21-05-2013, 04:05 PM
SAMPLING THEOREM VERIFICATION
Aim:
To verify the sampling theorem.
Apparatus:
1. Sampling theorem verification trainer kit
2. Function Generator (1MHz)
3. Dual Trace Oscilloscope (20MHz)
Theory:
The analog signal can be converted to a discrete time signal by a process called sampling. The sampling theorem for a band lilmited signal of finite energy can be stated as, “A band limited signal of finite energy, which has no frequency component higher than W Hz is completely described by specifying the valules of the signal at instants of time separated by 1/2W seconds.”
Procedure:
1. The circuit is connected as per the circuit diagram shown in the fig1.
2. Switch on the power supply and set at +11V and -11V.
3. Apply the sinusoidal signal of approximately 4V (p-p) at 105Hz frequency and pulse signal of 11V(p-p) with frequency between 100Hz and 4KHz.
4. Connect the sampling circuit output and AF signal to the two inputs of oscilloscope.
5. Initially set the potentiometer to minimum level andsampling frequency to 200Hz and observe the output on the CRO. Now by adjusting the potentiometer, vary the amplitude of modulating signal and observe the output of smplling circuit. Note thet the amplitude of the sampling pulses will be varying in accordance with the amplitude of the modulating signal.
6. Design the reconstructing circit. Depending on sampling frequency, R & C values are calculated using the relations Fs = 1/Ts, Ts=RC. Choosing an appropriate value for C, R can be found using the relation R= Ts/C.
7. Connect the sampling circuit output to the reconstructing circuit shown in Fig:2.
8. Observe the output of the reconstructing circuit (AF signal) for different sampling frequencies. The original AF signal would appear only when the sampling frequency is 200Hz or more.