Lecture 12: 02/10/2012

Today’s topic was the FFT. We didn’t get all the way through it, but Prof. Rudich will finish up on Monday. We started with definitions and assumptions about the ring we work with, but as a running example we used the simple ring Z_11. The key points of the FFT are that if we convert between coefficients and the sample point representation of a polynomial, we can compute the convolution by performing a linear number of multiplications.

The bulk of the lecture dealt with which sample points should we use: the nth roots of unity. They have some really nice properties that make the FFT work in sub-quadratic time.

We’ll finish discussing the matrix of the roots and its inverse on Monday. Please try to review the lecture in Kozen and bring some good questions to lecture.

Have a great weekend!

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s