Chris@184: KISS FFT - A mixed-radix Fast Fourier Transform based up on the principle, 
Chris@184: "Keep It Simple, Stupid."
Chris@184: 
Chris@184:     There are many great fft libraries already around.  Kiss FFT is not trying
Chris@184: to be better than any of them.  It only attempts to be a reasonably efficient, 
Chris@184: moderately useful FFT that can use fixed or floating data types and can be 
Chris@184: incorporated into someone's C program in a few minutes with trivial licensing.
Chris@184: 
Chris@184: USAGE:
Chris@184: 
Chris@184:     The basic usage for 1-d complex FFT is:
Chris@184: 
Chris@184:         #include "kiss_fft.h"
Chris@184: 
Chris@184:         kiss_fft_cfg cfg = kiss_fft_alloc( nfft ,is_inverse_fft ,0,0 );
Chris@184: 
Chris@184:         while ...
Chris@184:         
Chris@184:             ... // put kth sample in cx_in[k].r and cx_in[k].i
Chris@184:             
Chris@184:             kiss_fft( cfg , cx_in , cx_out );
Chris@184:             
Chris@184:             ... // transformed. DC is in cx_out[0].r and cx_out[0].i 
Chris@184:             
Chris@184:         free(cfg);
Chris@184: 
Chris@184:     Note: frequency-domain data is stored from dc up to 2pi.
Chris@184:     so cx_out[0] is the dc bin of the FFT
Chris@184:     and cx_out[nfft/2] is the Nyquist bin (if exists)
Chris@184: 
Chris@184:     Declarations are in "kiss_fft.h", along with a brief description of the 
Chris@184: functions you'll need to use. 
Chris@184: 
Chris@184: Code definitions for 1d complex FFTs are in kiss_fft.c.
Chris@184: 
Chris@184: You can do other cool stuff with the extras you'll find in tools/
Chris@184: 
Chris@184:     * multi-dimensional FFTs 
Chris@184:     * real-optimized FFTs  (returns the positive half-spectrum: (nfft/2+1) complex frequency bins)
Chris@184:     * fast convolution FIR filtering (not available for fixed point)
Chris@184:     * spectrum image creation
Chris@184: 
Chris@184: The core fft and most tools/ code can be compiled to use float, double,
Chris@184:  Q15 short or Q31 samples. The default is float.
Chris@184: 
Chris@184: 
Chris@184: BACKGROUND:
Chris@184: 
Chris@184:     I started coding this because I couldn't find a fixed point FFT that didn't 
Chris@184: use assembly code.  I started with floating point numbers so I could get the 
Chris@184: theory straight before working on fixed point issues.  In the end, I had a 
Chris@184: little bit of code that could be recompiled easily to do ffts with short, float
Chris@184: or double (other types should be easy too).  
Chris@184: 
Chris@184:     Once I got my FFT working, I was curious about the speed compared to
Chris@184: a well respected and highly optimized fft library.  I don't want to criticize 
Chris@184: this great library, so let's call it FFT_BRANDX.
Chris@184: During this process, I learned:
Chris@184: 
Chris@184:     1. FFT_BRANDX has more than 100K lines of code. The core of kiss_fft is about 500 lines (cpx 1-d).
Chris@184:     2. It took me an embarrassingly long time to get FFT_BRANDX working.
Chris@184:     3. A simple program using FFT_BRANDX is 522KB. A similar program using kiss_fft is 18KB (without optimizing for size).
Chris@184:     4. FFT_BRANDX is roughly twice as fast as KISS FFT in default mode.
Chris@184: 
Chris@184:     It is wonderful that free, highly optimized libraries like FFT_BRANDX exist.
Chris@184: But such libraries carry a huge burden of complexity necessary to extract every 
Chris@184: last bit of performance.
Chris@184: 
Chris@184:     Sometimes simpler is better, even if it's not better.
Chris@184: 
Chris@184: FREQUENTLY ASKED QUESTIONS:
Chris@184: 	Q: Can I use kissfft in a project with a ___ license?
Chris@184: 	A: Yes.  See LICENSE below.
Chris@184: 
Chris@184: 	Q: Why don't I get the output I expect?
Chris@184: 	A: The two most common causes of this are 
Chris@184: 		1) scaling : is there a constant multiplier between what you got and what you want?
Chris@184: 		2) mixed build environment -- all code must be compiled with same preprocessor 
Chris@184: 		definitions for FIXED_POINT and kiss_fft_scalar
Chris@184: 
Chris@184: 	Q: Will you write/debug my code for me?
Chris@184: 	A: Probably not unless you pay me.  I am happy to answer pointed and topical questions, but 
Chris@184: 	I may refer you to a book, a forum, or some other resource.
Chris@184: 
Chris@184: 
Chris@184: PERFORMANCE:
Chris@184:     (on Athlon XP 2100+, with gcc 2.96, float data type)
Chris@184: 
Chris@184:     Kiss performed 10000 1024-pt cpx ffts in .63 s of cpu time.
Chris@184:     For comparison, it took md5sum twice as long to process the same amount of data.
Chris@184: 
Chris@184:     Transforming 5 minutes of CD quality audio takes less than a second (nfft=1024). 
Chris@184: 
Chris@184: DO NOT:
Chris@184:     ... use Kiss if you need the Fastest Fourier Transform in the World
Chris@184:     ... ask me to add features that will bloat the code
Chris@184: 
Chris@184: UNDER THE HOOD:
Chris@184: 
Chris@184:     Kiss FFT uses a time decimation, mixed-radix, out-of-place FFT. If you give it an input buffer  
Chris@184:     and output buffer that are the same, a temporary buffer will be created to hold the data.
Chris@184: 
Chris@184:     No static data is used.  The core routines of kiss_fft are thread-safe (but not all of the tools directory).
Chris@184: 
Chris@184:     No scaling is done for the floating point version (for speed).  
Chris@184:     Scaling is done both ways for the fixed-point version (for overflow prevention).
Chris@184: 
Chris@184:     Optimized butterflies are used for factors 2,3,4, and 5. 
Chris@184: 
Chris@184:     The real (i.e. not complex) optimization code only works for even length ffts.  It does two half-length
Chris@184:     FFTs in parallel (packed into real&imag), and then combines them via twiddling.  The result is 
Chris@184:     nfft/2+1 complex frequency bins from DC to Nyquist.  If you don't know what this means, search the web.
Chris@184: 
Chris@184:     The fast convolution filtering uses the overlap-scrap method, slightly 
Chris@184:     modified to put the scrap at the tail.
Chris@184: 
Chris@184: LICENSE:
Chris@184:     Revised BSD License, see COPYING for verbiage. 
Chris@184:     Basically, "free to use&change, give credit where due, no guarantees"
Chris@184:     Note this license is compatible with GPL at one end of the spectrum and closed, commercial software at 
Chris@184:     the other end.  See http://www.fsf.org/licensing/licenses
Chris@184: 
Chris@184:     A commercial license is available which removes the requirement for attribution.  Contact me for details.
Chris@184: 
Chris@184:   
Chris@184: TODO:
Chris@184:     *) Add real optimization for odd length FFTs 
Chris@184:     *) Document/revisit the input/output fft scaling
Chris@184:     *) Make doc describing the overlap (tail) scrap fast convolution filtering in kiss_fastfir.c
Chris@184:     *) Test all the ./tools/ code with fixed point (kiss_fastfir.c doesn't work, maybe others)
Chris@184: 
Chris@184: AUTHOR:
Chris@184:     Mark Borgerding
Chris@184:     Mark@Borgerding.net