Books & Papers on Wavelets and Time-Frequency Analysis

Note:  If the reference can be freely downloaded, then the hyperlink is marked in boldface red.  Other hyperlinks, marked in blue, are to commercial sites.

P.S. Addison. (2005). Wavelet transforms and the ECG: a review.  Physiol. Meas., Vol. 26, R155--R199.

M. Akay. (1996). Diagnosis of Coronary Artery Disease Using Wavelet-Based Neural Networks. In A Aldroubi, M. Unser, Eds.. In Wavelets in Medicine
and Biology.
CRC Press, Boca Raton, FL, 513--526.

A. Aldroubi, M. Unser, Eds.. (1996). Wavelets in Medicine and Biology. CRC Press, Boca Raton, FL..

J.F. Alm and J.S. Walker. (2002). Time-frequency analysis of musical instruments. SIAM Review, Vol. 44, 457--476.

R.B. Ash. (1990). Information Theory. Dover, NY.

G. Assayag, H. Feichtinger, and J.F. Rodrigues, Eds. (2002). Mathematics and Music: a Diderot Mathematical Forum. Springer, NY.

Audacity software:

Avian music website:

M. Babbitt,  Set structure as a compositional determinant.  J of Music Theory, 5 (1961), 72-94.  If you have access to JSTOR then
you can download the article from here.

S.I. Baskakov. (1986). Signals and Circuits. Mir, Moscow.

T.C. Bell, J.G. Cleary, I.H. Witten. (1990). Text Compression.  Prentice-Hall, Englewood Cliffs, NJ

D. Benson. (2006). Music: A Mathematical Offering. To be published by Cambridge University Press, Cambridge, UK.

Book's website:

J.N. Bradley, C.M. Brislawn, T. Hopper. (1993). The FBI Wavelet/Scalar Quantization Standard for gray-scale fingerprint image compression. SPIE, Vol. 1961, Visual Information Processing II (1993), 293--304.

O. Bratteli and P. Jorgensen. (2002). Wavelets through a Looking Glass.  Birkhauser, Boston.

W.L. Briggs, V.E. Henson. (1995). The DFT. An Owner's Manual. SIAM, Philadelphia, PA.

E.O. Brigham. (1978). The Fast Fourier Transform. Prentice-Hall, Englewood Cliffs, NJ.

C.M. Brislawn. (1995). Fingerprints Go Digital. Notices of the Amer. Math. Soc., Vol. 42, 1278--1283.

B. Burke. (1994). The Mathematical Microscope: waves, wavelets, and beyond. In A Positron Named Priscilla, Scientific Discovery at the Frontier, 196--235, Nat. Academy Press. Edited by M. Bartusiak.

C.S. Burrus, R.H. Gopinath, H. Guo. (1998). Introduction to Wavelets and Wavelet Transforms, A Primer. Prentice-Hall, Englewood Cliffs, NJ.

Calderbank, A. R., et al. (1998). Wavelet transforms that map integers to integers.  Applied and Computational Harmonic Analysis, Vol. 5, 332--369.

P.G. Casazza. (2000). The Art of Frame Theory. Taiwanese J. of Mathematics, Vol. 4, No. 2, 129--201.

Y.-J. Chen, S. Oraintara, K. Amaratunga. (2005).  Dyadic-based factorization for regular paraunitary filter banks and M-band orthogonal wavelets with structural vanishing moments.
IEEE Transactions on Signal Processing, Vol.~53, 193--207.

X. Cheng, J.V. Hart, J.S. Walker.(2007). Time-frequency analysis of musical rhythm. Preprint.

H.A. Chipman, E.D. Kolaczyk, and R.E. McCulloch. (1997). Adaptive Bayesian wavelet shrinkage. J. American Statistical Association, Vol. 92, 1413--1421.

O. Christiansen. (2002). Time-frequency analysis and its applications in denoising. Thesis, Department of Informatics, University of Bergen.

C.K. Chui, Ed. (1992).  Wavelets: a tutorial in theory and applications. Academic Press, Boston.

C.K. Chui. (1997). Wavelets: A Mathematical Tool for Signal Analysis. SIAM, Philadelphia, PA.

E. Coen. (1999). The Art of Genes. Oxford University Press, Oxford, UK.

R. Cogan. (1984). New Images of Musical Sound.  Harvard University Press, Cambridge, MA.

Cohen, A., Daubechies, I., and Feauveau, J.-C. (1992). Biorthogonal bases of compactly supported wavelets. Commun.\ on Pure and Appl.\ Math., Vol. 45, 485--560.

R. Coifman and D. Donoho. (1995)  Translation-invariant denoising.  In Wavelets and Statistics,  A. Antoniadis, G. Oppenheim (Eds.), Springer, NY.

R.R. Coifman, M.V. Wickerhauser. (1993). Wavelets and Adapted Waveform Analysis. A Toolkit for Signal Processing and Numerical Analysis. In I. Daubechies (Ed.), Different Perspectives
on Wavelets.
AMS, Providence, RI, pp. 119--154.

R.R. Coifman, M.V. Wickerhauser. (1994). Wavelets and Adapted Waveform Analysis. In J.J. Benedetto, M.W. Frazier, (Eds.), Wavelets. Mathematics and Applications. CRC Press, Boca Raton, FL, 399--424.

R. Coifman and Y. Zeevi, Eds. (1988). Signal and Image Representation in Combined Spaces. Wavelet Analysis and Applications, Vol. 7, Academic Press, Boston, MA.

T.M. Cover, J.A. Thomas. (1991). Elements of Information Theory. Wiley, New York, NY.

Curvelet website:

I. Daubechies. (1992). Ten Lectures on Wavelets. SIAM, Philadelphia, PA.

I. Daubechies, S. Maes. (1996). A Nonlinear Squeezing of the Continuous Wavelet Transform Based on Auditory Nerve Models. In A. Aldroubi, M. Unser, (Eds.), Wavelets in Medicine and Biology. CRC Press, Boca Raton, FL, 527--546.

I. Daubechies and W. Sweldens. (1998).  Factoring Wavelet Transforms into Lifting Steps. J. Fourier Anal. Appl., Vol. 4, No. 3, 247--269. 

G.M. Davis. (1998).  A wavelet-based analysis of fractal image compression. IEEE Trans. on Image Proc., Vol. 7, 141--154.

G.M. Davis and A. Nosratinia. (1998).  Wavelet-based Image Coding: An Overview.  Applied and Computational Control, Signals and Circuits, Vol. 1, 205--269.

D. Donoho. (1993).  Nonlinear Wavelet Methods for Recovery of Signals, Densities, and Spectra from Indirect and Noisy Data   In I. Daubechies (Ed.)  Different Perspectives on Wavelets. AMS, Providence, RI, 173--205.

D.L. Donoho and E. Candes. (2005). Continuous Curvelet Transform I: Resolution of Wavefront Set.
Applied and Computational Harmonic Analysis, Vol. 19, 162-197.

D.L. Donoho and E. Candes. Continuous Curvelet Transform II: Discretization and Frames.  To appear in Applied and Computational Harmonic Analysis.

D. Donoho et al. (1995). Wavelet shrinkage: asymptopia?  J. Royal Stat.\ Soc. B, Vol. 57, 301--369.

D.L. Donoho and A.G. Flesia. (2001).  Can recent innovations in harmonic analysis `explain' key findings in natural image statistics? Network Computations in Neural Systems, Vol. 12, 371--393.     

D. Donoho and I. Johnstone. (1994).  Ideal spatial adaptation via wavelet shrinkage.  Biometrika, Vol. 81, 425--455.

D. Donoho and I. Johnstone. (1995).  Adapting to unknown smoothness via wavelet shrinkage.  American Statistical Assoc., Vol. 90, 1200--1224.

M. D\"orfler. (2002).  Gabor Analysis for a Class of Signals called Music.  Dissertation, University of Vienna.

M. Dorfler, H. Feichtinger (2004). Quilted Gabor Families I: Reduced Multi-Gabor Frames.  Appl. Comput. Harmon. Anal., Vol.~356, 2001-2023.

R.L. Fante. (1988).  Signal Analysis and Estimation.  Wiley, New York, NY.

H. Feichtinger and T. Strohmer, Eds. (1998).  Gabor Analysis and Algorithms.  Birkh\"auser, Boston, MA.

H. Feichtinger and T. Strohmer, Eds. (2002).  Advances in Gabor Analysis.  Birkh\"auser, Boston, MA.

D. Field. (1993). Scale Invariance and Self-Similar ``Wavelet'' Transforms: An Analysis of Natural Scenes and Mammalian Visual Systems.  In Wavelets, Fractals and Fourier Transforms, M. Farge, J.C.R. Hunt, J.C. Vassilicos, editors   Clarendon Press, 151--193.

D. Field. (1994). What is the Goal of Sensory Coding? Neural Computations, Vol. 6, 559--601.

D. Field. (1999).  Wavelets, vision and the statistics of natural scenes.  Phil. Trans. R. Soc. London A, Vol. 357, 2527-2542.

M. Frazier. (2001)   An Introduction to Wavelets Through Linear Algebra.  Springer, New York, NY.

T. Gardner and M. Magnasco. (2006). Sparse time-frequency representations.  Proc. Nat. Acad. Sci., Vol.~103, 6094-6099.

H.-Y Gao. (1998)  Wavelet shrinkage denoising using the non-negative garrote.  J. of Computational and Graphical Statistics, Vol. 7, 469-488.  If you have
access to JSTOR you can dowmload the paper from here.

R. Gregory, Ed. (2004). The Oxford Companion to the Mind, Oxford University Press.

K. Gr\"ochenig. (2001). Foundations of Time-Frequency Analysis. Birkh\"auser, Boston, MA.

I. Guskov, W. Sweldens, and P. Schr\"oder. (1999). Multiresolution Signal Processing for Meshes.
SIGGRAPH 1999, 325-334. Available at Wim Swelden's website. .

R.W. Hamming. (1987). Numerical Methods for Scientists and Engineers. Dover, NY.

D.K. Hammond and E.P. Simoncelli. Image denoising with an orientation-adaptive Gaussian scale mixture model.
To appear in Proc.\ 13th IEEE Int'l Conference on Image Processing, Atlanta, Georgia, 8--11 Oct. 2005.

D. Hankerson, G.A. Harris, P.D. Johnson, Jr. (2003). Introduction to Information Theory and Data Compression, 2nd Edition. CRC Press.

L. Harkleroad. (2006).  The Math Behind the Music. Cambridge University Press, Cambridge, UK.

D.J Heeger, E.P. Simoncelli, and J.A. Movshon. (1996). Computational models of cortical visual processing. Proc. National Academy of Science, Vol. 93, 623-627..

V.K. Heer, H-E Reinfelder. (1990). Comparison of reversible methods for data compression. In Medical Imaging IV,
354-365. Proceedings SPIE, No. 1233.

E. Hernandez, G. Weiss. (1996). A First Course on Wavelets. CRC Press, Boca Raton, FL.

W. Hodges and R. Wilson. (2002).  Musical patterns.  In G. Assayag, H.G. Feichtinger,
and J.F. Rodrigues (editors), Mathematics and Music. Springer-Verlag, New York.

B. Burke Hubbard. (1998). The World According to Wavelets, Second Edition. AK Peters, Wellesley, MA.

P. Isihara and M. Knapp.~(1993). Basic Z_12 analysis of musical chords. UMAP Journal, 14, 319-348.

B. J\"ahne. (2002). Digital Image Processing, 5th Ed. Springer, NY.

B.D. Johnson. (2002). Wavelets: generalized quasi-affine and oversampled-affine frames.
Thesis, Washington University in St. Louis.

A. Khodakovsky, P. Schr\"oder, and W. Sweldens. (2000). Progressive Geometry Compression.
SIGGRAPH 2000, 271--278. Available at Wim Swelden's website.

M. Kobayashi. (1996). Listening for Defects: Wavelet-Based Acoustical Signal Processing in Japan. SIAM News, Vol. 29, No. 2.

D. Kroodsma. (2005). The Singing Life of Birds. Houghton-Mifflin, NY.

Legall, D., Tabatai, A. (1988). Subband coding of digital images using symmetric short kernel filters and arithmetic coding techniques.
In Int. Conf. Acoustic, Speech, Signal Processing, New York, 761-765.

F. Lerdahl and R. Jackendoff.. (1983). A Generative Theory of Tonal Music. MIT Press, Cambridge, MA.

F. Lerdahl and R. Jackendoff.. (1992). An Overview of Hierarchical Structure in Music. In Machine Models of Music, S. Schwanauer and D. Levitt, Eds.,
MIT Press, Cambridge, MA, 289--312.

J. Li. (2002). Image Compression---The mechanics of the JPEG 2000.   A web article from (search on JPEG 2000).

H. Longuet-Higgins (1994). Artificial Intelligence and Musical Cognition.  Phil. Trans. Roy. Soc. London, A349, 115-131.  If you have access to JSTOR, then
you can download the article from here.

A.K. Louis, P. Maass, A. Rieder. (1997).  Wavelets, Theory and Applications. Wiley, New York, NY.

G. Loy. (2007).  Musimathics: The Mathematical Foundations of Music, Vol.~2.  MIT Press, Cambridge, MA.

F. Luisier, T. Blu, and M. Unser. (2007). A New SURE Approach to Image Denoising: Inter-scale Orthonormal Wavelet Thresholding.
IEEE Trans. Image Processing, Vol..16, 593-606.

S. Lyu and E.P. Simoncelli. (2007).  Statistical Modeling of Images with Fields of Gaussian Scale Mixtures.
In Adv. Neural Information Processing Systems, Vol. 19.

F.B. Mache. (1993).  Music, Myth and Nature. Contemporary Music Studies, Vol. 6. Taylor \& Francis, London.

S. Mallat. (1999). A Wavelet Tour of Signal Processing. Second Edition. Academic Press, San Diego, CA.

H.S. Malvar, D.H. Staelin. (1989). The LOT: transform coding without blocking effects.  IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 37, 553-559.

G. Mazzola. (2002). The Topos of Music. Birkhauser, Basel.

Y. Meyer. (1993). Wavelets. Algorithms and Applications.  SIAM, Philadelphia, PA.

M. Nelson. (1991). Arithmetic Coding + Statistical Modeling  = Data Compression.  Webpage article at

A. Nestke and T. Noll. (2000).  Inner Metrical Analysis. In J. Haluska (Ed.), Music and Mathematics, Tatra Mountains Mathematical Publications, Bratislava.

T.Q. Nguyen. (1992). A class of generalized cosine-modulated filter bank.  Proceedings 1992 IEEE International Symposium on Circuits and Systems, Vol.~2, 943--946.

NuHAG webpage:

W. O'Grady, M. Dobrovolsky, M. Arnoff. (1993).  Contemporary Linguistics, An Introduction.  St. Martins Press, New York.

S. Oraintara, P. Heller, T. Tran, and T. Nguyen. (2001).  Lattice structure for regular paraunitary linear-phase filterbanks and M-band orthogonal symmetric wavelets.
IEEE Transactions on Signal Processing, Vol.~49, 2659-2672.

S. Pinker. (1997).  How the Mind Works. Norton, NY.

J. Portilla, V. Strela, M. Wainwright, and E.P. Simoncelli. (2003).   Image denoising using scale mixtures of Gaussians in the wavelet domain.
IEEE Trans Image Processing, Vol. 12, 1338--1351.

R.L. de Queiroz, T.Q. Nguyen, K.R. Rao. (1996). The GenLOT: generalized linear-phase lapped orthogonal transform  IEEE Transactions on Signal Processing, Vol. 44, 497--507.

K.R. Rao. (1982). Fast transforms: algorithms, analyses, applications. Academix Press, San Diego, CA.

M. Rabbini, P.W. Jones. (1991). Digital Image Compression Techniques.  SPIE Press, Bellingham, WA.

H.L. Resnikoff, R.O. Wells, Jr. (1998). Wavelet Analysis. The Scalable Structure of Information.  Springer, New York, NY.

D. Rothenberg. (2005). Why Birds Sing: A Journey into the Mystery of Bird Song. Basic Books, NY.

J.C. Russ. (1995). The Image Processing Handbook. CRC Press, Boca Raton, FL.

A. Said. (2004). Introduction to Arithmetic Coding -- Theory and Practice.  Chap. 5 of  Lossless Compression Handbook (2003), K.~Sayood (Ed.),
Academic Press, San Diego, 101--152.

S. Schwanauer and D. Levitt, Eds. (1993). Machine Models of Music. MIT Press, Cambridge, MA.

L. Senhadji, L. Thoraval, and G. Carrault. (1996). Continuous Wavelet Transform: ECG recognition based on phase and modulus
representations and hidden markov models. In A. Aldroubi, M. Unser, editors. Wavelets in Medicine and Biology. CRC Press. Boca Raton, FL, 439--464.

W. Sethares. (2007).  Rhythm and Transforms. Springer, NY.

W. Sethares. (2007).  Rhythm and Transforms. An extended abstract of his plenary address to the Mathematics and Computation in Music conference
in Berlin, May 18, 2007.

E.P. Simoncelli and B.A. Olshausen. (2001). Natural image statistics and neural representation.  Annual Review of Neuroscience, Vol. 24, 1193-1216.

L.M. Smith (2000).  A multiresolution time-frequency analysis and interpretation of musical rhythm.  Thesis, University of Western Australia.

L.M. Smith's webpage:

N. Spender. (2004). Music, psychology of. Article in The Oxford Companion to the Mind, 625--632, Oxford University Press, Oxford, UK.

G. Strang, T. Nguyen. (1996). Wavelets and Filter Banks. Wellesley-Cambridge Press, Boston.

R.S. Strichartz. (1993). How to Make Wavelets. The American Mathematical Monthly, Vol. 100, 539--556.  Available from

W. Sweldens. (1996). The lifting scheme: a custom-design construction of biorthogonal wavelets. Applied and Computational Harmonic Analysis,
Vol. 3, No. 2, 186--200.

W. Swelden's paper archive:

D.S. Taubman and M.W. Marcellin. (2002).  JPEG2000:  Image compression fundamentals, standards and practice.  Kluwer, Boston, MA.

J. Tian and R.O. Wells, Jr. (1996). A lossy image codec based on index coding. IEEE Data Compression Conference, DCC '96, p. 456.

J. Tian and R.O. Wells, Jr. (1998). Embedded image coding using wavelet difference reduction.
Wavelet Image and Video Compression, P. Topiwala, ed., Kluwer, Norwell, MA, 289--301.

L.N. Trefethen. (1998). Maxims About Numerical Mathematics, Computers, Science, and Life. SIAM News, Vol. 31, No. 1.

UCSD Video Processing page:

Michael Unser's webpage:

M. Unser, T.~Blu.~(2003).  Wavelet Theory Demystified.  IEEE Transactions on Signal Processing, Vol. 51, 470-483.

M. Unser, T. Blu. (2003).  Mathematical Properties of the JPEG2000 Wavelet Filters.  IEEE Transactions on Image Processing, Vol. 12, 1080-1090.

M. Vetterli, J. Kova\v cevi\'c. (1995). Wavelets and Subband Coding.  Prentice-Hall, Englewood Cliffs, NJ.

J.S. Walker. (1988). Fourier Analysis. Oxford, New York, NY.

J.S. Walker. (1996). Fast Fourier Transforms, Second Edition. \CRC.

J.S. Walker. (1997). Fourier Analysis and Wavelet Analysis. Notices of the Amer. Math. Soc., Vol. 44, 658--670.

J.S. Walker. (2000). Lossy image codec based on adaptively scanned wavelet difference reduction. Optical Engineering, Vol. 39, 1891--1897.

J.S. Walker. (2002). Tree-adapted wavelet shrinkage. Advances in Imaging and Electron Physics, Vol. 104, 343-394.

J.S. Walker and T.Q. Nguyen. (2000). Adaptive scanning methods for wavelet difference reduction in lossy image compression. IEEE Int'l Conference on Image Processing, Vancouver,
Sept. 2000, Vol. 3, 182--185.

J.S. Walker and T.Q. Nguyen. (2000). Wavelet-based image compression.  Handbook of Transforms and Data Compression,
Chap. 6, 267--312, CRC Press, Boca Raton, FL.   Extract of pages on wavelet image compression.

J.S. Walker and Y.-J. Chen. (2006). Denoising Gabor transforms. Preprint.

J.S. Walker and G.W. Don. (2006).  Music:  A time-frequency approach.  Preprint.

D.F. Walnut. (2002). An Introduction to Wavelet Analysis. Birkhauser, Boston.

B.A. Wandell. (1995). Foundations of Vision. Sinauer Associates, Sunderland, MA.

Z. Wang and A.C. Bovik. (2002). A universal image quality index.  IEEE Signal Processing Letters, Vol. 9, 81-84.

Z. Wang, A.C. Bovik, and E.P. Simoncelli. (2005). Structural approaches to image quality assessment.
Chapter 8.3 in Handbook of Image and Video Processing, 2nd Edition, Alan Bovik (Ed.), Academic Press, San Diego, CA.

Z. Wang and E.P. Simoncelli. (2004). Local phase coherence and the perception of blur.  Adv. Neural Information Processing Systems, Vol.~16.

A.B. Watson. (1987). Efficiency of a model human image code.  J Optical Soc. Am., Vol. 4, 2401--2417.  Download a scanned version by clicking here.

The Wavelet Digest website:

Why Birds Sing website:

M.V. Wickerhauser. (1993). Best-adapted Wavelet Packet Bases. In I. Daubechies, editor, Different Perspectives on Wavelets. AMS, Providence, RI, 155--172.

M.V. Wickerhauser. (1994). Adapted Wavelet Analysis from Theory to Software. A.K. Peters, Wellesley, MA.

L. Ying, L. Demanet, E. J. Candes. (2005). 3D Discrete Curvelet Transform. Proceedings of SPIE---Volume 5914, Wavelets XI, M. Papadakis, A.F. Laine, M.A. Unser (Ed.s).

R. Young. (1980). An Introduction to Nonharmonic Fourier Series. Academic Press, NY.