13 Teaching DSP and Dynamic Measurements at the Graduate Level at Michigan Technological University 149 13.4.1 Basic Data Acquisition This assignment includes the acquisition of data using both a digital oscilloscope and the NI software. This assignment is given in the first week of the semester with the sole purpose of exposing the students to the process of acquiring data using both instruments, importing the data into Matlab, and plotting the data in Matlab. 13.4.2 Sampling and Quantization This assignment involves acquiring data using both the oscilloscope and the NI system as well as simulating both systems in Matlab. The students are given signal characteristics, frequency and amplitude as well as waveform type, which they use a signal generator to generate for acquisition and which they must generate themselves in Matlab. If the data is generated in Matlab, the students use “uencode” and “udecode” to simulate the effects of quantization. The students then plot the functions, sine waves and square waves of varying amplitudes, and see the effects of both sampling and quantization as the NI 9234 module has a 24 bit ADC while the oscilloscope has an 8 bit ADC. 13.4.3 Leakage, Windows, and FFT The students first acquire data which are sine waves with different frequencies. The students set the sample frequency of the NI system based on a combination of a few digits of their student ID numbers, this forces the students to have different sample rates and hence differences in their assignments as a way to reduce collaboration and at least require them to each acquire their own data. In this assignment the students must generate frequencies with minimum leakage, maximum leakage, and then apply the Rectangular, Hanning, and Flattop windows to their effects on these frequencies. This assignment also has the students using the “FFT” command in Matlab to compute linear spectra. The “FFT” command in Matlab requires that the students apply several scaling factors to their results and discard the negative frequency information. The scaling which the students must do includes applying the Amplitude Correction Factor based on the window used, dividing by the blocksize, multiplying all frequencies above DC by 2 to account for energy discarded with the negative frequencies. No averaging is done as a part of this assignment. The students struggle to get the scaling correct, the most common error being the wrong scaling to the DC component of the spectra, the students want to multiply this value by 2 but since there is no DC component discarded with the negative frequencies this frequency is not multiplied by 2. In the lectures to support this assignment, the Fourier Transform is derived using both the mathematics of the transform and a series of pictures/plots which show that the reason the that transform works so well, and that any transform works, is that the kernel of the transform “looks like” the aspects of the data that is desired to be understood. Having the students realize that we are performing this “coordinate transformation” so that the data is easier to understand helps them gain much more confidence as to why the transform works. I have them visualize trying to describe a pop can using a Cartesian coordinate system, a Spherical coordinate system, and a Cylindrical coordinate system and ask them which is easier to do: : : obviously the cylindrical coordinate system because the can looks like a cylinder. It would be very difficult to look at the coordinates of a can in spherical coordinates and realize what you were looking at! 13.4.4 FRF and Coherence This assignment includes the students making FRF measurements with broadband random noise and estimating the gain of the system using individual sine waves. Students also acquire the time domain signals of the broadband input and the response. In this assignment, the system used in the experiments is shown in Fig. 13.1. In this assignment the students program in Matlab both the H1 and H2 FRF estimators as well as coherence. Linear averaging is implemented as part of the processing. The FRFs and the individual frequency based gain measurements are overlaid in plots so that the students can see that it does not matter whether an FRF is measured using broadband or individual frequencies for a linear system. The most common mistake the students make in this assignment is averaging the linear
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