lecture 1+2.pdf
- 1. Signal • A signal is a physical quantity, or quality, which conveys information Example: • voice of my friend is a signal which causes me to perform certain actions or react in a particular way • My friend's voice is called an excitation • My action or reaction is called a response
- 2. System • A system is an entity that manipulates one or more signals to accomplish a function, thereby yielding new signals.
- 3. Signal Processing • The conversion from excitation to response is called signal processing • A typical reason for signal processing is to eliminate or reduce an undesirable signal • We convert the original signal into a form that is suitable for further processing • One fundamental representation of a signal is as a function of at least one independent variable
- 4. Analog vs. Digital Signal Processing 8 Analog Signal Processor Analog input Signal x(t) Analog output Signal y(t) Analog Signal Processing Digital Signal Processor A/D converter D/A converter Digital Signal Processing Analog input Signal x(t) Analog output Signal y(t)
- 5. Advantages of Digital Signal Processing • A digital programmable system allows flexibility in reconfiguring the DSP operations simply by changing the program. Reconfiguration of an analogue system usually implies a redesign of hardware, testing and verification that it operates properly. • DSP provides better control of accuracy requirements. • Digital signals are easily stored on storage media i.e. hard disk 9
- 6. • The DSP allows for the implementation of more sophisticated signal processing algorithms. • In some cases a digital implementation of the signal processing system is cheaper than its analogue counterpart. • DSP consume relatively less power than analog counterpart. • DSP processor can be reuse for many applications 10 Advantages of Digital Signal Processing
- 7. DSP Applications • Touch-Tone™ telephones • Edge detection in images • Digital signal and image filtering • Seismic analysis • Text recognition • Music synthesis • Bar code readers • RADAR • Sonar processing • Satellite image analysis • Digital mapping • Cellular telephones • Digital cameras • Detection of narcotics and explosives 11
- 8. DSP Applications • Echo cancellation • Antilock brakes • Signal and image compression • Noise reduction • Companding • High definition television (HDTV) • Digital audio • Encryption • Motor control • Smart appliances • Home security • High speed modems 12
- 9. DSP Applications Medical Applications • CT scans • Magnetic resonance image (MRI) scans • Diagnostic ultrasound imaging • Electrocardiogram(ECG) analysis • Electroencephalogram(EEG) analysis • Medical image processing • Cochlear implants • Remote medical monitoring • Speech synthesis • Speech recognition • Hearing aid 13
- 11. DSP Examples 50/60 Hz Interference Cancellation in Electrocardiography 15
- 12. DSP Examples Signal Spectrum Analysis 16
- 13. DSP Examples Compact-Disc Recording & Playback System 17
- 14. DSP Examples Digital Image Enhancement using Histogram Equalization 18
- 15. Analog vs. Digital Signal Processing 3 Analog Signal Processor Analog input Signal x(t) Analog output Signal y(t) Analog Signal Processing Digital Signal Processor A/D converter D/A converter Digital Signal Processing Analog input Signal x(t) Analog output Signal y(t)
- 16. Typical Digital Signal Processing System 4 It consists of • an analog filter called (anti-imaging) filter, • an analog-to-digital conversion (ADC) unit, • a digital signal (DS) processor, • a digital-to-analog conversion (DAC) unit, • and an analog filter called reconstruction (anti-image) filter.
- 17. 5 Typical Digital Signal Processing System
- 18. A/D & D/A Conversion 6
- 19. Analog to Digital (A/D) Conversion • Most signals of practical interest are analog in nature Examples: Voice, Video, RADAR signals, Transducer/Sensor output, Biological signals etc • So in order to utilize those benefits, we need to convert our analog signals into digital • This process is called A/D conversion 7
- 20. Analog to Digital Conversion A/D conversion can be viewed as a three step process 8
- 21. Analog to Digital Conversion A/D conversion can be viewed as a three step process 9
- 22. Analog to Digital Conversion Sample & Hold (Sampler) • Analog signal is continuous in time and continuous in amplitude. • It means that it carries infinite information of time and infinite information of amplitude. • Analog (continuous-time) signal has some value defined at every time instant, so it has infinite number of sample points. 10
- 23. Analog to Digital Conversion Sample & Hold (Sampler) • It is impossible to digitize an infinite number of points. • The infinite points cannot be processed by the digital signal (DS) processor or computer, since they require an infinite amount of memory and infinite amount of processing power for computations. • Sampling is the process to reduce the time information or sample points. 11
- 24. Analog to Digital Conversion Sample & Hold (Sampler) • The first essential step in analog-to-digital (A/D) conversion is to sample an analog signal. • This step is performed by a sample and hold circuit, which samples at regular intervals called sampling intervals. • Sampling can take samples at a fixed time interval. • The length of the sampling interval is the same as the sampling period, and the reciprocal of the sampling period is the sampling frequency fs. 12
- 25. Analog to Digital Conversion Sample & Hold (Sampler) • After a brief acquisition time, during which a sample is acquired, the sample and hold circuit holds the sample steady for the remainder of the sampling interval. • The hold time is needed to allow time for an A/D converter to generate a digital code that best corresponds to the analog sample. • If x(t) is the input to the sampler, the output is x(nT), where T is called the sampling interval or sampling period. • After the sampling, the signal is called “discrete time continuous signal” which is discrete in time and continuous in amplitude. 13
- 26. Analog to Digital Conversion Sample & Hold (Sampler) 14
- 27. Analog to Digital Conversion Sample & Hold (Sampler) Figure below shows an analog (continuous-time) signal (solid line) defined at every point over the time axis (horizontal line) and amplitude axis (vertical line). Hence, the analog signal contains an infinite number of points. 15
- 28. Analog to Digital Conversion Sample & Hold (Sampler) • Each sample maintains its voltage level during the sampling interval 𝑻 to give the ADC enough time to convert it. • This process is called sample and hold. 16
- 29. Nyquist–Shannon Sampling Theorem The sampling theorem guarantees that an analogue signal can be perfectly recovered as long as the sampling rate is at least twice as large as the highest-frequency component of the analogue signal to be sampled. 17
- 32. 20 Example: For the following analog signal, find the Nyquist sampling rate, also determine the digital signal frequency and the digital signal Nyquist–Shannon Sampling Theorem
- 33. 21 Example: Find the sampling frequency of the following signal. So sampling frequency should be Nyquist–Shannon Sampling Theorem
- 34. Exercise Determine the Nyquist sampling rate of a signal x(t) = 3sin(5000t + 17o) 22 Nyquist–Shannon Sampling Theorem