Changeset 3957 for trunk/MagicSoft/Mars/mtools

Timestamp:

05/04/04 15:27:25 (21 years ago)

Author:

tbretz

Message:

*** empty log message ***

File:

• trunk/MagicSoft/Mars/mtools/MFFT.cc (modified) (1 diff)

trunk/MagicSoft/Mars/mtools/MFFT.cc

@@ -63 +63 @@
 //     * If the PSD does NOT CONVERGE to 0 at the maximum bin,              //
 //       you HAVE TO sample your data finer!                                //
-//                                                                          //
+//
+// Fourier-Transformation:
+// =======================
+
+// (taken from http://www.parasitaere-kapazitaeten.net/Pd/ft.htm)
+//
+//  The Fourier-Transformation is a mathematical function that breaks
+// down a signal (like sound) into its frequency-spectrum as a set of
+// sinusoidal components, converting it from the Time Domain to the
+// Frequency Domain.
+// 
+//  In the Time Domain the signal x[ ] consists of N samples, labeled
+// from 0 to N-1. In the Frequency Domain the RFFT produces two signals
+// (signalvectors), treated as complex numbers representing the Real Part:
+// Re X[ ] and the Imaginary Part: Im X[ ]. They are seen as the Cosine-
+// und Sine-Components of the base frequencies. Each of these two signals
+// contains one more sample than the half of the original signal: N/2 + 1
+// samples. (this results from the fact, that the sine-components of the
+// first frequency (0) and the last (nyquist, N/2) are always 0). With the
+// complex Fourier-Transformation N complexe values are transformed to N
+// new complex values. For both it applies to: the Frequency Domain
+// contains exactly the same information as the Time-Domain.
+// 
+//  A Real FFT over 64 samples produces values for 33 cosine- and 33
+// sine-wave-amplitudes with the frequencies 0, 1, 2, 3, ..., 30, 31, 32.
+// The first value (frequency 0) is the DC (direct current), the other
+// values have to be seen in practice as factors of a
+// fundamental-frequency which can be calculated by dividing samplerate by
+// windowsize. The highest frequency is the nyquist-frequency
+// (samplerate/2).
+// 
 //////////////////////////////////////////////////////////////////////////////