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This experiment enables a student to learn
- How to view the real life analog signal with an oscilloscope.
- How to set the amplitude, frequency and phase of the signal source.
- How to set the sampling frequency of the source such that the signal is exactly reconstructed from its samples.
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The real life signals that we encounter in our day to day basis are mostly analog signals. These signals are defined continuously in time and have infinite range of amplitude values. In order to process these signals to obtain meaningful information, they need to be converted to a format which is easily handled by computing resources like microprocessors, computers etc... The first step in this process is to convert the real-time signal into discrete-time signals. Discrete-time signals are defined only at a particular set of time instances. They can thus be represented as sequence of numbers with continuous range of values.
The process of converting an analog signal (denoted as x(t)) to a digital signal (denoted as x(n)) is called the analog-to-digital conversion (referred to as digitization), usually performed by an analog-to-digital converter (ADC). Here t is the continuous time variable and n is the sequence order. In many applications after the processing of the digital signal is performed, x(n) needs to be converted back to analog signal x(t) before it is applied to appropriate analog device. This reverse process is called digital-to-analog conversion and is typically performed using a digital-to-analog converter (DAC).
The typical block diagram of an ADC is shown in Fig. 1 below.
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The process of digitization consists of first sampling (digitization in time) and quantization (digitization in amplitude). In this experiment we will study and understand the principle of sampling, while the principle of quantization will be studied in the next experiment. The sampling process depicts an analog signal as a sequence of values. The basic sampling function can be carried out with an ideal 'sample-and-hold' circuit which maintains the sampled signal until next sample is taken. An ideal sampler can be considered as a switch that periodically opens and closes every T seconds. The sampling frequency (fs in Hertz) is thus defined as
fs=1T....(1)
The sampled discrete time signal x(nT) , n=0,1,2,.... of the original continuous time signal x(t) is shown in Fig. 2 below.
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In order to represent an analog signal x(t) by a discrete-time signal x(nT) accurately, so that the analog signal can be exactly reconstructed back from the discrete-time signal, the sampling frequency fs must be at least twice the maximum frequency component (fM) of the original analog signal. Thus we have,
fs≥2fm....(2)
The minimum sampling rate is called the Nyquist rate and the above Sampling Theorem is called the Shannon's Sampling Theorem. When an analog signal is sampled at fs , frequency components higher than fs/2 fold back into the frequency range [0, fs/2]. This folded frequency components overlap with the original frequency components in the same range and leads to an undesired effect known as aliasing. In this case, the original analog signal cannot be recovered from the sample data.
Consider an analog signal of frequency 1Hz as shown in Fig. 3(a) below. The sampling frequency is 4Hz. The sampled signal is shown in Fig. 3(b), Note that an exact reconstruction of the missing samples is obtained so long as the Shannon's Sampling Theorem is satisfied.
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Now let's consider, the analog signal of frequency 5Hz as shown in Fig. 4(a) below. The sampling frequency is same as above, i.e. 4Hz. The sampled signal is shown in Fig. 4(b), Note that the reconstruction of the original analog signal is not possible since the sampling frequency does not satisfy Shannon's Sampling Theorem. In this case the reconstructed signal has a frequency of 1Hz. The signal of 5Hz is folded back as 1Hz, into the range determined by the sampling frequency leading to the problem of aliasing.
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1.Click on the Experiment tab SIMULATORIt will open the workspace.
2.See the movie in experiment page by pressing help button ? to understand how the following steps are to be executed.
3.In the workspace click on Browse BlocksBROWSE BLOCKS.to understand how the following steps are to be executed.
4.Drag Sinewave Generator in the left side of the workspace. Click it to parameterize the sinusoidal signal output. Make amplitude = 3V, frequency = 19 Hz, phase=0 angle.
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5.Drag Sampling Block in the workplace. Place it after Sinewave Generator to its right. Click it to parameterize. Make sampling frequency =40 Hz. It will show no. of sample as 80 for display. The display is conformed for 2 sec.
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6.Drag the scope in the workspace after sampler to its right.
7.For making connection, take the cursor to the node provided in each block where form connection is to be made. Click on it a circle will appear in the background. If pointed properly a yellowish tinge will appear click at that time to enable connection.
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8.Connect sinewave generator O/P to I/O of sampler by clicking at both blocks and a link will appear.
9.Similarly connect sampler O/P to one of the I/O of scope.
10.Click somewhere in the middle of the link connecting signal generator & sampler. Keep clicking at bends till you connect it to the other input of the scope.
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11.Click on the scope, a new window will appear. It shows that the sinusoidal signal as well as sample in red dots.
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12.Move the cursor from one sample to another by draging the slider provide along the x-axis and you will find sample values in the boxes at bottom left part of the window. Note the first 15 values in a note book. This 15 values will go as table 1 in your report.
13.In this window, you can change parameters like frequency, amplitude and phase angle of sinusoidal signal generator & sampling frequency.
14.Change the sinusoidal signal generator O/P amplitude to 1.5V and note 1st 15 values. This will form Table 2 in your report. In your observation & discussion part of the reporting, you have to compare Table 1 and Table 2.
15.Change sampling frequency to 43 Hz and amplitude of sinusoidal signal generator at 1V. Note first 15 readings to from Table 3. Compare Table 1 and Table 3
16.Make sampling frequency 40Hz, amplitude of sinusoidal signal generator 10V, phase=30. Table 1st reading to from Table 4. Compare Table 1 and Table 4.
17.Under sampling:Change the Sinusoidal signal generator frequency 50Hz, amplitude 1.4V, phase=0. Sampling frequency= 40 Hz. Take 1st 15 readings. This will from Table 5. Compare Table 1 and Table 5.
18.Change the Sinusoidal signal generator frequency=30Hz, Amplitude=1V, Phase=0, sampling frequency = 40Hz. Take 15 readings. This will produce Table 6. Compare Table 1 and Table 6
19.Optional: Select sinusoidal signal generator frequency and sampling frequency simultaneously to form more Table, Table 7 and Table 8 which leads to nyquist rate from observation phenomenon.
20.Click on Report Generation button. The reporting window will appear. Here on by clicking Add Table , you can add tables. In each tables, by clicking add row will be able to add row.
21.For each table make a screenshot of your plots by taking print screen and edit in any image editor to upload a image for each table.
22.The observation and discussion box, appears at the end. Then click Yes I have finished my Experiment button to submit your report.
23.Note: if at any time during making circuit if you face any problem please use reset button to erase the circuit and draw the circuit freshly.
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Quizzes content.....
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Books:
- Discrete-Time Signal Processing, A. V. Oppenheim and R. W. Schafer, Englewood Cliffs, NJ: Prentice Hall, 1989.
- 2.C. E. Shannon, "Communication in the presence of noise," Proc. Institute of Radio Engineers, vol. 37, no. 1, pp. 10-21, Jan 1949.
- 3.H. Nyquist, "Certain topics in telegraph transmission theory," Trans. AIEE, vol. 47, pp. 617-644, Apr 1928.
Video Lectures: