Complex Calculation: Definition, operations and properties of complex numbers. Function of a complex variable. Limits. Continuity. Derivatives: Cauchy-Riemann conditions and sufficient derivability conditions. Analytical functions. Undefined integrals. Curvelinous paths and integrals. Waste. The Residue Theorem. Poles. Quotients of analytical functions Applications: Calculation of integrals using residues. Introduction to Signal Processing: Digital Devices, Sampling, Quantization, Aliasing and Reconstruction. Continuous Sinusoid: Amplitude and Phase, Frequency, Fourier Transform and Frequency Response. Discrete Sinusoids: Frequency, Fourier Transform, Frequency Response, Summary of Sinusoids. Sampling: Sampling a frequency, Aliasing, Anti-Aliasing Filter and Filter design. Reconstruction: Analog Digital Conversion, DA Conversion Distortions, Compensating for Distortions and Advantages of Increasing the Sample Rate.
- Churchill, Ruel V. Complex variables and their applications. McGraw-Hill do Brasil, 1980.
- Simon Haykin, Barry Van Veen, Signals and Systems. Editora Bookman, Porto Alegre 2002.
- James H. McClellan, C. Sidney Burrus, Alan V. Oppenheim, Thomas W. Parks, Computer Based Exercises for Signal Processing using Matlab. Publisher Prentice Hall, USA 1996.
- Lyons, R.G. (2010). Understanding digital signal processing. Prentice Hall (3rd ed.).
- Oppenheim, A.V. & Schafer, R.W. (2007). Discrete-time digital signal processing. Prentice Hall (3rd ed.).
- Monson H. Hayes, Digital Signal Processing. Editora Bookman, Porto Alegre 2006.
- S. Foucart and R. Holger, A mathematical introduction to compressive sensing, Basel: Birkhäuser, 2013.
- Cai, J. F., Candès, E. J., & Shen, Z., A singular value thresholding algorithm for matrix completion, SIAM Journal on Optimization, 20 (4), 2010.