==============================================================================
FFTReal
Version 2.00, 2005/10/18
Fourier transformation (FFT, IFFT) library specialised for real data
Portable ISO C++
(c) Laurent de Soras <laurent.de.soras@club-internet.fr>
Object Pascal port (c) Frederic Vanmol <frederic@fruityloops.com>
==============================================================================
1. Legal
--------
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
Check the file license.txt to get full information about the license.
2. Content
----------
FFTReal is a library to compute Discrete Fourier Transforms (DFT) with the
FFT algorithm (Fast Fourier Transform) on arrays of real numbers. It can
also compute the inverse transform.
You should find in this package a lot of files ; some of them are of interest:
- readme.txt: you are reading it
- FFTReal.h: FFT, length fixed at run-time
- FFTRealFixLen.h: FFT, length fixed at compile-time
- FFTReal.pas: Pascal implementation (working but not up-to-date)
- stopwatch directory
3. Using FFTReal
----------------
Important - if you were using older versions of FFTReal (up to 1.03), some
things have changed. FFTReal is now a template. Therefore use FFTReal<float>
or FFTReal<double> in your code depending on the application datatype. The
flt_t typedef has been removed.
You have two ways to use FFTReal. In the first way, the FFT has its length
fixed at run-time, when the object is instanciated. It means that you have
not to know the length when you write the code. This is the usual way of
proceeding.
3.1 FFTReal - Length fixed at run-time
--------------------------------------
Just instanciate one time a FFTReal object. Specify the data type you want
as template parameter (only floating point: float, double, long double or
custom type). The constructor precompute a lot of things, so it may be a bit
long. The parameter is the number of points used for the next FFTs. It must
be a power of 2:
#include "FFTReal.h"
...
long len = 1024;
...
FFTReal <float> fft_object (len); // 1024-point FFT object constructed.
Then you can use this object to compute as many FFTs and IFFTs as you want.
They will be computed very quickly because a lot of work has been done in the
object construction.
float x [1024];
float f [1024];
...
fft_object.do_fft (f, x); // x (real) --FFT---> f (complex)
...
fft_object.do_ifft (f, x); // f (complex) --IFFT--> x (real)
fft_object.rescale (x); // Post-scaling should be done after FFT+IFFT
...
x [] and f [] are floating point number arrays. x [] is the real number
sequence which we want to compute the FFT. f [] is the result, in the
"frequency" domain. f has the same number of elements as x [], but f []
elements are complex numbers. The routine uses some FFT properties to
optimize memory and to reduce calculations: the transformaton of a real
number sequence is a conjugate complex number sequence: F [k] = F [-k]*.
3.2 FFTRealFixLen - Length fixed at compile-time
------------------------------------------------
This class is significantly faster than the previous one, giving a speed
gain between 50 and 100 %. The template parameter is the base-2 logarithm of
the FFT length. The datatype is float; it can be changed by modifying the
DataType typedef in FFTRealFixLenParam.h. As FFTReal class, it supports
only floating-point types or equivalent.
To instanciate the object, just proceed as below:
#include "FFTRealFixLen.h"
...
FFTRealFixLen <10> fft_object; // 1024-point (2^10) FFT object constructed.
Use is similar as the one of FFTReal.
3.3 Data organisation
---------------------
Mathematically speaking, the formulas below show what does FFTReal:
do_fft() : f(k) = sum (p = 0, N-1, x(p) * exp (+j*2*pi*k*p/N))
do_ifft(): x(k) = sum (p = 0, N-1, f(p) * exp (-j*2*pi*k*p/N))
Where j is the square root of -1. The formulas differ only by the sign of
the exponential. When the sign is positive, the transform is called positive.
Common formulas for Fourier transform are negative for the direct tranform and
positive for the inverse one.
However in these formulas, f is an array of complex numbers and doesn't
correspound exactly to the f[] array taken as function parameter. The
following table shows how the f[] sequence is mapped onto the usable FFT
coefficients (called bins):
FFTReal output | Positive FFT equiv. | Negative FFT equiv.
---------------+-----------------------+-----------------------
f [0] | Real (bin 0) | Real (bin 0)
f [...] | Real (bin ...) | Real (bin ...)
f [length/2] | Real (bin length/2) | Real (bin length/2)
f [length/2+1] | Imag (bin 1) | -Imag (bin 1)
f [...] | Imag (bin ...) | -Imag (bin ...)
f [length-1] | Imag (bin length/2-1) | -Imag (bin length/2-1)
And FFT bins are distributed in f [] as above:
| | Positive FFT | Negative FFT
Bin | Real part | imaginary part | imaginary part
------------+----------------+-----------------+---------------
0 | f [0] | 0 | 0
1 | f [1] | f [length/2+1] | -f [length/2+1]
... | f [...], | f [...] | -f [...]
length/2-1 | f [length/2-1] | f [length-1] | -f [length-1]
length/2 | f [length/2] | 0 | 0
length/2+1 | f [length/2-1] | -f [length-1] | f [length-1]
... | f [...] | -f [...] | f [...]
length-1 | f [1] | -f [length/2+1] | f [length/2+1]
f [] coefficients have the same layout for FFT and IFFT functions. You may
notice that scaling must be done if you want to retrieve x after FFT and IFFT.
Actually, IFFT (FFT (x)) = x * length(x). This is a not a problem because
most of the applications don't care about absolute values. Thus, the operation
requires less calculation. If you want to use the FFT and IFFT to transform a
signal, you have to apply post- (or pre-) processing yourself. Multiplying
or dividing floating point numbers by a power of 2 doesn't generate extra
computation noise.
4. Compilation and testing
--------------------------
Drop the following files into your project or makefile:
Array.*
def.h
DynArray.*
FFTReal*.cpp
FFTReal*.h*
OscSinCos.*
Other files are for testing purpose only, do not include them if you just need
to use the library ; they are not needed to use FFTReal in your own programs.
FFTReal may be compiled in two versions: release and debug. Debug version
has checks that could slow down the code. Define NDEBUG to set the Release
mode. For example, the command line to compile the test bench on GCC would
look like:
Debug mode:
g++ -Wall -o fftreal_debug.exe *.cpp stopwatch/*.cpp
Release mode:
g++ -Wall -o fftreal_release.exe -DNDEBUG -O3 *.cpp stopwatch/*.cpp
It may be tricky to compile the test bench because the speed tests use the
stopwatch sub-library, which is not that cross-platform. If you encounter
any problem that you cannot easily fix whil
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multimedia_qt多媒体_QT视频播放_qt播放器_qt播放器_qt播放视频_ (341个子文件)
engine.cpp 26KB
main.cpp 20KB
mainwidget.cpp 15KB
waveform.cpp 15KB
audioinput.cpp 13KB
audiorecorder.cpp 13KB
audiooutput.cpp 12KB
audiodevices.cpp 11KB
spectrumanalyser.cpp 9KB
spectrograph.cpp 8KB
frequencymonitor.cpp 8KB
ClockCycleCounter.cpp 7KB
test.cpp 7KB
settingsdialog.cpp 6KB
main.cpp 6KB
audiodecoder.cpp 6KB
wavefilewriter.cpp 6KB
tonegeneratordialog.cpp 6KB
main.cpp 6KB
wavfile.cpp 5KB
radio.cpp 5KB
qmlapplicationviewer.cpp 5KB
utils.cpp 5KB
progressbar.cpp 5KB
levelmeter.cpp 5KB
main.cpp 4KB
tonegenerator.cpp 4KB
performancemonitor.cpp 3KB
frequencyspectrum.cpp 3KB
filereader.cpp 3KB
frequencymonitordeclarative.cpp 3KB
StopWatch.cpp 3KB
performancemonitordeclarative.cpp 3KB
qaudiolevel.cpp 3KB
qmlcamera.cpp 3KB
main.cpp 2KB
main.cpp 2KB
main.cpp 2KB
main.cpp 2KB
main.cpp 2KB
main.cpp 2KB
main.cpp 2KB
fftreal_wrapper.cpp 2KB
fftrealu.def 296B
fftrealu.def 212B
testapp.dpr 4KB
FFTReal.dsp 6KB
FFTReal.dsw 537B
pagecurl.fsh 7KB
toon.fsh 5KB
sobeledgedetection1.fsh 4KB
isolate.fsh 4KB
sharpen.fsh 4KB
ripple.fsh 4KB
glow.fsh 4KB
emboss.fsh 4KB
billboard.fsh 4KB
shockwave.fsh 3KB
gaussianblur_v.fsh 3KB
gaussianblur_h.fsh 3KB
magnify.fsh 3KB
tiltshift.fsh 3KB
warhol.fsh 3KB
posterize.fsh 3KB
pixelate.fsh 3KB
vignette.fsh 3KB
blackandwhite.fsh 3KB
wobble.fsh 3KB
sepia.fsh 3KB
selectionpanel.fsh 2KB
engine.h 9KB
waveform.h 6KB
rgbframehelper.h 6KB
spectrumanalyser.h 6KB
spectrum.h 5KB
mainwidget.h 5KB
frequencymonitor.h 4KB
FFTReal.h 4KB
utils.h 4KB
trace.h 4KB
audioinput.h 4KB
trace.h 4KB
audiooutput.h 4KB
levelmeter.h 4KB
FFTRealFixLen.h 3KB
spectrograph.h 3KB
settingsdialog.h 3KB
frequencyspectrum.h 3KB
TestAccuracy.h 3KB
qmlapplicationviewer.h 3KB
performancemonitor.h 3KB
ClockCycleCounter.h 3KB
audiodecoder.h 3KB
FFTRealPassInverse.h 3KB
tonegeneratordialog.h 3KB
audiorecorder.h 3KB
audiodevices.h 3KB
progressbar.h 3KB
performancemonitordeclarative.h 3KB
radio.h 3KB
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