如何在MATLAB中将定点（Q格式）数字转换为浮点数

Question

Why int16 doesn't retrieve the sign from an hex string?

MATLAB:

>> single(int16(hex2dec('ffff')))
ans =

       32767

ie

>> int16(hex2dec('ffff')) == int16(hex2dec('8fff'))

ans =

     1

To put it in its general context, I want to rewrite the following numpy Python snippet code in MATLAB:

>>> import numpy as np 
>>> i='ffff'
>>> q='3fff'
>>> i_float = np.int16(int(i,16))
>>> i_float = i_float * 2 ** -15
>>> i_float
-3.0517578125e-05
>>> q_float = np.int16(int(q,16))
>>> q_float = q_float * 2 ** -15
>>> q_float
0.499969482421875

Answer 1

Here's what I've got. (Yes, it seems to be more convoluted than it should be.)

i_hex = 'ffff'
q_hex = '3fff'

i_int16 = typecast(uint16(hex2dec(i_hex)),'int16')
i_float = single(i_int16) * 2 ^ -15

q_int16 = typecast(uint16(hex2dec(q_hex)),'int16')
q_float = single(q_int16) * 2 ^ -15

Output:

i_hex = ffff
q_hex = 3fff
i_int16 = -1
i_float =   -3.05175781250000e-05
q_int16 = 16383
q_float =  0.499969482421875

hex2dec converts hex to a double, so I cast it to a uint16 so as to preserve the sign bit (which hex2dec refuses to do). Then I typecast the result to a signed int16 . This just takes the bits of the uint16 and interprets them as an int16 . Then cast it to a single and bitshift.

Note: I used format long to see as many decimal places as I could.