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FFT and IFFT using CMSIS DSP library, q15 fractional format

jeremy plantier
Hello,

I am currently trying to use the CMSIS DSP library to implement DSP functionality, by doing FFT or IFFT.

I don't have an embedded Floating point Unit, thus I would like to use the fixed q15 fractional format.
By reading the CMSIS documentation html page, it is specified that the FFT/IFFT output format is different from the input one...
For example, for a FFT length of 256, the input format is q15 (1.15) and the output format is 9.7. With 8 bits to upscale.
If I want to perform an FFT and directly fllowed by an IFFT, I have to convert output FFT data  which are in 9.7 into a q15 for IFFT Input format...

My question is, from my understanding, the conversion from q15 to 9.7 or the reverse, would be just done by a simple shift of 8 bits...?
But, I guess that data may be lost between each conversion...?
It is very confused to me...

Could someone help me ...?

Thanks!

PjEmY
  • Arm Employee Badge
    Note: This was originally posted on 15th June 2012 at http://forums.arm.com

    My question is, from my understanding, the conversion from q15 to 9.7 or the reverse, would be just done by a simple shift of 8 bits...?


    Yes. (The only possible got-cha is if the q numbers are signed as you have to be wary of what you shift into/out of the sign bit position - so you may need sign extension in some cases, rather than shifting zeros into the MSB).

    But, I guess that data may be lost between each conversion...?


    Yes. You are converting from a number with 15 fractional bits (more precision, less dynamic range) to a number with 7 fraction bits (less precision, more dynamic range). Any such conversion is obviously going to lose data off one end of the number ...

    Could someone help me ...?


    Doesn't seem like you need much =P
  • Note: This was originally posted on 18th June 2012 at http://forums.arm.com

    Thank you isogen74.

    Actually, I performed what I wanted latter during the last week.

    My problem was just to perform the right up scalling before sending data to the DAC. I am currently using the Q15 fractional format because it is the only SIMD instructions optimized format (without FPU use) available in the DSP CMSIS library.

    Now I have to implement Filtering (FIR) functions to avoid the resulting additional noise which appears after FFT/IFFT.

    Thank you again for your help!



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  • Note: This was originally posted on 3rd July 2012 at http://forums.arm.com

    Hi,

    I'm currently using CMSIS DSP Lib for my STM32F105R8T6 (Cortex - M3). I tried to run Q15 CIFFT Radix-2 function but the result is quite weird ( max value = 11 ??? while my input signal's amplitude = 1 ( 32767 in Q15 format )). This is my code :




    status = arm_cfft_radix2_init_q15(&CFFT_R2_Q15, CfftLen, CifftFlagOFF, bitRevf) ;  // instance for calculating fft(x)
arm_cfft_radix2_q15(&CFFT_R2_Q15, x) ;           // calculate fft


status = arm_cfft_radix2_init_q15(&CIFFT_R2_Q15, CifftLen, CifftFlagON, bitRevi) ;  // instance for calculating ifft(x)
arm_cfft_radix2_q15(&CIFFT_R2_Q15, x) ;           //calculate ifft




    x : array of 4096 element (real, image interleaved)
    fftsize = 2048
    Because the Real FFT function cost too much ROM space so I have to use Complex FFT to calculate real signal ( complex signal with image part = 0 ).

    I hope someone could help me with this CIFFT function.

    Thank you !
  • Note: This was originally posted on 18th January 2013 at http://forums.arm.com


    Hi,

    I'm currently using CMSIS DSP Lib for my STM32F105R8T6 (Cortex - M3). I tried to run Q15 CIFFT Radix-2 function but the result is quite weird ( max value = 11 ??? while my input signal's amplitude = 1 ( 32767 in Q15 format )). This is my code :




    status = arm_cfft_radix2_init_q15(&CFFT_R2_Q15, CfftLen, CifftFlagOFF, bitRevf) ;  // instance for calculating fft(x)
arm_cfft_radix2_q15(&CFFT_R2_Q15, x) ;           // calculate fft


status = arm_cfft_radix2_init_q15(&CIFFT_R2_Q15, CifftLen, CifftFlagON, bitRevi) ;  // instance for calculating ifft(x)
arm_cfft_radix2_q15(&CIFFT_R2_Q15, x) ;           //calculate ifft




    x : array of 4096 element (real, image interleaved)
    fftsize = 2048
    Because the Real FFT function cost too much ROM space so I have to use Complex FFT to calculate real signal ( complex signal with image part = 0 ).

    I hope someone could help me with this CIFFT function.

    Thank you !


    Hi Protokov! try to divide by the number of element