udecode

Decode 2ⁿ-level quantized integer inputs to floating-point outputs

Syntax

x = udecode(y,n)

x = udecode(y,n,v)

x = udecode(y,n,v,OFM)

Description

x = udecode(y,n) performs the inverse operation of uencode by reconstructing floating-point values from an array of 2ⁿ-level quantized integers y. The udecode function returns a floating-point output array x with values within the range from -1 to 1.

x = udecode(y,n,v) returns a floating-point output array with values within the range from -v to v.

x = udecode(y,n,v,OFM) also specifies a method to treat overflows in the quantized integer input y.

Examples

Use udecode to Decode Integers

Create a vector of 8-bit signed integers. Decode with three bits.

u = int8([-1 1 2 -5]);
ysat = udecode(u,3)

ysat = 1×4

   -0.2500    0.2500    0.5000   -1.0000

Notice the last entry in u saturates to 1, the default peak input magnitude. Change the peak input magnitude to 6.

ysatv = udecode(u,3,6)

ysatv = 1×4

   -1.5000    1.5000    3.0000   -6.0000

The last input entry still saturates. Wrap the overflows.

ywrap = udecode(u,3,6,'wrap')

ywrap = 1×4

   -1.5000    1.5000    3.0000    4.5000

Add more quantization levels.

yprec = udecode(u,5)

yprec = 1×4

   -0.0625    0.0625    0.1250   -0.3125

Input Arguments

y — Quantized integer inputs

vector | matrix | multidimensional array

Quantized integer inputs, specified as a vector, matrix, or multidimensional array.

• Signed inputs — Specify int8, int16 or int32 values.

• Unsigned inputs — Specify uint8, uint16 or uint32 values.

The udecode function decodes the real and imaginary components of complex-valued inputs y independently.

Example: y = int16([-6 9 23 1 10 -7])

Data Types: int8 | int16 | int32 | uint8 | uint16 | uint32
Complex Number Support: Yes

n — Measure of number of quantization levels

positive integer scalar

Measure of number of quantization levels, specified as a positive integer scalar between 2 and 32, inclusive. The value of 2ⁿ indicates the number of quantization levels established for the quantized array y, and defines a quantization range for y.

The quantization range depends on the value of n and the sign nature of y:

• Signed inputs — From –2ⁿ/2 to (2ⁿ/2) – 1.

• Unsigned inputs — From 0 to (2ⁿ – 1).

The udecode function considers any value from y outside the quantization range as an overflow.

Data Types: double

v — Unsaturation amplitude

1 (default) | positive scalar

Unsaturation amplitude, specified as a positive scalar. The udecode decodes y such that the output x has values in the range [-v,v], preventing signal saturation in the floating-point output.

Data Types: double

OFM — Method to treat overflows

"saturate" (default) | "wrap"

Method to treat overflows, specified as:

• "saturate" — Saturate overflows. The udecode function treats overflowing elements in y by reassigning their values equal to the closest endpoint of the quantization range.

  • Signed inputs — udecode sets overflowing elements to -2^n/2 (overflow below quantization range) or 2^n/2-1 (overflow above quantization range).

  • Unsigned inputs — udecode sets overflowing elements to 2^n-1 (overflow above quantization range).

• "wrap" — Wrap all overflows. The udecode treats overflowing entries in y by using the modulo 2ⁿ operation to reassign their values.

  • Signed inputs — udecode sets overflowing elements yOF to mod(yOF+2^n/2,2^n)-(2^n/2).

  • Unsigned inputs — udecode sets overflowing elements yOF to mod(yOF,2^n).

Data Types: char | string

Output Arguments

x — Unencoded floating-point outputs

vector | matrix | multidimensional array

Unencoded floating-point outputs, returned as a vector, matrix, or multidimensional array. The output array x has the same dimension as y.

Algorithms

The algorithm adheres to the definition for uniform decoding specified in ITU-T Recommendation G.701. Integer input values are uniquely mapped (decoded) from one of 2ⁿ uniformly spaced integer values to quantized floating-point values in the range [-v,v]. The smallest integer input value allowed is mapped to -v and the largest integer input value allowed is mapped to v. Values outside of the input range are either saturated or wrapped, according to specification.

References

[1] International Telecommunication Union. General Aspects of Digital Transmission Systems: Vocabulary of Digital Transmission and Multiplexing, and Pulse Code Modulation (PCM) Terms. ITU-T Recommendation G.701. March, 1993.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced before R2006a

R2024b: udecode supports C/C++ code generation

The udecode function supports C/C++ code generation. You must have MATLAB^® Coder™ to use this functionality.