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
|
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
|
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
|
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.
|
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 |
|
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,
|
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) |
Information on project management and practices in business life such as risk management and change management; awareness about entrepreneurship, innovation and sustainable development. |
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2) |
Sufficient knowledge in mathematics, science and engineering related to their branches; the ability to apply theoretical and practical knowledge in these areas to model and solve engineering problems. |
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3) |
The ability to identify, formulate, and solve complex engineering problems; selecting and applying appropriate analysis and modeling methods for this purpose. |
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4) |
The ability to design a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; the ability to apply modern design methods for this purpose. (Realistic constraints and conditions include such issues as economy, environmental issues, sustainability, manufacturability, ethics, health, safety, social and political issues, according to the nature of design.) |
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5) |
Ability to develop, select and use modern techniques and tools necessary for engineering applications; ability to use information technologies effectively. |
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6) |
Ability to design experiments, conduct experiments, collect data, analyze and interpret results for examination of engineering problems. |
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7) |
Effective communication skills in Turkish oral and written communication; at least one foreign language knowledge. |
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8) |
Yaşam boyu öğrenmenin gerekliliği bilinci; bilgiye erişebilme, bilim ve teknolojideki gelişmeleri izleme ve kendini sürekli yenileme becerisi. |
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9) |
Professional and ethical responsibility. |
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10) |
Information on the effects of engineering applications on health, environment and safety in the universal and social dimensions and the problems of the times; awareness of the legal consequences of engineering solutions. |
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11) |
The ability to work effectively in disciplinary and multidisciplinary teams; individual work skill. |
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