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#X text 504 163 real part;
#X text 489 398 imaginary part;
#X obj 80 545 loadbang;
#X text 94 166 <- frequency;
#X text 133 182 (as multiple;
#X text 135 198 of SR/64 \, the;
#X text 133 215 fundamental);
#X text 170 345 of a cycle;
#X text 431 638 updated for PD version 0.39;
#X obj 89 590 s \$0-snap;
#X obj 69 286 r \$0-snap;
#X text 127 315 <- phase in;
#X text 161 331 hundredths;
#X text 113 264 <- frequency \, Hz.;
#X text 87 415 given the real and imaginary part;
#X text 88 431 of a complex-valued signal. Here;
#X text 87 447 the imaginary part is zero (the;
#X text 86 400 fft~ computes the Fourier transform \,;
#X text 186 541 real and imaginary;
#X text 186 557 outputs are graphed;
#X text 185 574 separately.;
#X text 86 464 input is real-valued). The output;
#X text 85 482 is a (real \, imaginary) pair for each;
#X text 86 500 frequency from 0 to 63 (in units of;
#X text 87 520 SR/64).;
#X text 145 -36 The "fft~" object has separate inlets for the real
and imaginary parts of a complex-valued signal and outputs its Fourier
transform \, again using separate outlets for the real and imaginary
part. The transform is done on one block of samples (here the block
size is 64 \, Pd's default.) The outputs give the complex amplitudes
of the harmonics of the input signal \, from DC up. The harmonics are
tuned to the fundamental frequency of the analysis \, 1/64th of the
sample rate. If the frequency (in harmonics) is an integer \, the result
is two harmonics symmetric about the Nyquist frequency. Fractional
frequencies spill across harmonics. Changing the initial phase rotates
energy from real to imaginary and back.;
#X text 26 -24 ANALYSIS;
#X text 27 -42 FOURIER;
#X msg 38 79 0;
#X msg 38 100 10;
#X msg 38 121 10.5;
#X text 159 283 bang-on-snapshot;
#X text 157 297 from below;
#X text 100 363 sync phase with snapshots;
#X obj 37 423 fft~;
#X msg 274 614 \; pd dsp 1;
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