Jeff WangKay-Won ChangMarch 18, 2011

DEMO

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

●     Connecting microphone directly to DSK to offer “real-time” guitar tuning