dmitry1945
commented
8 months ago Dear @Bobobel,
thank you for the issue.
We will change the documentation (or the code). The factor of 2 is related to calculation performance.
Regards, Dmitry
Open Bobobel opened 8 months ago
dmitry1945
commented
8 months ago Dear @Bobobel,
thank you for the issue.
We will change the documentation (or the code). The factor of 2 is related to calculation performance.
Regards, Dmitry
Bobobel
commented
8 months ago Dear dmitry1945,
I am not shure if my last mail arrived this way. I have a more serious problem with fft_main_sc16 (see my version in last mail from Feb. 3rd: When I scale sin signals up to an amplitude of 32767 everything worked as expected. When I scale a rectangluar signal (puls 0.5 and amplitude 1) upto 25000 : results OK, with little deviations But when I scale higher, e.g. 28000 or 32767 (max), then I have got lower results. Here is an ouput of two rectangular signals: x1 scaled to 16383 and x2 to 32766 (frequencies 1/16 resp. 1/32,amplitudes 1 and 2 with a scaling factor of 16383):
I (1577) main: FFT for 256 complex points took 23239 cycles I (1587) main: End Example. Start example with N=256, ifactor=16383. i, x1, x2, R(y1), I(y1), R(y2), I(y2), y1p, y2p 0, 0, -32766, 57, 0, -260, 0,-49.17037,-35.98840 1, 16383, -32766, 120, -51, -503, -100,-41.98312,-30.08816 2, 16383, -32766, 107, -98, -474, -195,-41.05473,-30.09325 3, 16383, -32766, 83, -142, -426, -283,-39.96571,-30.11207 4, 16383, -32766, 51, -181, -363, -361,-38.80250,-30.10336 5, 16383, -32766, 13, -213, -285, -425,-37.70413,-30.10734 6, 16383, -32766, -32, -236, -198, -472,-36.75051,-30.10505 7, 16383, -32766, -80, -250, -102, -502,-35.90568,-30.09810 8, 16383, -32766, -131, -257, 23959, 3577,-35.08611, 3.39724 9, -16383, 32766, -180, -250, 98, -502,-34.51521,-30.11136 10, -16383, 32766, -228, -236, 194, -472,-33.96652,-30.13113 11, -16383, 32766, -271, -213, 281, -425,-33.53934,-30.14506 12, -16383, 32766, -311, -181, 359, -361,-33.16578,-30.15148 13, -16383, 32766, -342, -143, 423, -284,-32.90759,-30.14507 14, -16383, 32766, -366, -98, 470, -196,-32.71753,-30.14958 15, -16383, 32766, -380, -50, 500, -100,-32.61765,-30.13813 16, 16383, 32766, 3707, -20586, 510, -1, 2.12216,-30.13645 17, 16383, 32766, -380, 50, 500, 100,-32.61765,-30.13813
As you see for i=8 in signal 2 R(y2)=23959 I(y2)=3577 while for i=16: R(y1)=3707, I(y1)=-20585 (phase was -90° with x2, so we have switched R and I) Signal never went beyond +-32767 but the spectral components display an overflow:
With a scaling factor of 8191 I have got R(y2)=-20783, I(y2)=1785 and therefor a doubling gives R=-41566 and overflow +2^16 = 23970 (almost the number above, deviation due to 8191 and 16383 not doubling).
As you see: the problem willnot occur with simpletests using sin, but with real complex signals there will be! Is there a chance to handle overflow and "underrun" in your assembler codings? Otherwise you should tell people in the docs that there is a severe problem because aou have missed the "factor 2 because of efficiency" as you explained before.
With other tests I had an irregular phase change in spectrum in complex summed signals. With the above foundings I have an explanation now as well.
Sorry for my insisting on that subject, but I plan a frequency analysis for real signals in sc16, 16 bit, and with that I have investigated these problems.
Thank you for your work and kind regards from
Jürgen/Bobobel
Answers checklist.
General issue report
I know that the prefactor of FFT/DFT is under heavy discussion. But for me the Parseval–Plancherel identity has to be obeyed! Please check your example dsps_fft_main.c without windowing and you will see, that the absolute magnitudes of x1 and x2 are not represented in the frequency domain but with a factor of 2. Their relative value is OK, so you did not notice a problem. This was hidden because you used the windowing facility (thanks for showing that anyway!). Thanks for that DSP component!