# ECE 429

## Digital Signal Processing

**Usually offered:**Spring

**Required course: **No

### Course Level

### Units

### Instructor(s)

### Prerequisite(s)

### Course Texts

Alan V. Oppenheim and Ronald W. Schafer, Discrete-Time Signal Processing, Third Edition, Prentice Hall, 2010. (ISBN: 0131988425)

### Schedule

### Course Description

**Specific Course Information:****2021-2022 Catalog Data: **Discrete-time signals and systems, z-transforms, discrete Fourier transform, fast Fourier transform, digital filter design.

### Learning Outcomes

**Specific Goals for the Course:****Outcomes of Instruction:** 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-to-digital (A/D) and digital-to-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 or sinusoid) and 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 tradeoff between reduced resolution and spectral leakage.
- Compare the characteristics (advantages & 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

**Brief list of topics to be covered:**

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

### Relationship to Student Outcomes

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

1. An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics.

2. An ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors.