EE 524 #18: Computation of the Discrete Fourier
Transform
October 30, 2013
Contents
Introduction 1
Properties of the twiddle factor
2
Buttery owgraph and notation 2
The FFT Idea Using a Matrix Approach 3
Decimation-in-time FFT: Algebraic Derivation 5
Non-
EE 524 #16: The Discrete Fourier Transform
October 25, 2013
Contents
Denition 1
Sampling the DTFT 3
Length-N sequence x [n]
4
Innite-length aperiodic sequence x [n]
4
Zero-padding 7
Relationship between CTFT, DTFT, and DFT 8
Periodic (Circular) Convolutio
EE 524 #17: Fourier Analysis of Signals Using the
DFT
October 30, 2013
Contents
Introduction 1
Filtered CT signal 2
Windowing 3
Block of L signal samples
3
Windowed block of L signal samples.
Windows
3
4
Zero-padding 12
Potential problems and solutions 13
EE 524: Review II
Aleksandar Dogandi
November 1, 2013
Topics:
discrete-time Fourier transform (DTFT)
properties,
application to correlation, matched-lter receiver;
discrete Fourier transform (DFT) and discrete-time Fourier series (DTFS)
properties,
EE 524, Fall 2013
Homework #6
due Oct. 23/25 (on/o campus)
(a)
(b)
Figure 1: (a) Block diagram of a demodulation system and (b) message signal.
1. (9 points) Problem 56 in 3 of the textbook.
2. (7 points) Parts (a) and (d) of Problem 27 in 4 of the textbo
EE 524, Fall 2013
Homework #7 due Oct. 30/Nov. 1 (on/o campus)
1. (7 points) Problem 9 in 7 of the textbook. Consider only the case where N % +1.
2. (6 points) Problem 11 in 7 of the textbook.
3. Consider the matrix T of eigenvectors of N
2
1
1
1
61
q
q2
EE 524, Fall 2013
Homework #5
due Oct. 16/18 (on/o campus)
1. (9 points) We are given the following three clues about a discrete-time (DT) linear
time-invariant (LTI) system with impulse response h[n] and frequency response H f (! ):
(i) the system is cau
EE 524: Digital Signal Processing
Aleksandar Dogandi
November 8, 2013
Exam II
Name:
1. Exam duration: 1:5 h.
2. Open book, open notes, no calculators.
3. Please do preliminary calculations on your own scratch paper (do not hand in).
4. Show enough neat wo
E E 524: Review I
September 25, 2013
Topics:
Linear systems as matrices,
Matrix decompositions,
Circulant systems,
Frequency response,
Z transform,
Properties of the Z transform.
T
1. (a) For an N N matrix A, if u1 = u1 [1]; u1 [2]; : : : ; u1 [N ]