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    <p>well, A raw array of size 512 of complex numbers expressing the input wave, when processed with FFT we will replace the imaginary parts with zero (according to intended use), leaving the real parts, then pass the array to the FFT with Sample rate : 8192 Hz.</p> <p>Now we have a 512 array of FFTed real values, each value is an irrational number, every irrational number express several useful values.</p> <p>To get the fundamental frequency we have to divide the sample rate by the buffer size:</p> <p>8192/512 = 32;</p> <p>32 is the resolution of the FFT values means that we're getting to know the high amplitude frequencies near the numbers that are multiples of 32.</p> <p>Like if we have a wave of</p> <p>frequency : 3 48 23 128 Amplitude : 10 5 12 8 dB (ref = 1)</p> <p>after FFT we get:</p> <p>frequency : 0 32 64 128 Amplitude : 9 8 2 8</p> <p>FFT is frequency domain means it arranges according to frequency Time-domain on the other side means arranging by time we listen to music from second zero to second N.</p> <p>FFT can only listen when it arranged by Frequency from frequency 0 to frequency N.</p> <p>So it arranges frequencies in ascending order, since it didn't take all the actual samples from the audio (which are approaching infinite) like taking every nanosecond &amp; less to the FFT, luckily this doesn't happen FFT takes samples from the audio, takes a sample every (1/sample rate) second. this samples get buffered (in our case : 512), each 512 samples buffered into FFT, the output is 512 FFT values.</p> <p>Since FFT arranges frequencies, it messes with the time samples, samples now arranged according to their frequencies.</p> <p>The frequencies shown on regular base which is the fundamental frequency which is sample rate divided by buffer size, which is in our case 8192/512 = 32.</p> <p>So, frequencies power shown every 32 frequencies, the power of the nearest frequency is shown according to how much the power frequency is near to the index.</p> <p>High resolution can be achieved by using higher sample rate.</p> <p>To show frequencies we print the index in ascending corresponding to the Amplitude.</p> <p>Amplitude = 20log10(output/ref)</p> <p>Amplitudes printed next to each Index show the power of the frequency &amp; get more accurate according to the precision of the resolution.</p> <p>Conclusion, FFT produces an index of amplitudes, each amplitude expresses the power of its corresponding index (frequency).</p>
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