The maximum/minimum value of the input/output of fft functions

[LinChihShan]

Hi,

I would like to know the minimum and maximum values of the input and output values for the FFT series functions.

The specific situation is as follows: I am using riscv_dsp_rfft_q15 to convert a time-domain signal into its frequency spectrum, performing some processing, and then using riscv_dsp_rifft_q15 to convert the spectrum back to the time-domain signal. However, the time-domain signal overflow.

I am confident that the Q format has been implemented according to the specifications in the Andes DSP Library User Manual, and I am also confident that my algorithm itself is correct. When I scale down the entire signal by a few times, the overflow issue is alleviated or disappears. Therefore, I suspect that there may be specific input/output range constraints for the FFT functions—especially for the IFFT series input.

Thank you for taking the time to read this. I look forward to your reply. Thank you.

[Songhh514]

Hi,
Which size are you using? The input for the riscv_dsp_rfft_q15 must be in the range [0x8000, 0x7FFF] and corresponds to the floating point [-1.0, 1.0). We have updated some new algorithms for the newest version. Maybe you can get a new try.

[LinChihShan]

Hi,

My point is that when I use your function like int32_t riscv_dsp_cifft_rd4by2_q15(q15_t *src, uint32_t m), do I need to constrain the values inside the src array? It appears that during the internal butterfly computations, the values keep accumulating, and in extreme cases, this could potentially lead to overflow.

[Songhh514]

Yes, the cifft must constrain the value. You can refer the following size and input format in the docs riscv_dsp_cifft_q15' note

[LinChihShan]

I think I understand the meaning of this table. My understanding is that the table indicates, when using a 2^m-point IFFT, what the Q formats of the input and output should be. However, this is not exactly what I originally meant.

What I actually want to know is the integer value range of the input, rather than the fractional precision implied by the Q format.

Taking m = 10 as an example, the input is specified as Q12.4. This means that the actual numerical value represented by the input field is integer_value / (2^4)

Up to this point, I can follow the reasoning. However, what I want to clarify is whether this implies that I must constrain the integer values in this field to the range of +15 to -16. That does not seem reasonable, since such a constraint would result in extremely low data resolution.

On the other hand, we can see that in the forward FFT implementation, each butterfly stage performs a right shift by 1 bit to prevent overflow. In contrast, the inverse FFT does not apply such scaling, which therefore implies a risk of overflow.

Is there a solution that can balance both data precision and overflow prevention?

Thank you again for taking the time to reply. I really appreciate it.