Week |
Subject |
Related Preparation |
1) |
• Syllabus.
• Filters
• Signals and their frequency domain representation, Bode plots.
• Digital Filters, analog filters
• Low pass, band pass and high pass filters
• Band stop filters
• Real filters and their characteristics: passband ripple, stopband ripple, transition region.
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Review the Syllabus.
Acquire a copy of the book.
Review some of the topics covered in the first half of the book, in particular section 4.5 and Chapter 8
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2) |
Structures for realization of discrete-time systems
• Structures for FIR systems
o Direct-form structures
o Cascade-form structures
o Frequency-sampling structures
o Lattice structure
• Structures for IIR systems
o Direct-form structures
o Signal flow graphs and transposed structures
o Cascade-form structures
o Parallel-form structures
o Frequency-sampling structures
o Lattice and lattice-ladder structures for IIR systems |
Begin reading chapter 7.
Review problems solved in class and other problems in the book
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3) |
• Review of the z-transform.
• State-space system analysis and structures
o State-Space Descriptions of Systems Characterized by Difference Equations
o Solution of the State-Space Equations.
o Relationships Between Input-Output and State-Space Descriptions,
o State-Space Analysis in the z-Domain,
o Additional State-Space Structures. |
Continue reading chapter 7, also review chapter 3.
Review problems solved in class and other problems in the book.
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4) |
• Representation of Numbers
o Fixed-Point Representation of Numbers
o Binary Floating-Point Representation of Numbers.
o Errors Resulting from Rounding and Truncation.
• Quantization of Filter Coefficients.
o Analysis of Sensitivity to Quantization of Filter Coefficients.
o Quantization of Coefficients in FIR Filters.
• Round-off effects in digital filters
o Limit-Cycle Oscillations in Recursive Systems.
o Scaling to Prevent Overflow,
o Statistical Characterization of Quantization Effects in Fixed-Point Realizations of Digital Filters.
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Finish reading chapter 7.
Review problems solved in class and other problems in the book.
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5) |
• Random variables
• Random processes
• probability density functions,
• expectation,
• autocorrelation,
• stationary random processes
• ergodic random processes |
Read Appendix A and B in the textbook
Review problems solved in class.
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6) |
• Sampling of Bandpass Signals
o Representation of Bandpass Signals
o Sampling of Bandpass Signals
o Discrete-Time Processing of Continuous-Time Signals
• Analog-to-Digital Conversion
o Sample-and-Hold.
o Quantization and Coding, |
Start reading chapter 9 in the textbook
Review problems solved in class, review all problems in chapter 9
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7) |
• Analog-to-Digital Conversion
o Analysis of Quantization Errors,
o Oversampling A/D Converters,
• Digital-to-Analog Conversion
o Sample and Hold,
o First-Order Hold.
o Linear Interpolation with Delay,
o Oversampling D/A Converters, |
Continue reading chapter 9 in the textbook
Review problems solved in class, review all problems in chapter 9
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8) |
Multirate signal processing
• Introduction to multirate digital signal processing
• Decimation by a factor D
• Interpolation by a factor I
• Sampling rate conversion by a rational factor
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Read chapter 10 in the textbook
Review problems solved in class, review all problems in chapter 10.
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9) |
• Filter design and implementation for sampling rate conversion
o Direct form FIR filter structures
o Polyphase filter structures
o Time-variant filter structures
• Multistage implementation of sampling rate conversion
• Sampling rate conversion of bandpass signals
• Sampling rate conversion by an arbitrary factor
• Application of multirate signal processing |
Read chapter 10 in the textbook
Review problems solved in class, review all problems in chapter 10.
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10) |
Linear Prediction and Optimum Linear Filters
• Innovations representation of a stationary random process
o Rational power spectra
o Relationships between the filter parameters and the autocorrelation sequence.
• Forward and backward linear prediction
o Forward linear prediction
o Backward linear prediction
o The Optimum Reflection Coefficients for the Lattice Forward and backward predictors
o Relationship of an AR Process to Linear Prediction.
• Solution of the normal equations
o The Levinson-Durbin Algorithm.
o The Schiir Algorithm.
• Properties of the linear prediction error filters
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Start reading chapter 11 in the textbook
Review problems solved in class, review all problems in Chapter 11 |
11) |
• Explain what AR, MA and ARMA stand for, and why a process may be modeled as such.
• Describe a Wiener filter.
• Derive the coefficients of an FIR Wiener filter for a given process.
• Define the Linear mean-square estimation problem.
• Explain the orthogonality principle and how it is used to find the coefficients of the LMMSE estimator.
• Describe the IIR and non-causal Wiener filters and how these are derived.
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Read chapter 11 in the textbook
Review problems solved in class, review all problems in Chapter 11
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12) |
Power spectrum estimation
• Estimation of spectra from finite-duration observations of signals
o Computation of the Energy Density Spectrum.
o Estimation of the Autocorrelation and Power Spectrum of Random Signals: The Periodogram.
o The Use of the DFT in Power Spectrum Estimation,
• Nonparametric methods for power spectrum estimation
o The Bartlett Method: Averaging Periodograms,
o The Welch Method: Averaging Modified Periodograms,
o The Blackman and Tukey Method: Smoothing the Periodogram,
o Performance Characteristics of Nonparametric Power Spectrum Estimators,
o Computational Requirements of Nonparametric Power Spectrum Estimates,
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Read chapter 12 and the handouts in the textbook
Review problems solved in class, and all problems in Chapter 12.
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13) |
• Parametric Methods for Power Spectrum Estimation
o Relationships Between the Autocorrelation and the Model Parameters,
o The Yule-Walker Method for the AR Model Parameters,
o The Burg Method for the AR Model Parameters,
o Unconstrained Least-Squares Method for the AR Model Parameters,
o Sequential Estimation Methods for the A R Model Parameters,
o Selection of AR Model Order,
o MA Model for Power Spectrum Estimation,
o ARMA Model for Power Spectrum Estimation,
o Some Experimental Results,
• Minimum Variance Spectral Estimation |
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14) |
• Eigenanalysis Algorithms for Spectrum Estimation
o Pisarenko Harmonic Decomposition Method,
o Eigen-decomposition of the Autocorrelation Matrix for Sinusoids in White Noise,
o MUSIC Algorithm.
o ESPRIT Algorithm,
o Order Selection Criteria.
o Experimental Results,
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Read chapter 12 and the handouts in the textbook
Review problems solved in class, and all problems in Chapter 12.
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15) |
• Unitary Transforms, Wavelets and Their Applications
o Karhunen-Loeve Transform
o Discrete Cosine Transform
o Wavelet Transforms
o Subband coding |
Read chapter 12 and the handouts in the textbook
Review problems solved in class, and all problems in Chapter 12. |
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Program Outcomes |
Level of Contribution |
1) |
Has sufficient background in mathematics, science and engineering related fields. |
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2) |
Uses the theoretical and practical knowledge in mathematics, science and their fields together for engineering solutions. |
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3) |
Identifies, formulates and solves engineering problems, selects and applies appropriate analytical methods and modeling techniques for this purpose. |
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4) |
Analyze a system, system component or process and design it under realistic constraints to meet desired requirements; apply modern design methods accordingly. |
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5) |
Selects and uses the modern techniques and tools necessary for engineering applications. |
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6) |
Design experiments, conduct experiments, collect data, analyze and interpret results. |
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7) |
Works individually and in multi-disciplinary teams. |
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8) |
Accesses information and conducts resource research for this purpose, uses databases and other information sources. |
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9) |
Accesses information and conducts resource research for this purpose, uses databases and other information sources. |
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10) |
Accesses information and conducts resource research for this purpose, uses databases and other information sources. |
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11) |
Uses the theoretical and practical knowledge in mathematics, science and their fields together for engineering solutions. |
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12) |
Identifies, formulates and solves engineering problems, selects and applies appropriate analytical methods and modeling techniques for this purpose. |
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13) |
Analyze a system, system component or process and design it under realistic constraints to meet desired requirements; apply modern design methods accordingly. |
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14) |
Selects and uses the modern techniques and tools necessary for engineering applications. |
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15) |
Works individually and in multi-disciplinary teams |
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16) |
Uses information and communication technologies together with computer software required by the field at least Advanced Level of European Computer Skills License. |
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17) |
Communicate effectively verbally and in writing; use a foreign language at least at level B1 of the European Language Portfolio. |
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18) |
Communicates using technical drawing. |
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19) |
Accesses information and conducts resource research for this purpose, uses databases and other information sources. |
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20) |
Becomes aware of the universal and social effects of engineering solutions and applications; entrepreneurship and innovation and have knowledge about the problems of the age. |
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21) |
Has professional and ethical responsibility. |
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22) |
Have awareness of project management, workplace practices, employee health, environmental and occupational safety; the legal consequences of engineering applications. |
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23) |
Demonstrates awareness of the universal and social impact of engineering solutions and applications; is aware of entrepreneurship and innovation and has knowledge about the problems of the age. |
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