Converting 10-bit unsigned to 16-bit signed. SOLVED

Projects Programming
1

I'm trying to use the FHT library to produce a frequency spectrum of an audio signal by following an example here. After reading the ADCL and ADCH registers, the contents are combined into an int, k.

byte m = ADCL;
byte j = ADCH;
int k = (j << 8) | m;

I'm happy so far. This is then supposedly converted to a 16-bit signed integer, but I just cannot follow the logic.

k -= 0x0200;
k <<= 6;

I was expecting some bitwise inversion and then adding 1.

By hand, as far as I can tell...
0x3FF (Full scale ADC) converts to 0x7FC0 (32,704), which is close enough to 32,767 I suppose.
0x001 (smallest possible ADC ) converts to 0x8040 (I think), which is -32,704.

So, is this a widely accepted approximation or have I mis-calculated or missed the point? I've searched but haven't found this method anywhere else.

2

The "happy face" in your code will not compile, which is why we suggest to use code tags.

There are many acceptable ways of doing that conversion.

3

The ADC produces numbers in the range 0 - 1023.
The FHT library requires signed numbers. The range 0 - 1023 is converted to the range -512 - +511 by subtracting 512 (0x200). Then it is shifted up 6 bits (i.e. multiply by 64) resulting in a range of -32768 to 32767 which is the full range of a 16-bit number.

I was expecting some bitwise inversion and then adding 1.

Why? All that does is form the twos complement of a number which is easily written in C with the minus sign.

Pete

4

Thank you. That was succinct and understandable.