Digital Signal ProcessingLaajuus (3 ECTS)

Objective

After completion of this course the student will understand the fundamentals of digital signal processing. The student will be familiar with the most common operations involved in digital signal processing chain. The student will understand the importance of sampling operation and its key characteristics, applied to low pass signal but also to a band pass signal. The reconstruction will be presented also.

The student will understand as well the fundamentals of linear quantification and the concept of signal to quantization noise ratio. The linear time invariant systems, the difference equation, impulse response and discrete convolution will be introduced as will be the concept of stability and frequency responses.

The student will be able to apply these concepts to linear Digital filter implementation as FIR and IIR, where the Z transform will be illustrated and used.

Content

1. Time and frequency domain.
2. Analogue and digital signals.
3. Multiplication vs. Convolution.
4. Uniform sampling, Shannon.
5. Band-pass signal case.
6. Sampling error, anti-aliasing filter.
7. Linear quantization, SQNR.
8. Digital sequences.
9. Linear time invariant systems, impulse response, difference equation, convolution.
10. Time domain response.
11. Frequency response.
12. Stability criteria.
13. Z transform, transfer function H(z), properties.
14. Digital Filtering.
15. FIR and IIR implementation, basic method for synthesis.
16. Complexity.

Assessment criteria, satisfactory (1)

1. The student is able to explain qualitatively the sampling operation principle
2. The student is able to realize a basic anti-aliasing filter given specification
3. The student is able to analyze quantitatively the effects of the sampling on a low pass signal
4. The student is able to specify the ADC converter resolution based on a SQNR requirement
5. The student can derive from a given linear time invariant system block diagram, the difference equation
6. The student can derive the time domain response, the stability criteria and its frequency response

Assessment criteria, good (3)

1. Evaluation criterias for Satisfactory (1)
2. The student can derive the impulse response h(n) from either a difference equation or (and) from a Z transform equation
3. The student can explicitly state the stability criteria from H(z)
4. The student can derive an LTI system frequency response from its H(z) and vice-versa
5. The student can analyze (time, frequency and Z domains) IIR and FIR basic configurations

Assessment criteria, excellent (5)

1. Evaluation criterias for Satisfactory (1)
2. Evaluation criterias for Good (3)
3. The student can use impulse response method to synthesize basic digital filter configuration
4. The student is able to compare different synthesis methods in terms of signal responses, implementation complexities and so forth
5. Given requirements, the student is able to synthesize basic chain from analogue domain to digital domain using appropriate basic filtering algorithms