Decode 2n-level quantized integer inputs to floating-point outputs
y = udecode(u,n)
y = udecode(u,n,v)
y = udecode(u,n,v,'SaturateMode')
y = udecode(u,n) inverts
the operation of uencode and
reconstructs quantized floating-point values from an encoded multidimensional
array of integers u. The input argument n must
be an integer between 2 and 32. The integer n specifies
that there are 2n quantization levels for
the inputs, so that entries in u must be either:
Signed integers in the range [-2n/2, (2n/2) – 1]
Unsigned integers in the range [0, 2n – 1]
Inputs can be real or complex values of any integer data type
(uint8, uint16, uint32, int8, int16, int32). Overflows (entries in u outside
of the ranges specified above) are saturated to the endpoints of the
range interval. The output y has the same dimensions
as u. Its entries have values in the range [-1,1].
y = udecode(u,n,v) decodes u such
that the output y has values in the range [-v,v],
where the default value for v is 1.
y = udecode(u,n,v, decodes 'SaturateMode')u and
treats input overflows (entries in u outside of [-v,v])
according to 'saturatemode', which can
be set to one of the following:
'saturate' — Saturate overflows.
This is the default method for treating overflows.
Entries in signed inputs u whose
values are outside of the range [-2n/2, (2n/2) – 1] are assigned the value determined by the closest endpoint
of this interval.
Entries in unsigned inputs u whose
values are outside of the range [0, 2n-1]
are assigned the value determined by the closest endpoint of this
interval.
'wrap' — Wrap all overflows
according to the following:
Entries in signed inputs u whose
values are outside of the range [-2n/2, (2n/2) – 1] are wrapped back into that range using modulo 2n arithmetic
(calculated using u = mod(u+2^n/2,2^n)-(2^n/2)).
Entries in unsigned inputs u whose
values are outside of the range [0, 2n – 1] are wrapped back into the
required range before decoding using modulo 2n arithmetic
(calculated using u = mod(u,2^n)).
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 allowable input range are either saturated or
wrapped, according to specification.
The real and imaginary components of complex inputs are decoded independently.
[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.