Digital Signal Processing / Processamento Digital de Sinais

Correspondence between the materials studied in this course and the Bibliography

 

The following table lists the parts of the books from the Bibliography that correspond to each of the topics studied in our course. The book by Oppenheim and Schafer (2nd. edition) is denoted by "O", and the book by Kay is denoted by "K".

Topic Book chapters/sections
Discrete-time signals and systems. O – 1, 2.0-2.5
Discrete-time Fourier transform (DTFT). O – 2.6.1, 2.7-2.9, 5.2
Short-time Fourier transform and spectrogram. O – 10.2.1, 10.3.1; examples: 10.5 (note 1)
Z transform. O – 3
Sampling. O – 4.0-4.4.1, 4.8.1, 4.8.4
Discrete-time Fourier series (DTFS) and discrete Fourier transform (DFT). O – 8.0-8.2, 8.5-8.7 (note 2)
Structures of discrete-time filters. O – 6.0-6.3.2, 6.4
Design of discrete-time filters. O – 7.0-7.2.1
Basic concepts of random signals. O – A.1-A.4 (note 3)
Estimation - basic concepts. MVU estimators. K – 1, 2
Cramιr-Rao lower bound K – 3.1-3.7
Mximum-likelihood estimation K – 7.1-7.6, 7.8 (note 4)
Least squares K – 8.1-8.5
Bayesian estimation K – 10.1-10.6, 11.1-11.5

Notes

  1. Section 10.3.1 of the book studies the time-dependent Fourier transform (TDFT), which is closely related to the short-time Fourier transform (STFT). You obtain the STFT if you change, in Eq. (10.18) of the book, x[n+m]w[m] to  x[m]w[m-n]. It is easy to see that the magnitudes of the TDFT and the STFT are the same (the two transforms differ only in the phase). The spectrogram, which is the squared magnitude of the STFT, is, therefore, also the squared magnitude of the TDFT. Note that, in this section, the book uses 'lambda' as frequency variable, instead of the usual 'omega'.
  2. We also studied Parseval's theorem (or Parseval's relation) for the DFT; the book doesn't cover it.
  3. Section 2.2 of the book goes into more detail than we did, on the processing of random signals by LTI systems and on the concept of power spectral density.
  4. The part of Section 7.8 that was studied doesn't include Theorem 7.5 and what follows it.