tomwalters@0: /*
tomwalters@0:   FFT program adapted from routines given in Numerical Recipes.
tomwalters@0: 
tomwalters@0:   The output framewidth = ( input framewidth + padding ) / 2  spectral points.
tomwalters@0: 
tomwalters@0:   Padding with zeroes is recommended to counter end-effects (See NR, p416).
tomwalters@0:   It is also necessary since framewidth + padding must be a power of 2
tomwalters@0:   (sample points at given rate).
tomwalters@0:   This is because the fft method is "radix-2", and because the output is
tomwalters@0:   symmetrical so that just half the points are unique.
tomwalters@0:   Therefore each input frame is padded with zeroes to the next power of 2
tomwalters@0:   larger than the input framewidth.
tomwalters@0: 
tomwalters@0:   If necessary, extra padding can be enforced using the padding option to
tomwalters@0:   add extra zeroes, padding to a larger power of 2.
tomwalters@0:   The amount of extra padding is "exponential", expanding the basic size to:
tomwalters@0: 	( framewidth + padding ) * 2**n
tomwalters@0:   where the padding option is n.
tomwalters@0:   (n=0 by default, so that no extra padding is added. When n=1 then padding is
tomwalters@0:   added to double the size, and when n=2 the size is quadrupled, etc.).
tomwalters@0: 
tomwalters@0:   Frames are selected from the input stream using the "frames" option,
tomwalters@0:   which has syntax: [[-]frame=a[-b]]. Input frames  are numbered 1,2,...
tomwalters@0:   For example:
tomwalters@0:     frame=a      Select just the a'th frame.
tomwalters@0:     frame=a-b    Select frames from the a'th to b'th inclusive.
tomwalters@0:   The strings "min" and "max" can be used as specifiers, meaning eg:
tomwalters@0:     frame=min    Select the first frame.
tomwalters@0:     frame=max    Select the last frame.
tomwalters@0:     frame=a-max  Select frames from the a'th to the last inclusive.
tomwalters@0:     frame=min-b  Select frames from the first to the b'th inclusive.
tomwalters@0:   The default selects all frames, (ie frame=min-max).
tomwalters@0: 
tomwalters@0:   Several forms of fft processing are provided, according to the "spectrum"
tomwalters@0:   option:  log/magnitude/phase/complex/inverse/verbose.
tomwalters@0: 
tomwalters@0:   Log and magnitude are both magnitude spectra (log is log10 of magnitude).
tomwalters@0:   Phase is the phase spectrum.
tomwalters@0:   Complex is the full complex spectrum, in <real,imag> pairs.
tomwalters@0:   Inverse transform reads framewidth numbers which are interpreted as
tomwalters@0:   <real,imag> pairs, (ie framewidth/2 complex numbers),
tomwalters@0:   and outputs the inverse transform scaled by 1/framewidth.
tomwalters@0:   Verbose prints the spectrum in ASCII on the stdout.
tomwalters@0: 
tomwalters@0: 
tomwalters@0:   Examples:
tomwalters@0: 
tomwalters@0: 1. To print the input and output frame sizes in sample points, eg for a
tomwalters@0:    subsequent plotting program, use the size option:
tomwalters@0: 
tomwalters@0: fft ... size=on
tomwalters@0: 
tomwalters@0: 2. An fft of a waveform sampled at 10kHz, computed within a frame of 12.8ms,
tomwalters@0:    plotting the 2nd frame in a sequence of frames with half-frame overlap.
tomwalters@0: 
tomwalters@0: fft samp=10kHz width=12.8ms frstep=6.4ms frame=2 file | x11plot
tomwalters@0: 
tomwalters@0: 3. An animated plot of successive fft spectra of a waveform sampled at 10kHz,
tomwalters@0:    each computed within a frame of 12.8ms, and shifted by 2 sample points.
tomwalters@0: 
tomwalters@0: fft samp=10kHz width=12.8ms frstep=2p file | x11play -n64
tomwalters@0: 
tomwalters@0: 4. Using the complex output from fft, and inverse transform without windowing
tomwalters@0:    to recover original input.
tomwalters@0: 
tomwalters@0: fft samp=10kHz frame=2 spec=complex window=off file > foo
tomwalters@0: fft samp=10kHz frame=1 spec=inverse window=off foo | x11plot
tomwalters@0: 
tomwalters@0: */
tomwalters@0: 
tomwalters@0: #include <stdio.h>
tomwalters@0: #include <math.h>
tomwalters@0: #include "options.h"
tomwalters@0: #include "units.h"
tomwalters@0: #include "strmatch.h"
tomwalters@0: #include "sigproc.h"
tomwalters@0: 
tomwalters@0: char applic[]     = "fast Fourier transform of contiguous frames.\n      i/p and o/p data in binary shorts." ;
tomwalters@0: 
tomwalters@0: static char *helpstr, *debugstr, *sampstr, *widthstr, *padstr, *wstr, *sstr, *sizestr ;
tomwalters@0: static char *startstr, *shiftstr, *framestr, *smagstr, *slogstr, *sphasestr, *echostr ;
tomwalters@0: 
tomwalters@0: static Options option[] = {
tomwalters@0:     {   "help"      ,   "off"       ,  &helpstr     ,   "help"                                          , DEBUG   },
tomwalters@0:     {   "debug"     ,   "off"       ,  &debugstr    ,   "debugging switch"                              , DEBUG   },
tomwalters@0:     {   "samplerate",   "20kHz"     ,  &sampstr     ,   "samplerate "                                   , VAL     },
tomwalters@0:     {   "start"     ,   "0"         ,  &startstr    ,   "Start point in i/p file."                      , VAL     },
tomwalters@0:     {   "frames"    ,   "1-max"     ,  &framestr    ,   "Select frames inclusively"                     , VAL     },
tomwalters@0:     {   "frstep"    ,   "16ms"      ,  &shiftstr    ,   "Step between input frames."                    , VAL     },
tomwalters@0:     {   "width"     ,   "32ms"      ,  &widthstr    ,   "Width of input frames."                        , VAL     },
tomwalters@0:     {   "padding"   ,   "0"         ,  &padstr      ,   "Exponential frame padding"                     , SVAL    },
tomwalters@0:     {   "window"    ,   "on"        ,  &wstr        ,   "Hamming window"                                , SETFLAG },
tomwalters@0:     {   "spectrum"  ,   "magnitude" ,  &sstr        ,   "log/magnitude/phase/complex/inverse/verbose"   , SETFLAG },
tomwalters@0:     {   "scalemag"  ,   "0.08"      ,  &smagstr     ,   "scale magnitude  spectrum"                     , SVAL    },
tomwalters@0:     {   "scalelog"  ,   "10"        ,  &slogstr     ,   "scale log  spectrum"                           , SVAL    },
tomwalters@0:     {   "scalephase",   "100"       ,  &sphasestr   ,   "scale phase spectrum"                          , SVAL    },
tomwalters@0:     {   "size"      ,   "off"       ,  &sizestr     ,   "print input/output frame size in samples"      , SETFLAG },
tomwalters@0:     {   "echo"      ,   "off"       ,  &echostr     ,   "echo buffered input without processing"        , SVAL    },
tomwalters@0:    ( char * ) 0 } ;
tomwalters@0: 
tomwalters@0: 
tomwalters@0: int     samplerate  ;
tomwalters@0: int     width       ;
tomwalters@0: int     step        ;
tomwalters@0: int     zeroes      ;
tomwalters@0: int     dowindow    ;
tomwalters@0: double  scale       ;
tomwalters@0: int     echo        ;
tomwalters@0: 
tomwalters@0: float  *vec, *window ;
tomwalters@0: short  *obuf ;
tomwalters@0: 
tomwalters@0: int     allbins  ;
tomwalters@0: int     halfbins ;
tomwalters@0: 
tomwalters@0: #define MAG     1       /* magnitude spectrum */
tomwalters@0: #define PHASE   2       /* phase spectrum     */
tomwalters@0: #define INV     3       /* inverse transform  */
tomwalters@0: #define VERB    4       /* verbose (ASCII)    */
tomwalters@0: #define LOG     5       /* log magnitude      */
tomwalters@0: #define COMP    6       /* complex spectrum   */
tomwalters@0: 
tomwalters@0: int     output ;
tomwalters@0: 
tomwalters@0: main (argc, argv)
tomwalters@0: int     argc;
tomwalters@0: char  **argv;
tomwalters@0: {
tomwalters@0:     FILE     *fp  ;
tomwalters@0:     short    *buf ;
tomwalters@0:     int       a, b ;
tomwalters@0:     int       isign ;
tomwalters@0: 
tomwalters@0:     fp = openopts( option,argc,argv ) ;
tomwalters@0:     if ( !isoff( helpstr ) )
tomwalters@0: 	helpopts( helpstr, argv[0], applic, option ) ;
tomwalters@0: 
tomwalters@0:     samplerate = to_Hz( sampstr ) ;
tomwalters@0:     dowindow   = ison( wstr ) ;
tomwalters@0:     echo       = ison( echostr ) ;
tomwalters@0:     width      = to_p( widthstr, samplerate )  ;
tomwalters@0:     step       = to_p( shiftstr, samplerate )  ;
tomwalters@0:     zeroes     = ( getpower( width ) << atoi( padstr ) ) - width ;
tomwalters@0: 
tomwalters@0:     allbins    = width + zeroes ;
tomwalters@0:     halfbins   = allbins / 2    ;
tomwalters@0: 
tomwalters@0:     if ( iststr( sstr, "magnitude" ) )  {
tomwalters@0: 	output = MAG ;
tomwalters@0: 	scale = atof( smagstr ) ;
tomwalters@0: 	isign = 1 ;
tomwalters@0:     }
tomwalters@0:     else if ( iststr( sstr, "log" ) )  {
tomwalters@0: 	output = LOG ;
tomwalters@0: 	scale = atof( slogstr ) ;
tomwalters@0: 	isign = 1 ;
tomwalters@0:     }
tomwalters@0:     else if ( iststr( sstr, "phase" ) ) {
tomwalters@0: 	output = PHASE ;
tomwalters@0: 	scale = atof( sphasestr ) ;
tomwalters@0: 	isign = 1 ;
tomwalters@0:     }
tomwalters@0:     else if ( iststr( sstr, "complex" ) ) {
tomwalters@0: 	output = COMP ;
tomwalters@0: 	isign = 1 ;
tomwalters@0:     }
tomwalters@0:     else if ( iststr( sstr, "inverse" ) ) {
tomwalters@0: 	output = INV ;
tomwalters@0: 	scale = 1./(double)width ;
tomwalters@0: 	isign = (-1) ;
tomwalters@0:     }
tomwalters@0:     else if ( iststr( sstr, "verbose" ) ) {
tomwalters@0: 	output = VERB ;
tomwalters@0: 	isign = 1 ;
tomwalters@0:     }
tomwalters@0:     else {
tomwalters@0: 	fprintf(stderr,"unknown spectrum \n");
tomwalters@0: 	exit( 1 ) ;
tomwalters@0:     }
tomwalters@0: 
tomwalters@0:     /* frame size printout */
tomwalters@0: 
tomwalters@0:     if ( ison( sizestr ) ) {
tomwalters@0: 	fprintf(stderr,"fft sizes in sample points:\n" ) ;
tomwalters@0: 	fprintf(stderr,"    input  frame size = %d  (framewidth=%d + padding=%d)\n", width+zeroes, width, zeroes ) ;
tomwalters@0: 	fprintf(stderr,"    output frame size = %d \n", (width + zeroes)/2 ) ;
tomwalters@0: 	exit( 0 ) ;
tomwalters@0:     }
tomwalters@0: 
tomwalters@0:     /* parse bounds on number of frames */
tomwalters@0: 
tomwalters@0:     if ( selector( framestr, &a, &b ) == 0 ) {
tomwalters@0: 	fprintf(stderr,"fft: bad frame selector [%s]\n", framestr ) ;
tomwalters@0: 	exit( 1 ) ;
tomwalters@0:     }
tomwalters@0: 
tomwalters@0:     /* Allocate working space */
tomwalters@0: 
tomwalters@0:     obuf  = (short *)malloc( halfbins * sizeof(short) ) ;
tomwalters@0:     vec   = (float *)malloc( allbins * sizeof(float) ) ;
tomwalters@0:     if ( dowindow )
tomwalters@0: 	window = hamming( width ) ;
tomwalters@0: 
tomwalters@0: 
tomwalters@0:     /* Compute fft for each frame of width shorts in the input stream */
tomwalters@0: 
tomwalters@0:     if ( seekbytes( fp, (int)( to_p( startstr, samplerate ) * sizeof(short) ) ) == 0 ) {
tomwalters@0: 	fprintf(stderr,"improper seek\n") ;
tomwalters@0: 	exit( 1 ) ;
tomwalters@0:     }
tomwalters@0: 
tomwalters@0:     while ( ( buf = getframe( fp, a, width, step ) ) != (short *)0  && ( a<=b || b==0 ) ) {
tomwalters@0: 	if ( echo ) fwrite( buf, sizeof(short), width, stdout ) ;
tomwalters@0: 	else process( buf, isign ) ;
tomwalters@0: 	a++ ;
tomwalters@0:     }
tomwalters@0:     if ( a<=b && b>0 )
tomwalters@0: 	fprintf(stderr,"warning: not enough frames for request\n");
tomwalters@0: 
tomwalters@0:     fclose( fp ) ;
tomwalters@0: }
tomwalters@0: 
tomwalters@0: 
tomwalters@0: process( buf, isign )
tomwalters@0: short *buf ;
tomwalters@0: int    isign ;
tomwalters@0: {
tomwalters@0:     short *bptr     = buf ;
tomwalters@0:     short *endptr   = buf + width ;
tomwalters@0:     short *optr     = obuf ;
tomwalters@0:     short *endbin   = obuf + halfbins ;
tomwalters@0:     float *wptr     = window ;
tomwalters@0:     float *vptr     = vec    ;
tomwalters@0:     float *endvec   = vec + allbins ;
tomwalters@0: 
tomwalters@0:     if ( dowindow )
tomwalters@0: 	while ( bptr < endptr )
tomwalters@0: 	    *vptr++ =  *bptr++  *  *wptr++ ;
tomwalters@0:     else
tomwalters@0: 	while ( bptr < endptr )
tomwalters@0: 	    *vptr++ =  *bptr++ ;
tomwalters@0: 
tomwalters@0:     while ( vptr < endvec )         /* padding */
tomwalters@0: 	*vptr++ =  0 ;
tomwalters@0: 
tomwalters@0:     fft( vec, width+zeroes, isign ) ;
tomwalters@0: 
tomwalters@0:     vptr = vec ;
tomwalters@0:     switch ( output ) {
tomwalters@0: 
tomwalters@0: 	case COMP  :  while ( vptr < endvec )
tomwalters@0: 			  *optr++ = (short)( *vptr++ ) ;
tomwalters@0: 		      fwrite( obuf, sizeof(short), allbins, stdout ) ;
tomwalters@0: 		      break;
tomwalters@0: 	case PHASE :  phase( vec, allbins ) ;
tomwalters@0: 		      while ( optr < endbin )
tomwalters@0: 			  *optr++ = (short)( scale * *vptr++ ) ;
tomwalters@0: 		      fwrite( obuf, sizeof(short), halfbins, stdout ) ;
tomwalters@0: 		      break;
tomwalters@0: 	case MAG   :  mag( vec, allbins ) ;
tomwalters@0: 		      while ( optr < endbin )
tomwalters@0: 			  *optr++ = (short)( scale * *vptr++ ) ;
tomwalters@0: 		      fwrite( obuf, sizeof(short), halfbins, stdout ) ;
tomwalters@0: 		      break;
tomwalters@0: 	case LOG   :  mag( vec, allbins ) ;
tomwalters@0: 		      while ( optr < endbin )
tomwalters@0: 			  *optr++ = (short)( scale * 10 * log10(*vptr++) ) ;
tomwalters@0: 		      fwrite( obuf, sizeof(short), halfbins, stdout ) ;
tomwalters@0: 		      break;
tomwalters@0: 	case INV   :  while ( vptr < endvec )
tomwalters@0: 			  *optr++ = (short)( scale * *vptr++ ) ;
tomwalters@0: 		      fwrite( obuf, sizeof(short), allbins, stdout ) ;
tomwalters@0: 		      break;
tomwalters@0: 	case VERB  :  print_complex_spectrum( (complex *)vec, halfbins, samplerate ) ;
tomwalters@0: 		      break;
tomwalters@0: 
tomwalters@0:     }
tomwalters@0: }
tomwalters@0: 
tomwalters@0: 
tomwalters@0: /*
tomwalters@0:  Pretty-print complex k-spectrum on the stdout.
tomwalters@0: */
tomwalters@0: 
tomwalters@0: print_complex_spectrum(C,k,samplerate)
tomwalters@0: complex *C;
tomwalters@0: int      k, samplerate;
tomwalters@0: {
tomwalters@0:     float res;      /* frequency resolution. */
tomwalters@0:     int   i;
tomwalters@0: 
tomwalters@0:     res = (float)(samplerate>>1) / (float)k;
tomwalters@0:     for (i=0; i<k ; i++) {
tomwalters@0: 	printf ("%3d.  %6.1fHz.  Re=%9.2f  Im=%9.2f  mod=%8.2f  arg=%4.2f\n",
tomwalters@0: 		i, i*res, Re(&C[i]), Im(&C[i]), mod(&C[i]), arg(&C[i]) );
tomwalters@0:     }
tomwalters@0: }
tomwalters@0: