype` object describing fixed-point or floating-point data type
`sqrt`	Square root of `fi` object
`globalfimath`	Configure global fimath and return handle object
`resetglobalfimath`	Set global fimath to MATLAB factory default
`removeglobalfimathpref`	Remove global fimath preference

Examples and How To

CORDIC

Develop Fixed-Point Algorithms

Develop and verify a simple fixed-point algorithm.

Compute Sine and Cosine Using CORDIC Rotation Kernel

This example shows how to compute sine and cosine using a CORDIC rotation kernel in MATLAB.

Calculate Fixed-Point Arctangent

This example shows how to use the CORDIC algorithm, polynomial approximation, and lookup table approaches to calculate the fixed-point, four quadrant inverse tangent.

Convert Cartesian to Polar Using CORDIC Vectoring Kernel

This example shows how to convert Cartesian to polar coordinates using a CORDIC vectoring kernel algorithm in MATLAB.

Lookup Tables

Normalize Data for Lookup Tables

This example shows how to normalize data for use in lookup tables.

Implement Fixed-Point Log2 Using Lookup Table

This example shows how to implement fixed-point log2 using a lookup table. Lookup tables generate efficient code for embedded devices.

Implement Fixed-Point Square Root Using Lookup Table

This example shows how to implement fixed-point square root using a lookup table.

System Objects

Convert dsp.FIRFilter Object to Fixed-Point Using the Fixed-Point Converter App

This example converts a dsp.FIRFilter System object™, which filters a high-frequency sinusoid signal, to fixed-point using the Fixed-Point Converter app.

Application Areas

Fixed-Point Design Exploration in Parallel

This example shows how to explore and test fixed-point designs by distributing tests across many computers in parallel.

Real-Time Image Acquisition, Image Processing, and Fixed-Point Blob Analysis for Target Practice Analysis

Acquire real-time images from a webcam, process the images using fixed-point blob analysis, and determine world coordinates to score target practice using a laser pistol

Concepts

fimath for Rounding and Overflow Modes

Why the order in which you set overflow action and rounding method matters.

fimath for Sharing Arithmetic Rules

Using a fimath object to share modular arithmetic information among multiple fi objects.

fimath ProductMode and SumMode

Understand the differences among the different settings of the ProductMode and SumMode properties.

fi Object Properties

Defines the fi object properties.

fipref Object Properties

Defines the fipref object properties.

quantizer Object Properties

Defines the quantizer object properties.

Ways to Construct fi Objects

Teaches you how to create fi objects

fi Object Properties

Tells you how to find more information about the properties associated with fi objects, and shows you how to set these properties

fi Object Functions

Introduces the functions in the toolbox that operate directly on fi objects

How Functions Use fimath

Describes which functions ignore or discard fimath.

fimath Object Construction

How to create fimath objects.

fimath Object Properties

How to find more information about the properties associated with fimath objects, and how to set these properties.

fipref Object Construction

Teaches you how to create fipref objects

fipref Object Properties

Tells you how to find more information about the properties associated with fipref objects, and shows you how to set these properties

fi Object Display Preferences Using fipref

Gives examples of using fipref objects to set display preferences for fi objects

Data Type Override Preferences Using fipref

Describes how to use the fipref object to perform data type override

numerictype Object Construction

Teaches you how to create numerictype objects

numerictype Object Properties

Tells you how to find more information about the properties associated with numerictype objects, and shows you how to set these properties

numerictype Objects Usage to Share Data Type and Scaling Settings of fi objects

Gives an example of using a numerictype object to share modular data type and scaling information among multiple fi objects

Troubleshooting

Resolve Error: Mismatched fimath

Troubleshoot mismatched fimath errors.

fi Constructor Does Not Follow globalfimath Rules

Troubleshoot getting the fi constructor to follow globalfimath rules.

Frequently Asked Questions About Fixed-Point Numbers

Describes the meaning of negative fraction length and fraction length greater than word length.

Why Does the Fixed-Point Converter App Not Propose Data Types for System Objects?

Troubleshoot missing data type proposals for System objects.

Featured Examples

Develop Fixed-Point Algorithms

Develop and verify a simple fixed-point algorithm.

Open Script

Calculate Fixed-Point Arctangent

Use the CORDIC algorithm, polynomial approximation, and lookup table approaches to calculate the fixed-point, four quadrant inverse tangent. These implementations are approximations to the MATLAB® built-in function atan2. An efficient fixed-point arctangent algorithm to estimate an angle is critical to many applications, including control of robotics, frequency tracking in wireless communications, and many more.

Open Script

Calculate Fixed-Point Sine and Cosine

Use both CORDIC-based and lookup table-based algorithms provided by the Fixed-Point Designer™ to approximate the MATLAB® sine (SIN) and cosine (COS) functions. Efficient fixed-point sine and cosine algorithms are critical to many embedded applications, including motor controls, navigation, signal processing, and wireless communications.

Open Script

Compute Sine and Cosine Using CORDIC Rotation Kernel

Compute sine and cosine using a CORDIC rotation kernel in MATLAB®. CORDIC-based algorithms are critical to many embedded applications, including motor controls, navigation, signal processing, and wireless communications.

Open Script

Perform QR Factorization Using CORDIC

Write MATLAB® code that works for both floating-point and fixed-point data types. The algorithm used in this example is the QR factorization implemented via CORDIC (Coordinate Rotation Digital Computer).

Open Script

Convert Cartesian to Polar Using CORDIC Vectoring Kernel

Convert Cartesian to polar coordinates using a CORDIC vectoring kernel algorithm in MATLAB®. CORDIC-based algorithms are critical to many embedded applications, including motor controls, navigation, signal processing, and wireless communications.

Open Script

Compute Square Root Using CORDIC

Compute square root using a CORDIC kernel algorithm in MATLAB®. CORDIC-based algorithms are critical to many embedded applications, including motor controls, navigation, signal processing, and wireless communications.

Open Script