1. Jeff Wang Kay-Won Chang March 18, 2011

2. DEMO

4. 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 Two Key Concepts

5. 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.

6. 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)http://www.xionlogic.com/products/os/fft/r2dif/fft_r2dif_sfg_8pt.jpg

7. 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

8. 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

11. ● 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

12. ● Frequency resolution ● Noticeable delay between playing a guitar note and seeing the note on computer display

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