3 Semester Credit Hours

Course Description

Advanced perspectives on fundamental DSP topics are formulated, studied, and utilized for the conceptual analysis of specialized DSP techniques in selected areas. The Discrete-Time Fourier Transform (DTFT) and the Discrete Fourier transform (DFT) are examined from the perspective of Discrete Hilbert Transform (DHT) relations. The Fast Fourier Transform (FFT) is studied from the perspective of alternative computational structures with differing properties. Digital upsampling and digital downsampling are viewed from the perspective of efficient multirate systems for fractional decimation. Filter banks are generalized beyond the traditional uniform DFT filter bank. Specialized topics addressed include quadratic time-frequency distributions, wavelets and wavelet transforms, two-dimensional IIR filters, different formulations of the discrete cosine transform (DCT), the periodogram and the averaged periodogram for spectral analysis, parametric signal modeling using the autocorrelation method, and computational alternatives for the complex cepstrum.

Prerequisites

• Digital Signal Processing I (NCSC 6552)

• General prerequisite: Students must have the knowledge resulting from completing all coursework in the curriculum for a BS degree in Electrical Engineering from an ABET-accredited engineering program in the United States or a CEAB-accredited program in Canada, or the equivalent from a foreign institution; performance level in this coursework should be equivalent to a cumulative undergraduate GPA of 2.9 or better on 4.0 scale
  

Course Objectives

• Describe and analyze  the conceptual underpinnings of Discrete Hilbert Transforms in DTFT and DFT contexts.
• Design and implement Hilbert Transformers to meet given specifications.
• Describe and analyze  the conceptual underpinnings for different approaches to Fast Fourier Transform (FFT) computation.
• Analyze and compare the relative merits of different algorithms for  Fast Fourier Transform (FFT) computation.
• Design and Implement different algorithms for FFT Computations.
• Describe and analyze the conceptual underpinnings of different discrete cosine transform (DCT) formulations.
• Analyze and compare the energy compaction property of the DCT relative to DFT and K-L transforms.
• Design and inplement DCT algorithms.
• Describe and analyze the conceptual underpinnings of spectral analysis.
• Design and implement the Periodogram and the Averaged Periodogram methods for spectral analysis.
• Describe and analyze the conceptual underpinnings of parametric signal modeling.
• Design and implement the autocorrelation method for parametric signal modeling.
• Describe and analyze  the conceptual underpinnings for efficient fractional decimation.
• Design and implement efficient structures for fractional decimation.
• Describe and analyze the conceptual underpinnings for alternative time-frequency distributions.
• Design and implement different time-frequency distributions.
• Describe and analyze the conceptual underpinnings for M-Channel QMF Filterbank systems.
• Design and implement different M-Channel QMF Filterbank systems.
• Describe and analyze the conceptual underpinnings of wavelet transforms.
• Design and implement wavelet transforms.
• Describe and analyze the conceptual underpinnings of 2D IIR filters.
• Design and implement 2D IIR filters. 
• Describe and analyze the conceptual underpinnings of 2D FIR filters.
• Design and implement 2D FIR filters.
• Describe and analyze the conceptual underpinnings of adaptive filters.
• Design and implement adaptive filters.

Course Topics

The following topics will be covered in the order given.

• Course Introduction
• DTFT Review
• DFT Review
• Hilbert Transforms
• Fast Fourier Transforms
• Discrete Cosine Transforms
• Spectral Analysis
• Parametric Signal Modeling
• Fractional Decimation
• Time-Frequency Analysis
• Time-Frequency Analysis
• M-Channel QMF Banks
• Discrete-Time Wavelet
• Transform
• 2D FIR Filters
• 2D IIR Filters
• Sensor Array Processing
• Course Review