Spectral Analysis
Decomposing audio with algorithms
Spring 2019 - Audio Tech Talk Series
February 5, 2019
Frequency
Time Domain -> Frequency domain
Fourier Transform
But first we have to talk about correlation...
440 Hz sine wave
Corrleation between 440 Hz and 200 Hz
Corrleation between 440 Hz and 440 Hz
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This is (almost) the Fourier Transform
How about a piano note?
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One more question?
How can we use this?
Frequency Analysis & Correction
Pitch Shifting
Pitch shifting our piano example...
Original
Shifted
Time Stretching
Fast Fourier Transform
| Samples | Length | N^2 | N/2*log2(N) | ratio |
|---|---|---|---|---|
| 64 | 0.001 | 4,096 | 192 | 21.3 |
| 256 | 0.006 | 65,536 | 1,024 | 64.0 |
| 1,024 | 0.023 | 1,048,576 | 5,120 | 204.8 |
| 4,096 | 0.093 | 16,777,216 | 24,576 | 682.7 |
| 16,384 | 0.372 | 268,435,456 | 114,688 | 2,340.6 |
| 65,536 | 1.486 | 4,294,967,296 | 524,288 | 8,192.0 |
| 131,072 | 2.972 | 17,179,869,184 | 1,114,112 | 15,420.2 |