jeff wang kay-won chang march 18, 2011. demo harmonic product spectrum (hps) pitch detection: obtain...
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Harmonic Product Spectrum (HPS)
• pitch detection: obtain fundamental frequency from FFT
Fast Fourier Transform (FFT)
• convert from discrete-time domain to discrete-frequency domain
• significantly faster than DFT
• radix-2 decimation in frequency algorithm provided by Johnny
• Idea: We can split a N-DFT into two N/2-DFT's, which lowers complexity. We can continuously split the N-DFT in halves until we reach the trivial 2-DFT.
• Butterfly diagram illustrates concept of continuously halving a 8-DFT into four 2-DFT's; reduce complexity from N^2 to NlogN
(Source: http://www.xionlogic.com/products/os/fft/r2dif/fft_r2dif_sfg_8pt.jpg)
• Output in bit-reversed order
• For example: Index 1
1) Write in binary (8 = 3 bits) 001
2) Flip order 100
3) Convert to decimal 4
4) X(4) is in index 1
• When a resonant system (e.g. blowpipe, plucked string) is excited, harmonics may be produced along with the fundamental tone
• A harmonic is any integer multiple of the fundamental frequency
• The human auditory system responds most sensitively to the fundamental frequency
● Implementing a Fourier Transform using the interrupt function
Fill Input Fill Input Fill Input…..FT FT FT
Fill Input using Interrupt FT Fill Input FT
● Frequency resolution● Noticeable delay between playing a guitar note and seeing the note on computer display