# ECE 429

## Digital Signal Processing

Spring

Required Course:
No

### Course Level

Undergraduate

### Units

3

### Prerequisite(s)

ECE 340A

### Course Texts

Oppenheim, Alan V., and Ronald W. Schafer. *Discrete-Time Signal Processing*. 3rd ed. Prentice Hall, 2010.

### Schedule

150 minutes lecture per week

### Course Description

Discrete-time signals and systems, z-transforms, discrete Fourier transform, fast Fourier transform, digital filter design.

May be convened with ECE 529.

### Learning Outcomes

By the end of this course, the student will be able to:

- State and apply the definitions of the following system properties: linearity, time invariance, causality, and BIBO stability.
- Describe the distinctions between analog, continuous-time, discrete-time and digital signals, and describe the basic operations involved in analog-digital (A/D) and digital-analog (D/A) conversion.
- State and apply the definition of a periodic discrete-time signal.
- State the sampling theorem and explain aliasing.
- Apply simple discrete-time signals to filters to obtain the output response.
- Convolve discrete-time signals.
- Calculate the z-transform X(z) of a simple signal x(n) (such as an exponential and sinusoid): specify the region of convergence (ROC) of X(z).
- Apply z-transform theorems.
- Given the transfer function H(z) and ROC of an LTI system, find the system poles (and zeros) and state whether or not the system is BIBO stable.
- Compute the discrete-time Fourier transform (DTFT) of a signal.
- Use the frequency response of a discrete-time system.
- Knowing the poles and zeros of a transfer function, make a rough sketch of the gain response.
- Design digital filters.
- Apply DFT properties to compute the DFT and IDFT of simple signals.
- Design the parameters associated with DFT implementation (sampling rate and record length) to provide an accurate analysis of the frequency and strength of dominant frequency components present in some given, unknown signal (e.g., for spectral analysis of a signal).
- Explain the need for zero padding and tapered windows when doing spectral analysis of real-world signals. Explain the terms picket fence effect and spectral leakage.
- Compare the characteristics (advantages and disadvantages) of IIR and FIR filters.
- Explain (using frequency domain sketches) the application of oversampling and subsequent decimation for recording in digital audio systems.

### Course Topics

- Introduction to DSP, classification of signals, digital frequency, sampling, aliasing, quantization noise, discrete-time system components, system properties, filter realizations, impulse response, convolution, correlation (9 lectures)
- Forward z-transform, time-shifting, DTFT existence, signal type from ROC, inverse z-transform, applying z-transform properties, poles and stability, system analysis using z-transform (5 lectures)
- Forward discrete-time Fourier transform (DTFT), symmetry, frequency shifting, modulation, filter design from lowpass prototypes, synthesis of filters using DTFT properties, DTFT analysis of downsampling/upsampling and expansion/compression operations, DTFT systems analysis, phase and group delay of filters, frequency response from poles and zeros, minimum-phase filters, forward DFT and inverse DFT, relationship to DTFT, applying DFT properties, convolution and correlation using DFT, DFT symmetry, sinusoidal analysis and frequency resolution, zero-padding and windowing, spectral analysis (16 lectures)
- Filter architectures and limit cycles (if time permits), linear-phase FIR filter types, FIR design by windowing, IIR design using bilinear transformation, decimation-in-time FFT, decimation-in-frequency FFT (9 lectures)

### Relationship to Student Outcomes

ECE 429 contributes directly to the following specific electrical and computer engineering student outcomes of the ECE department:

- Ability to apply knowledge of mathematics, science and engineering (high)
- Ability to design and conduct experiments, as well as to analyze and interpret data (low)
- Ability to design a system, component or process to meet desired needs within realistic constraints, such as economic, environmental, social, political, ethical, health and safety, manufacturability and sustainability (high)
- Ability to identify, formulate and solve engineering problems (high)
- Ability to use the techniques, skills and modern engineering tools necessary for engineering practice (high)

### Syllabus Prepared By

Jeff Rodriguez, 03/16/16