Indian Institute of Technology Kanpur s2

Indian Institute of Technology Kanpur EE 381 Electrical Engineering Lab-II 2003 – 04; Semester II Experiment #2 Coherent Multipoint Averager Goal: Extraction of a periodic signal immersed in noise using coherent multipoint averaging technique. Introduction: A periodic signal immersed in uncorrelated noise having zero mean can be reconstructed by coherently sampling the noisy waveform (i.e. sampling at the same instants in each period of the waveform) and averaging the corresponding samples over a large number of periods. Since noise in successive periods is independent, it averages to zero, while the signal being the same, adds up.

Let the input signal be yi= s + e i which is composed of a periodic portion s and a noise portion ei . If N copies of the signal are taken and averaged, the output signal would be,

y=1 s + 1 e oN邋 N i

Since the signal is the same in every copy, s= Ns . Since the noiseis assumed to be uncorrelated, the rms value of noise at the output can be expressed as

2 1 1 2 ei ( rms ) eo( rms ) =( 邋 e i) = e i = N N N The above equation suggests that by making N very large it is possible to reduce the noise at the output of the averager. Because of the difficulties in obtaining and averaging several copies of a continuous time signal, the averaging scheme described above is implemented at discrete time intervals only. If the periodic signal is sampled M times, then M output samples with reduced noise will be available. Specification: Design a multiple point coherent averaging scheme for a signal corrupted by noise.

Implement your design using the schematic shown in Fig. 1. The choice of Rs and Cj ; j = 0 7 determines the time constant of the integrator. Output Multiplexer Co

Experiment ei s Rs +

Signal Timing and Sampling Pulse Generator

Fig. 1: Schematic of a multipoint averager Use the circuit shown in Fig. 2 to obtain the periodic signal. Choose a clock frequency of 2kHz for the design. Choose the values of R and C such that the periodic signal resembles as shown in the figure. This ensures that the signal to be

0c03479ee848493fefdf0093d4c0eb6b.doc 1 of 2 Indian Institute of Technology Kanpur EE 381 Electrical Engineering Lab-II 2003 – 04; Semester II measured is in synchronization with the clock. The counter outputs Q0, Q1 and Q2 are used as the control input to the multiplexer.

Q0 s Divide by 16 counter Q 1 R Clock Q2 Q C 3 t

Fig. 2: Scheme to generate the signal

Use an opamp adder to sum the signal and noise. Use a potentiometer to set the noise level. Use the following integrated circuits in your design: Counter: CD4029; Multiplexer: CD4051; Opamp: ua741 Verification: Breadboard the counter and feed a clock of 2kHz and confirm its operation. Connect the Q3 output to Ext. Trig. of CRO and set the oscilloscope to Ext. Trig. mode during all observations. Breadboard the opamp adder, which is used to add noise to the signal. Observe and sketch the output of the adder (signal plus noise) for different values of potentiometer settings. Connect the signal and noise out of the adder to the multiplexer and integrator. Observe and sketch the waveform at the output (shown in Fig. 1) with (a) no noise added, (b) noise amplitude approximately equal to the signal amplitude, and (c) noise much greater than the signal amplitude. Repeat the above step for clock frequencies of 1kHz, 1.5kHz, 2kHz and 4kHz.

CD 4029

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