For today you should:
1) Read Chapter 6 (DCT)
2) Work on exercises.
Today:
1) DCT
For next time:
1) Read about the FFT in Chapter 9 of Think Complexity.
2) Work on exercises.
3) Come with case study ideas.
We'll do a diagnostic next time.
1) Synthesis
2) Synthesis as matrix multiplication
3) Analysis as matrix inversion
4) DCT
Use of the DCT: compression.
Exercise: Test the algorithmic complexity of analyze1, analyze2, and scipy.fftpack.dct
See Chapter 3 of Think Complexity.
Exercise: Use DCT to compress a WAV file.
1) Break wave into segments.
2) Compute DCT of each segment.
3) Set components below a threshold to 0.
4) Store the resulting sparse array efficiently.
5) Retrieve the sparse array and reassemble the wave.
6) Play the original and compressed versions back to back and see if you can hear the difference.
What's the most compression you can get before the quality degrades?