After I’ve made astonishing breakthrough in speed of the FFT algorithm based on RADIX-4 version, I decided to create a new project, which would take a full advantage of Radix-4 “rocket science” performance. Reviewing my “Voice Recognition” blog it looks logically to create just exactly opposite application – Voice Scrambler. To make it happened, I need FFT subroutine to be completed twice, in forward and reverse ( iFFT ) direction. Than simply manipulating individual frequencies (bins) position in the array, I could scramble a voice in well known old fashioned manner, inverting the spectrum of the human voice, making it sounds completely non intelligible (alien’s voice). For Pitch Shifting, bins have to be “progressively” spaced between each other, driving timbre up on the scale. It is possible to lower a Pitch as well, shrinking and over-lap bins, but I made only up shifting part for now.
Making preliminary calculation, I get: 10.1 milliseconds x 2 / 256 samples = 78.9 microseconds / sample. Or turning up side down, 12.67 kHz sampling frequency. It’s rough estimation, but regular “public phone quality” – 8 kHz sampling rate looks quite achievable. Next, as always, if CPU is o’k, let check into memory management. Unfortunately, arduino Uno (2 kB) wouldn’t allow to use fft-256, because: input buffer (256) + output (256) + fft processing ( real + imaginary) (512), plus multiply by 2 (integer size, 1024 x 2 = 2048) would occupy all available 2 kB. So, I have to decrease fft size on one level down, to fft-128, or even two level down – make fft-64, from original fft-256 (presumably good quality, comparable with MP3 codec). After completing a couple sketchy tests, fft-64 shows pure quality of speech and was rejected. Can’t say I did thoroughful research on this matter, may be fft-64 could still be good in other circumstances or with musical material content instead of speech.
O’k, fft-128 – compromise version was selected by God. But my code, published in “RADIX-4″ blog hasn’t included RADIX-8 section, which is required when size of the array isn’t a power of 4. Nothing to do, the only way to bring Scrambler project to life, is to write a missing section of the RADIX-8 code… So I did. Timing measurements show, that Radix-4 with new patch is running even faster, than extrapolated from fft-256 down to fft-128 speed of RADIX-4 without it, measurements result: 4.2 milliseconds (compare to extrapolated 4.6 milliseconds). By the way, as I mention in other post about Split-Radix, if it would be my next adventure. It was, I have re-written from “Matters Computational” http://www.jjj.de/ Split-Radix C/C++ code in my tools-box now, which is to my surprise shows practically no difference in speed with Radix-4 algorithm, same 10.1 (fft-256) milliseconds execution time, and loosing ! competition giving 4.6 milliseconds (fft-128).
Other things to explain, as Pitch Shifting considered to be most 
complicated task even for monstrous DSP processors, I’ve skipped two important procedures: windowing on input samples and add-overlap on the output flow, just because no processor’s time left. Luckily, due speech’s spectrum concentration around most noticeable “middle” area, cutting off “windowing” is only slightly increases noise level. On the other hand, missing add-overlap procedure has greater negative impact on the voice quality, ”robotize” it via parasitic amplitude modulation. When frequency bins re-mapped in the pull, running inverse iFFT doesn’t produce continuity ”match” with previous block as it should, because input has no a continuity disruption between samples blocks (128 samples, ~16 milliseconds of voice frame). Well, if I do everything right, there wouldn’t be any fun with arduino, would it be? Btw, there are two outputs buffer in the software, especially to track this issue. I was thinking to implement some kind of distortion estimator based on this information. Meanwhile, one of them could be removed to save some memory for other part of the program.
Hardware.
Arduino has 10 bits ADC, this is why I decided to build a DAC for audio output based on PWM TIMER0 feature, 5 to 5 bits split equally between pin 5 and 6. One PWM pin could only play 7 bits sound (don’t forget sign bit), which is too low. Weighted 32R-R ladder potentially allows to increase PWM frequency up to 250 kHz or so, and simplify requirements for output filter design. Nevertheless, I left “default” 31 kHz settings for TIMER0, just in case I need more research with 16 bits output later on, All it would takes to switch on “full” 16 bits, just add one 256 k resistor and divide integer in high and low byte.
Please, be advised, that included scrambler function was not fully tested, as I don’t have second arduino to do a decoding in real time-); (Probably, I can record a scrambled sound and decode it in the second passage trough the system – things TO DO.) The same time Pitch Shifting was successfully tested, as you can see in posted video clip. YouTube Video
Summary:
- Sampling rate 8 kHz. (easily to adjust by TIMER2 variable.)
- Output rate 8 kHz. (same as sampling, two processes are synchronous.)
- Delay 16 milliseconds. (1 block, or two blocks 32 milliseconds.)
- Input/Output resolution: 10 bits.
There are build-in command line interface:
- if (incomingByte == ‘m’) { // FREE MEMORY BYTES
- if (incomingByte == ‘x’) { // PRINT OUT INCOMING SAMPLING BUFFER
- if (incomingByte == ‘s’) { // SWITCHES – SCRAMBLING ON / OFF
- if (incomingByte == ‘y’) { // PRINT OUT OUTGOING BUFFER
- if (incomingByte == ‘f’) { // DATA AFTER FFT, FREQUENCIES BINS
- if (incomingByte == ‘p’) { // DATA AFTER PITCH SHIFTING – SCRAMBLING
- if ((incomingByte >= ’0′) && (incomingByte <= ’9′)) { // DIGITS ”1″ to “9″ – REGULATE MAGNITUDE OF SHIFTING, “0″ – SPECTRUM INVERSION.
Link to download an Arduino sketch: Pitch Shifting – Scrambler
