Digital communication engineeringLab report Sampling Experiment

Dineth Kanishka Ponnamperuma 15647272

ABSTRACT:In modern-day communication systems, digital communication has made the electronic and electrical based communication system very robust and dominant over analog communication techniques. A digital system introduces significantly low error rates, low distortion, less prone to noise, and has the ability to be transported in a reliable format. In all digital communications the analog information is converted digital equivalent and vice-versa. The conversion process from analog to digital involves three stages, first comes the sampling process then the sampled signal is introduced into amplitude qunatizer and in last encoding of the quantized signal is done.In this experiment, we come to understand the two sampling processes. The first one is the Natural sampling process in which the sample taken is not held until the next sampling instant. The second one is the Sample and hold process in which the taken sample is held until the next sampling instant. In this experiment we observe the sampled signal obtained by applying both sampling processes and compare them in order to determine which technique is more preferred over the other.

INTRODUCTION:

In signal processing, sampling is the reduction of a continuous signal to a discrete signal. A common example is the conversion of a sound wave (a continuous-time signal) to a sequence of samples (a discrete-time signal). Such a transformation process is commonly referred to as analog-to-digital conversion, which typically involves (i) sampling in time, (ii) quantizing in amplitude, and (iii) encoding into a binary format. This experiment demonstrates the sampling process based on (i) natural sampling, and (ii) sample and hold operation. (I) Natural samplingThe natural sampling process is performed in this experiment using an analog switch gated by a rectangular pulse train, g(t), of period T and duration , as shown in Fig. 1a. Whenever the switch is on, the sampled output, s(t), is a slice of the input waveform, v(t), as shown in Fig. 1b.

Nyquist sampling theory states that the sampling rate must be at least two times the frequency of the signal in order to obtain a true representation of the signals frequency.F(g) 2BWhere f(g) is the sampling rate and B is the highest frequency being measured. The error associated with sampling at a low rate is called aliasing.

Mathematically, the natural sampling process can be represented in the time domain asS (t) =V (t)*g (t)The Fourier transform of the output signal is given by:

Where the V (f) and G (f) are the Fourier transform of v (t) and g (t), respectively.

(II) Sample and hold In electronics, a sample and hold circuit is used to interface real-world signals, by changing analog signals to a subsequent system such as an analog-to-digital converter. The purpose of this circuit is to hold the analog value steady for a short time while the converter or other following system performs some operation that takes a little time.

In this experiment, this sample and hold operation is carried out by replacing the analog switch of Fig. 1a with an Integrate and Dump module. The resulting sampled waveform is shown in An objective of this experiment is to demonstrate that the holding function behaves as a lowpass filter with a frequency response given by

METHOD:TASK 1:1. Function Generator was used as the sampling clock source. Set it to provide an 8 kHz unipolar rectangular pulse output with an amplitude of 4 Volts as observed on Digital Oscilloscope.

2. Set the % Duty of the output pulse to 20 % from the function generator. 3. Connected the three TIMS modules and other external equipment

4. Connected all the ground terminals to the ground terminal on TIMS module. After the connections have been checked, power was switched on at the back of the TIMS System.

5. Adjusted the Audio Oscillator module to provide a 2 kHz, measured using the TIMS Frequency Counter, sinusoidal message signal. 6. Observed the sampled waveform at the output of the Dual Analog Switch. Used the RUN and STOP storage operations of the to take a snapshot of the waveform. 7. Set the range of the Tunable LPF module to WIDE.

8. Calculated the -3dB cutoff frequency of the module.

9. Observed the spectrum of the sampled waveform from dc to 3 KHz in Hanning window using the FFT function on the oscilloscope.

10. Set the sampling rate to 100KSa/s and observed the amplitude resolution in the Flat-top window.

11. Set the Low pass filter cutoff frequency to 3 KHz and observed and compared the waveforms.

TASK 2:1. Replaced the Dual Analog Switch with an Integrate and Dump module.

2. Repeated the sampling experiment, i.e., steps 1 8 of Task 1, using the Integrate and Dump module.

TASK 3:1. First used the Dual Analog Switch module for sampling.2. As input signal, needed an audio source. Therefore connected a broadcast radio channel as our audio source.3. Amplified the audio signal using the Buffer Amplifiers module on the TIMS. Ensured that the output is 4 V P-P. Used this filtered output instead of the Audio Oscillator connections.4. Set the Tunable LPF to 3 KHz, and then used it to reproduce the reconstructed audio signal.5. Connected the handset as the output device.6. Varied the sampling frequency from 8 KHz to 2 KHz and observed the distortion that arises due to aliasing.7. Repeated the experiment by changing the setup from Analog Switch to the Integrate and Dump module.RESULTTASK 1: Firstly, about the practical part, to obtain a unipolar pulse output, we need to adjust the offset Vdc of the input to 1 Volt. The -3dB cutoff frequency of the low pass filter is give by CLK frequency /100, so we set the CLK (Frequency Counter) of the Tunable LPF at 300 kHz. For this laboratory, we realize that before plugging in any cable to connect between devices and between components of the TIMS, we should check the input/output of every component before moving on setting the next part, therefore, we can manage our installation better and we can observe clearly the sampling procedures. The picture below shows the sampled waveform obtained with natural sampling:

The next picture is the reconstructed waveform compared to the input signal.

The reconstructed signal is a sinusoidal signal with f = 2kHz. The recovered signal is delayed compared to the original signal because the low pass filter itself has delay. Moreover, we can see the Vpp of the reconstructed signal is equal to 1.29 V which is smaller than the amplitude of the original value. However, as our reconstructed signal has exactly same form as the original value, despite some delay and amplitude scaling, we still can consider it is a successful recovery. In order to more understand about the spectral component of the output, we observe the FFT of the output:

By looking at the spectrum component, we can see the fundamental harmonic is at f = 2 kHz, then the next harmonic component is respectively 4 kHz, 6 kHz, etc... Basing on Nyquist criterion, the sampling frequency has to be greater or equal to 6 kHz, else aliasing occurs. In the next step, we try to change the sampling frequency from 8 kHz to 6 kHz, 4.5 kHz and 3.5 kHz then observe the changes. The following picture obtained when we changed the sampling frequency from 8 kHz to 6 kHz. We can see that the recovery signals still a sinusoidal signal because our sampling frequency still respects the Nyquist criterion.

The below picture shows the original signal and reconstructed signal when we changed the sampling frequency to 4.5 kHz. We can see the reconstructed signal started to become distorted because the sampling frequency is small than the Nyquist rated, hence aliasing occurred.

The next picture is the capture of the original and reconstructed signal when the sampling frequency equal to 3.5 kHz. Similarly to the previous case, the distortion of signal is significant because of the aliasing occurred

TASK 2: The picture below shows the sampled waveform obtained with sample-and-hold sampling, the sampled signal looks like a stair case approximation to the original analog signal.

The reconstructed signal is a sinusoidal signal with f = 2 kHz. We can see the Vpp of the reconstructed signal is equal to 8V which is greater than the amplitude of the original value. However, as our reconstructed signal has exactly same form as the original value, despite some delay and amplitude scaling, we still can consider it is a successful recovery.

In order to more understand about the spectral component of the output, we observe the FFT of the output:

The spectrum of a sample-and-hold sampling output consisted of uniformly spaced copies of the original analog spectrum where the space between adjacent copies is equal to the sampling rate. The magnitude decreases when the frequency decreases. Basing on Nyquist criterion, the sampling frequency has to be greater or equal to 6 kHz, else aliasing occurs. In the next step, we try to change the sampling frequency from 8 kHz to 6 kHz, 4.5 kHz and 3.5 kHz then observe the changes. The following picture obtained when we changed the sampling frequency from 8 kHz to 6 kHz. We can see that the recovery signals still a sinusoidal signal because our sampling frequency still respects the Nyquist criterion.

The below picture shows the original signal and reconstructed signal when we changed the sampling frequency to 4.5 kHz. We can see the reconstructed signal started to become distorted because the sampling frequency is small than the Nyquist rated, hence aliasing occurred.

The next picture is the capture of reconstructed signal when the sampling frequency equal to 3.5 kHz. Similarly to the previous case, the distortion of signal is significant because of the aliasing occurred

TASK 3: By using Analog Switch module, we tried to listen to the audio output by using the telephone headset, and then we varied the sampling frequency from 8 kHz to 2 kHz. From 8 kHz to 6 kHz, we could hear clearly the audio output without noise or strange sound. From 6 kHz to 4.7 kHz, we heard more noises and strange sound from the radio; moreover, the voice of talkers became distorted slowly. However, we still could guess and understand the conversation. From 4.7 kHz to 2 kHz, we only heard noise and distortion voice from the radio; hence, we did not understand the conversation. By using Integrated and Dump module, we did the same with what we did to the Analog Switch module. From 8 kHz to 6 kHz, we could listen to and understand the talkers. From 6 kHz to 3.6 kHz, we still could hear and understand the conversation besides noises and distorted voice. Fro, 3.6 kHz to 2 kHz, we could not recognize the voice, the noise as well as we could not understand anything on the radio. From the experiment, we conclude that the Integrated and Dump system has a lower minimum sampling frequency that human still can hear and understand the audio signal because it takes a sample and hold it until the next sample available when in the Analog switch system, it takes a sample whenever the analog switch is on.

DISSCUSSION:

In the first task we dealt with natural sampling in which the sample is not held until the next sample is taken, sampling was performed on a sinusoid signal of 2 KHz frequency which we obtained from the Audio Oscillator module. The signal is then fed to the Dual Analog Switch module which was the switch used to perform sampling. The switch was controlled by the frequency which we applied from the function generator. Then the sampled signal was given as an input to the Tunable LPF module to band limit the signal the signal so that Aliasing could be avoided. We were provided with a range of frequencies such as 8 kHz, 6 kHz, 4.5 kHz and 3.5 KHz. From 8 KHz to 6 KHz the sampled signal was not affected by Aliasing because the Nyquist criterion (f >= 6kHz) was being satisfied but as we had moved to 4.5 kHz, 3.5 kHz Aliasing occurred because they are smaller than the Nyquist rate, we can see the signal distorted.

In the second task, the experiment was a replica of the first part but this time Dual Analog Switch module was replaced with Integrate and Dump module which provided the sample and hold function. Again a sinusoidal wave of 2 KHz was applied to theIntegrator and Dump module from the Audio Oscillator module for sampling. Holding is performed to allow sufficient time for completing the quantizing and encoding operations before the arrival of the next sample. Then again the output from the Integrator and Dump module from Integrator and Dump was passed through the Tunable LPF module to band limit the signal, so the Aliasing can be avoided. We again used a range of frequencies such as 8KHz, 6KHz and 4.5 KHz. From 8 KHZ to 6 KHz the sampled signal was not affected by Aliasing, but as we came down to 4.5 KHz Aliasing occurred and it was very prominent.

In the Task 3, an external audio signal from a radio was given as a input to the TIMS (Telecommunications Modelling System) module for sampling. We used different frequencies from the function generator and listened to that signal on the handset to observe the effect of different sampling frequencies on it different frequencies and heard the output of the sampled signal on Telephone handset. By listening to the sound we observed that as the frequency was increased the signal became very clear and when the sampling frequency was deceased the signal became distorted and its quality decreased significantly due to Aliasing.

CONCLUSION:

In this experiment, we came to understand the sampling process. There were two sampling processes involved one is Natural sampling process in which we used the Dual Analogue Switch module and in the second Sample and hold process in which we used the Integrate and Dump module. We observed both the processes on an oscilloscope (to view sampled signal) in the frequency domain and a telephone headset (to hear sampled signal) which helped us to understand the differences between the two sampling processes. In conclusion, the Sample and Hold produced better results in producing an audio signal which has a louder volume (but has additional noise throughout the bandwidth) and the Natural Sampling process has a clear audio signal (but is softer than the sample and hold method).

The TIMS telecommunications modeling system was difficult to use accurately due to the noise (which distorts signal) produce by external sources. However by approximating the signal amplitude, the experiments were carried out and decent results were produced.

The Oscilloscope storage function proved to be an essential tool in viewing distorted signals. With the oscilloscope, it was easier to understand the effects of the cut-off frequency as the FFT signal peaks into cut off depending on the cut-off frequency.

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