DSP Digital Signal Processing

1. EMT 488/3 Digital Signal Processing DSPDigital Signal Processing

2. Breadth and depth of DSP Adapted from: Steven W. Smith, “The scientist and engineer’s guide to digital signal processing”, 2nd ed., California Technical Publishing, 1999.

3. What is DSP? • Digital signal processing (DSP) is the mathematics, the algorithms, and the techniques used to manipulate signals which have been converted into digital form. • The signals are normally data obtained from real world such as such as seismic vibrations, sound waves, and visual images. • Processing of the digital signal involves a number of goals such as enhancement of visual images, recognition and generation of speech, and compression of data for storage and transmission. Adapted from: Steven W. Smith, “The scientist and engineer’s guide to digital signal processing”, 2nd ed., California Technical Publishing, 1999.

4. Application of DSP Adapted from: Steven W. Smith, “The scientist and engineer’s guide to digital signal processing”, 2nd ed., California Technical Publishing, 1999.

5. Interdisciplinary subject Adapted from: Steven W. Smith, “The scientist and engineer’s guide to digital signal processing”, 2nd ed., California Technical Publishing, 1999. • As you go through the application in the book, DSP relies on the technical work in many adjacent fields. • DSP has fuzzy and overlapping borders with many other areas of science, engineering and mathematics. • If you want to specialize in DSP, these are the areas that you will also need to study.

6. DSP processors • In brief, DSP processors are processors or microcomputers whose hardware, software, and instruction sets are optimized for high-speed numeric processing applications­ an essential for processing digital data representing analog signals in real time. • What a DSP does is straightforward. When acting as a digital filter, for example, the DSP receives digital values based on samples of a signal, calculates the results of a filter function operating on these values, and provides digital values that represent the filter output; it can also provide system control signals based on properties of these values. The DSP’s high-speed arithmetic and logical hardware is programmed to rapidly execute algorithms modelling the filter transformation. Taken from: http://www.analog.com/en/analog-dialogue/articles/dsp-101-part-1.html

8. Analog to digital converter (ADC) • Sampling: Conversion of a continuous-time signal into a discrete-time signal obtained by taking samples of the continuous-time signal at discrete-time instants. If xa(t) is the input to the sampler, the output is xa(nT)  x(n), where T is the sampling period. Do you still remember the famous sampling theorem for reconstructing a signal? • Quantization: Conversion of a discrete-time continuous-valued signal into a discrete-time, discrete-valued (digital signal). The value of each signal sample is represented by a value selected by a value selected from a finite set of possible values. The difference between the unquantized sample x(n) and the quantized signal xq(n) is known as the quantization error. • Encoding: The discrete value xq(n) is represented by a b-bit binary sequence.

9. Sampling theorem • A bandlimited continuous-time signal, with highest frequency (bandwidth) B hertz, can be uniquely recovered from its samples provided that the sampling rate (Fs) is greater or equaled to 2B samples per second. Undersampling causes aliasing

10. Further reading • The Scientist and Engineer's Guide to Digital Signal Processing, particularly on chapter 1. • http://www.analog.com/en/design-center/landing-pages/001/beginners-guide-to-dsp.html