FFT: Q31 format? & sine wave demo code

George Liu

Dear champs,

I want to using the FFT library(SPRC081) for our application and I have some questions about this library.

Could anyone help me?

1.What is meaning of the "Q31 format"?

For example, page.40 of fft_mdl.pdf says: "the input and output data of "void calc(RFFT32_handle) function" are in Q31 format".

Is there any application note or document explain the meaning of Q format?

2.Does anyone have a FFT demo code which input is a sine wave signal(Ex: 256 points, amplitude = +/- 32768)?

Thank you very much!

Warm regards,

George Liu

f8504228@gmail.com

over 17 years ago

0 DaveB123 over 17 years ago

TI__Expert 4745 points

George,

Q31 format (more generically Qnn) is referring to how the data is treated numerically by the code in the library.

The Q point is between the nn+1 and nn-th bit. The Q point is like the decimal point in the binary world. Bits to the right of the Q point are treated

as fractions...(e.g. 2**-1, 2**-2, etc.)

In Q31 then, the first bit (the 32nd bit) is actually the SIGN bit.

So, for example, 7fff hex is 0.999969482. 8000 hex is -1.0000

4000 hex is 0.5 and -0.5 is C000 hex.

The REASON for using Qnn is that when it is time to multiply...2 fractions always will yield a fraction.

This is standard practice in 16/32 bit DSP architectures.

TI also supports an improvement of standard Q format called IQ math.

I will look around and see what I can find to support your other question.

0 DaveB123 over 17 years ago in reply to DaveB123

TI__Expert 4745 points

Correction to above:

In Q31 there are 32 bits so 7ffff should be 7fff ffff and the corresponding decimal would be different as well.

0 Tim Love over 17 years ago in reply to DaveB123

TI__Expert 5340 points

George,
 
1) As mentioned above Q numbers are a way of representing a floating point value on a fixed point processor. For instance say you have a Q15 number. The 15 is the decimal part of the number. 
The Q value specifies how many binary digits are allocated for the fractional portion of the number. So for a Q31 number you would have 31 decimal numbers .You can get a little bit more of a 
description from the appnote SPRA109:
 
http://focus.ti.com/general/docs/techdocsabstract.tsp?abstractName=spra109
 
There is also an FAQ that discusses Q15 available here:
 
http://www-k.ext.ti.com/srvs/cgi-bin/webcgi.exe?Company={5761bcd8-11f5-4e08-84e0-8167176a4ed9},kb=dsp,case=5193,new
 
Another source that discusses this is SPRU422J. Please take a look at Appendix A and B:
 
http://focus.ti.com/lit/ug/spru422j/spru422j.pdf
 
Finally, there is an article in Wikipedia to discuss this:
 
http://en.wikipedia.org/wiki/Q_(number_format)
 
An overload of information J
 
2) The FFT library does include both 256 complex and real examples that use the Software Test Bench (STB) library to input a sine wave.  This library must be downloaded as well:
 
http://focus.ti.com/docs/toolsw/folders/print/sprc084.html
 
From looking at it though it doesn’t seem to have the amplitude you are looking for but you could modify this in the example.
 
Regards,
 
Tim Love

0 George Liu over 17 years ago in reply to Tim Love

TI__Intellectual 1785 points

Hello Ming and Tim,

After several days studying, I finally understand what is the meaning of Q format.

Thank YOU very much for your detail explaination!!

Warm regards,

George

0 Jonathan9420 over 11 years ago in reply to Tim Love

Expert 2056 points

I'm confused. TI says:

"Unless specifically noted, DSPLIB functions use Q15 format or to be more exact Q0.15." http://www.ti.com/lit/ug/spru422j/spru422j.pdf

but also:
"All fixed-point arithmetic is defined by a Q format. One such format is the Q15 (1.15)." http://www.ti.com/lit/an/spra109/spra109.pdf

ARM says:

"U Q15 is shorthand for unsigned Q1.15" and "Q31 is shorthand for signed Q1.31" http://infocenter.arm.com/help/index.jsp?topic=/com.arm.doc.dui0066g/Chdfaaei.html

Is it 0.15 or 1.15? Is it sometimes 2s-complement and sometimes something else?

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FFT: Q31 format? & sine wave demo code