I am kind of new to DSP stuff....i want to convert 1/211 in to Q format. Can any one tell me how to find it. And I need to find the quantization error in general for any number how do i do tha??? Thanks, Rohini.

# Q format

Started by ●June 22, 2006

Reply by ●June 22, 20062006-06-22

rohini wrote:> I am kind of new to DSP stuff....i want to convert 1/211 in to Q > format. Can any one tell me how to find it. And I need to find the > quantization error in general for any number how do i do tha??? > > Thanks, > Rohini. >Say you've got an n-bit number, such that i bits are the integer portion and q bits are the "quotient" or fraction portion (i.e. i+q=n). Now say x is the number you're trying to convert to fixed-point and x' is the fixed-point representation. x' = round(x * 2^q) quantization error = x - ( x' / 2^q ) So take your example of x=1/211. Let's say you're dealing with 16-bit numbers and you've decided to do q14 math. That means your total range is [-2,2) and your precision is 2^-14 (~6.1e-5). x' = round(1/211 * 2^(-14) = round(77.649) = 78 = 0x004E In binary this means you are representing 1/211 as 00.00 0000 0100 1110 You can now convert this back to decimal by doing 78 / 2^14 = 0.0047607421875. Therefore your quantization error is: Eq = 1/211 - 78 / 2^14 = -2.14e-5 I hope that helps you with q-math! I tried to make it general so you could apply it anywhere. Brad