rdoc/fft.rdoc in rb-gsl-1.16.0.4 vs rdoc/fft.rdoc in rb-gsl-1.16.0.5

- old
+ new

@@ -1,26 +1,26 @@ # # = Fast Fourier Transforms # Contents: -# 1. {Mathematical Definitions}[link:fft_rdoc.html#label-Mathematical+Definitions] -# 1. {Complex data FFTs}[link:fft_rdoc.html#label-Complex+data+FFTs] -# 1. {Overview of complex data FFTs}[link:fft_rdoc.html#label-Overview+of+complex+data+FFTs] -# 1. {Radix-2 FFT routines for complex data}[link:fft_rdoc.html#label-Radix-2+FFT+routines+for+complex+data] -# 1. {Example of the complex Radix-2 FFT}[link:fft_rdoc.html#label-Example+of+complex+Radix-2+FFT] -# 1. {Mixed-radix FFT routines for complex data}[link:fft_rdoc.html#label-Mixed-radix+FFT+routines+for+complex+data] -# 1. {GSL::FFT::ComplexWavetable class}[link:fft_rdoc.html#label-ComplexWavetable+class] -# 1. {GSL::FFT::ComplexWorkspace class}[link:fft_rdoc.html#label-ComplexWorkspace+class] -# 1. {Methods to compute the transform}[link:fft_rdoc.html#label-Methods+to+compute+transform] -# 1. {Example of the mixed-radix FFT}[link:fft_rdoc.html#label-Example+to+use+the+mixed-radix+FFT+algorithm] -# 1. {Real data FFTs}[link:fft_rdoc.html#label-Real+data+FFTs] -# 1. {Overview of real data FFTs}[link:fft_rdoc.html#label-Overview+of+real+data+FFTs] -# 1. {Radix-2 FFT routines for real data}[link:fft_rdoc.html#label-Radix-2+FFT+routines+for+real+data] -# 1. {Mixed-radix FFT routines for real data}[link:fft_rdoc.html#label-Mixed-radix+FFT+routines+for+real+data] -# 1. {Data storage scheme}[link:fft_rdoc.html#label-Data+storage+scheme] -# 1. {Wavetable and Workspace classes}[link:fft_rdoc.html#label-Wavetable+and+Workspace+classes] -# 1. {Methods for real FFTs}[link:fft_rdoc.html#label-Methods+for+mixed-radix+real+FFTs] -# 1. {Examples}[link:fft_rdoc.html#label-Examples] +# 1. {Mathematical Definitions}[link:rdoc/fft_rdoc.html#label-Mathematical+Definitions] +# 1. {Complex data FFTs}[link:rdoc/fft_rdoc.html#label-Complex+data+FFTs] +# 1. {Overview of complex data FFTs}[link:rdoc/fft_rdoc.html#label-Overview+of+complex+data+FFTs] +# 1. {Radix-2 FFT routines for complex data}[link:rdoc/fft_rdoc.html#label-Radix-2+FFT+routines+for+complex+data] +# 1. {Example of the complex Radix-2 FFT}[link:rdoc/fft_rdoc.html#label-Example+of+complex+Radix-2+FFT] +# 1. {Mixed-radix FFT routines for complex data}[link:rdoc/fft_rdoc.html#label-Mixed-radix+FFT+routines+for+complex+data] +# 1. {GSL::FFT::ComplexWavetable class}[link:rdoc/fft_rdoc.html#label-ComplexWavetable+class] +# 1. {GSL::FFT::ComplexWorkspace class}[link:rdoc/fft_rdoc.html#label-ComplexWorkspace+class] +# 1. {Methods to compute the transform}[link:rdoc/fft_rdoc.html#label-Methods+to+compute+transform] +# 1. {Example of the mixed-radix FFT}[link:rdoc/fft_rdoc.html#label-Example+to+use+the+mixed-radix+FFT+algorithm] +# 1. {Real data FFTs}[link:rdoc/fft_rdoc.html#label-Real+data+FFTs] +# 1. {Overview of real data FFTs}[link:rdoc/fft_rdoc.html#label-Overview+of+real+data+FFTs] +# 1. {Radix-2 FFT routines for real data}[link:rdoc/fft_rdoc.html#label-Radix-2+FFT+routines+for+real+data] +# 1. {Mixed-radix FFT routines for real data}[link:rdoc/fft_rdoc.html#label-Mixed-radix+FFT+routines+for+real+data] +# 1. {Data storage scheme}[link:rdoc/fft_rdoc.html#label-Data+storage+scheme] +# 1. {Wavetable and Workspace classes}[link:rdoc/fft_rdoc.html#label-Wavetable+and+Workspace+classes] +# 1. {Methods for real FFTs}[link:rdoc/fft_rdoc.html#label-Methods+for+mixed-radix+real+FFTs] +# 1. {Examples}[link:rdoc/fft_rdoc.html#label-Examples] # # == Mathematical Definitions # Fast Fourier Transforms are efficient algorithms for calculating the discrete # fourier transform (DFT), # @@ -57,11 +57,11 @@ # # # == Complex data FFTs # === Overview of complex data FFTs # The complex data FFT routines are provided as instance methods of -# {GSL::Vector::Complex}[link:vector_complex_rdoc.html]. +# {GSL::Vector::Complex}[link:rdoc/vector_complex_rdoc.html]. # # Here is a table which shows the layout of the array data, and the correspondence # between the time-domain complex data z, and the frequency-domain complex data x. # # index z x = FFT(z) @@ -80,11 +80,11 @@ # # When N is even the location N/2 contains the most positive and negative # frequencies +1/(2 Delta), -1/(2 Delta) which are equivalent. If N is odd then # general structure of the table above still applies, but N/2 does not appear. # -# {GSL::Vector::Complex}[link:vector_complex_rdoc.html] provides four methods for +# {GSL::Vector::Complex}[link:rdoc/vector_complex_rdoc.html] provides four methods for # shifting the frequency domain data between <b>FFT order</b>, shown in the table # above, and <b>natural order</b>, which has the most negative freqeuncy component # first, the zero frequency component in the middle, and the most positive # frequency component last. # @@ -261,22 +261,22 @@ # # == Real data FFTs # === Overview of real data FFTs # # The functions for real data FFTs are provided as instance methods of -# {GSL::Vector}[link:vector_rdoc.html]. While they are similar to those for +# {GSL::Vector}[link:rdoc/vector_rdoc.html]. While they are similar to those for # complex data, there is an important difference in the data storage layout # between forward and inverse transforms. The Fourier transform of a real # sequence is not real. It is a complex sequence with a special symmetry. A # sequence with this symmetry is called <tt>conjugate-complex</tt> or # <tt>half-complex</tt> and requires only as much storage as the original real # sequence instead of twice as much. # # Forward transforms of real sequences produce half complex sequences of the same # length. Backward and inverse transforms of half complex sequences produce real # sequences of the same length. In both cases, the input and output sequences -# are instances of {GSL::Vector}[link:vector_rdoc.html]. +# are instances of {GSL::Vector}[link:rdoc/vector_rdoc.html]. # # The precise storage arrangements of half complex seqeunces depend on the # algorithm, and are different for radix-2 and mixed-radix routines. The radix-2 # functions operate in-place, which constrains the locations where each element # can be stored. The restriction forces real and imaginary parts to be stored far @@ -286,11 +286,11 @@ # complex sequence produces by a radix-2 forward transform <b>cannot</b> be # recovered by a mixed-radix inverse transform (and vice versa). # # === Radix-2 FFT routines for real data # The routines for readix-2 real FFTs are provided as instance methods of -# {GSL::Vector}[link:vector_rdoc.html]. +# {GSL::Vector}[link:rdoc/vector_rdoc.html]. # # <b>The FFT methods described below return FFTed data, and the input vector is # not changed. Use methods with '!' as <tt>radix2_tranform!</tt> for in-place # transform.</b> # @@ -524,12 +524,12 @@ # #data2 = ffted.halfcomplex_inverse() # data2 = ffted.ifft # # graph(nil, data, data2, "-T X -C -g 3 -L 'Real-halfcomplex' -x 0 #{data.size}") # -# {prev}[link:eigen_rdoc.html] -# {next}[link:wavelet_rdoc.html] +# {prev}[link:rdoc/eigen_rdoc.html] +# {next}[link:rdoc/wavelet_rdoc.html] # -# {Reference index}[link:ref_rdoc.html] +# {Reference index}[link:rdoc/ref_rdoc.html] # {top}[link:index.html] # #