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