EXPERIMENT #7 DATA ACQUISITION 1/27/2010 Group: DATA ACQUISITION PURPOSE The objectives of this laboratory are: 1. To examine signal sampling, aliasing and signal reconstruction. 2. To implement a time division multiplexing system. 3. To investigate the quantization error associated with analog-to-digital conversion. EQUIPMENT LIST 1. PC with Matlab and Simulink. LABORATORY PROCEDURE I Sampling A. The time division Multiplexer (TDM MUX) module is used to recombine two analog signals into one data stream. The input A is connected to the OUT connector for a period T (T = 1/fs). During the next period, input B is connected to the OUT connector. The process then repeats. It should be obvious that each input, input A(or B) is “Sampled” at a rate equal to ½ fs as set by the Master clock. NOTE: The actual waveform sampling rate = ½ fs as set by the “DATA/Sampling RATE”, output, mentioned above (e.g. to sample a 1kHz cosine, using this equipment at the Nyquist rate then fs would have to be set to 4 kHz) B. Next the fs were set to 10kHz and the function generator frequency was set to 1kHz. The output signal OUT was observed on a scope and was also compared with the input on a dual channel scope. The value of fs was slightly adjusted for a stable display. The scope was moved to the sample-and-hold (S & H) output. We see that the amplitude variations during the sampled period are now replaced with a constant “flat top”. Figure 7a – Sampling using Sample and Hold The input signal looks like the one shown in figure below Figure 7a input of the sampling using sample and hold method Figure 7a Output of the Sample and hold circuit t The result when the input is overlapped with the output is what is shown below. C. Next the function generator was connected to both the inputs A and B. at the OUT connector of the TDM MUX, the generator’s signal appears undistorted. We see that after moving the scope tot he S & H connector the signal is now being sampled at fs. (See figure 7B). figure 7b(a) Time Division Multiplexing - Implementation figure 7b (b)Time division Multiplexing – Input signal figure 7b(c): Time division Multiplexing, Output D. The output spectrum of the S & H output is observed. Values of f and fs are varied and the effects of aliasing observed. E. Effect of filtering: The sampled signal was reconstructed by feeding through a 4 th order LPF to remove the aliasing frequencies. II Time Division Multiplexing A. Although multiplexing not classified as “data acquisition,” we shall make use of TDM modules at this time. Two sine waves were prepared to be multiplexed by setting the two VCO’s in open loop to 1 kHz and 2 kHz. Connect the 1 kHz sine wave to the A input and 2 kHz since wave to the B input (see figure 7c). Set fs for 10kHz. The output OUT and S & H outputs in time and frequency domain were observed. Yes, we can say that sampling frequency for the TDM system is fs/2. (i.e half the time you sample A and half the time you sample B) Figure 7c (a) Muxed signals B. The S & H signal was connected to the TDM DEMUX. Internal timing connects the TDM DEMUX input signal to the A output when the A input signal is selected by the MUX. Similarly, the B output is connected to the DEMUX input when the MUX selects input B. Thus, the TDM signal becomes “demultiplexed”. The Dual LPF was used to reconstruct the S & H DEMUX output waveforms. All the waveforms observed are attached. Figure 7c (a) Output of Signal 1 of TDM Figure 7c(b) Implementation of 2 signal TDM Figure 7c(c) Output of the two signal TDM III A/D conversion A. Now the conversion of analog to digital pulse is considered. This conversion is part of the pulse code modulation (PCM) system. B. There is an inherent noise component in the system due to the quantization of the signal in the PCM encoding and decoding. This noise is the error between the actual value of the analog input and the decoded analog signal from the PCM-ANALOG module. If we were to subtract the resulting quantified signal from the original signal, a noise voltage would result. This could then be used to form a quantization signal- to-noise power ratio. Figure 7(III) a – The pulse code modulation with variable quantization Here is a plot of the input signal (Analog) to the PCM system Figure 7(III)b Input signal The quantized signal is given below Figure 7(III)b Quantized signal The input file is quantified using the PCM encode and de-quantified using the PCM decode block. The block parameters are shown below Figure 7(III)b Quantizer parameters Figure 7(III)d DE- Quantizer parameters The output of the decoder is fed to a subractor block, which takes the difference of the input signal from the output and gives the signal noise generated. The noise generated and the numeric value is also shown. . EXPERIMENT #7 DATA ACQUISITION 1/27/2010 Group: DATA ACQUISITION PURPOSE The objectives of this laboratory are:. II Time Division Multiplexing A. Although multiplexing not classified as data acquisition, ” we shall make use of TDM modules at this time. Two sine waves