1 W. E. Dunn ME 360: FUNDAMENTALS OF SIGNAL PROCESSING, INSTRUMENTATION AND CONTROL Laboratory No. 2 Signal Conditioning and Analog-to-digital Signal Conversion Issues 1. CREDITS Originated: N. R. Miller, July 1997 Last Updated: D. Block, September 2009 2. OBJECTIVES (a) Become familiar with the PC-based signal conversion hardware and software available in the laboratory. (b) Study the problems of aliasing and quantization error associated with the digital representation of analog signals. (c) Demonstrate the noise attenuation techniques of filtering and integration. 3. KEY CONCEPTS (a) Information is irreversibly lost when an analog signal is converted to digital form. The loss is minimized by sampling at a high rate and using a high-resolution digital representation. (b) A digitized sine wave appears to be a sine wave at a lower frequency if the sampling rate is less than twice the frequency. This effect, known as aliasing, distorts the frequency spectrum of any signal by mapping higher frequency components into lower frequency components. (c) Aliasing cannot be detected by examining the digitized signal alone. (d) Thermocouples measure temperature by producing millivolt-level signals. The leads of a thermocouple act as an antenna to pick up electrical noise from the environment. The amplitude of this noise can cause problems when measuring the output of the thermocouple. 4. SYNOPSIS OF PROCEDURE (a) Observe the effect of aliasing using the function generator, oscilloscope, audio earphones, PC-based data acquisition hardware, and MATLAB software. (b) Observe quantization error in a ramp function using the PC-based digital-to-analog conversion hardware. (c) Investigate the use of a simple, RC, low-pass filter to attenuate high-frequency noise. (d) Measure the output of a Type-T thermocouple using the digital multimeter. 5. PROCEDURE The procedure is presented at three levels of detail. The lowest level of detail is set forth in the synopsis above and the headings of this section. Review this information first to get a good intuitive feel for the overall scope of the experiment. The second level of detail is a brief description of each specific task often accompanied by a schematic or sketch. This description together with the Data Sheet is usually sufficient to understand and carry out the procedure during the laboratory session. The first two levels of the procedure described above should be thoroughly reviewed before coming to the laboratory. Skip over the detailed procedure in preparing for the laboratory session as this information only makes sense when the equipment is at hand. Important General Information – Please Read Carefully (a) Always turn off the power supplies when changing connections. Dangling leads can easily contact the metal tabletop creating a short, blowing a fuse, creating an unsafe situation or damaging the equipment. (b) Disconnect the leads from the instruments when not in use. (c) If your station is missing something, ask your Laboratory Assistant to replace it. Do not take items from other stations.2 5.1 Power On the Computer and Start the MATLAB Software (a) Turn on the power to your station, power on the computer, and start the MATLAB software. 5.2 Sine-wave Reconstruction Using Sampled Data Overview of Procedure The purpose of this part of the experiment is to illustrate the effect of aliasing. Aliasing occurs when the sampling rate of a periodic signal is less than twice the frequency of the signal. For a 1000-Hz sine wave, aliasing occurs if the sampling rate is less than 2  (1000 Hz) = 2000 samples per second. Aliasing is seen in the reconstructed waveform, which appears to be sine wave at a lower frequency. For example, consider an 1100-Hz sine wave sampled at 2000 Hz. The reconstructed signal will appear to be a sine wave at 900 Hz. Aliasing alters the observed frequency spectrum of a signal by mapping higher frequency components into lower frequency components. The effect of aliasing on spectrum analysis can be reduced by passing the signal through an anti-aliasing filter before it is digitized. An anti-aliasing filter is a high-order, analog, low-pass filter with a cutoff frequency that is half the sampling rate. The anti-aliasing filter attenuates the troublesome high-frequency components of the signal. For example, consider again the case of an 1100-Hz signal sampled at 2000 Hz. The signal will be aliased appearing to be a sine wave at 900 Hz. The proper anti-aliasing filter will have a cutoff frequency of 1000 Hz. If possible, the better solution is to sample at a rate sufficiently high to resolve all components of the signal. In this case, we should sample at a rate greater than 2200 samples per second. To demonstrate the effect of aliasing, we shall produce a sine wave at a specified frequency using the function generator. We shall then set up the PC-based system to sample the signal at 2000 samples per second with an analog to digital converter (ADC) and simultaneously output the sampled signal by sending the digital data back out through a digital-to-analog converter (DAC). This approach will allow us to make an easy and direct comparison between (a) the original signal from the function generator and (b) the reconstructed signal from the PC-based system. We shall visually compare the two signals by displaying the original waveform on Channel 1 of the oscilloscope and the reconstructed waveform on Channel 2 of the oscilloscope. We shall also use audio headphones to hear the difference. The original signal will produce a tone in the left earphone, and the reconstructed signal will produce a second tone in the right earphone. Aliasing will be evident when the tones are different. We shall begin with a sine wave at 100 Hz. Because the sampling rate (2000 samples per second) is much greater than two times the frequency of the signal (2  100 Hz = 200 samples per second), the reconstructed signal will be a very good approximation of the original signal. We shall then increase the frequency of the sine wave using the controls of the function generator. Aliasing will begin when the frequency of the sine wave reaches half the sampling rate or 1000 Hz. At 1200 Hz, for example, the reconstructed waveform will appear to be sine wave at 800 Hz, and the reconstructed tone will be correspondingly lower in pitch than the original tone. The disparity will