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#X text 591 218 real part;
#X text 546 451 imaginary part;
#X obj 97 592 loadbang;
#X text 159 395 of a cycle;
#X text 448 707 updated for PD version 0.39;
#X obj 103 648 s \$0-snap;
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#X text 159 381 hundredths;
#X text 109 462 given the real and imaginary part;
#X text 110 478 of a complex-valued signal. Here;
#X text 109 494 the imaginary part is zero (the;
#X text 108 447 fft~ computes the Fourier transform \,;
#X text 253 666 real and imaginary;
#X text 253 682 outputs are graphed;
#X text 252 699 separately.;
#X text 108 511 input is real-valued). The output;
#X text 107 529 is a (real \, imaginary) pair for each;
#X text 108 547 frequency from 0 to 63 (in units of;
#X text 109 567 SR/64).;
#X text 163 24 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., f 67;
#X text 49 66 ANALYSIS;
#X text 50 48 FOURIER;
#X msg 60 118 0;
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#X msg 75 166 10.5;
#X text 175 331 bang-on-snapshot;
#X text 173 345 from below;
#X text 116 415 sync phase with snapshots;
#X obj 59 470 fft~;
#X msg 182 622 \; pd dsp 1;
#X text 103 207 <= frequency (as multiple of SR/64 \, the fundamental)
, f 26;
#X text 139 365 <= phase in;
#X text 127 307 <= frequency \, Hz.;
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