Telecommunications Lab 4 Pulse Code Modulation (1)

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Humber College *

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WLS5506

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Electrical Engineering

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Apr 3, 2024

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Student Name____ __________________ WLS 5003 Telecommunication System L AB 4 – P ULSE C ODE M ODULATION (PCM) Objectives: In this workshop you will: 1. Learn the steps to convert an analogue signal into a digital signal. 2. Learn about the effects of sampling rate on signal quality. 3. Learn about the effects of number of Quantization levels on signal quality. Equipment: 1. Internet network access 2. Matlab (Accessible through https://its.humber.ca/appstream ) Introduction You have learned in class that in order to be multiplexed onto a single line for transmission through trunked lined, the voice information from individual telephones is digitized first. After the voice information is digitized, the signals from several telephones are combined using time division multiplexing. In this lab, you will learn the effect that the sampling rate has on signal quality. First, you will go through some theoretical concepts then you will create a simulink project in Matlab to produce a PCM coding and decoding. In the simulink project you will observe the effect of low sampling rate vs. high sampling rate; then you will observe the effect of number of Quantization levels on output signal. Part 1 Nyquist Sampling rate and Quantization levels 1. Recall from the class, according to Nyquist sampling theorem what should be the minimum sampling rate (sampling frequency)? F s (minimum sampling rate) = 2f m (maximum frequency) 2. In a voice signal with bandwidth 4 kHz, what should be the minimum sampling frequency? F s (minimum sampling frequency) = 2f m F s = 2 x 4kHz = 8kHz Muhammad Masud (Fall 2020) Page 1

Student Name____ __________________ 3. A signal has 10 kHz of bandwidth with minimum frequency of 1000 Hz. Calculate the minimum sampling frequency for this signal. f m (maximum frequency) = 10kHz + 1000Hz = 11000Hz Fs (minimum sampling frequency) = 2fm = 2x11000 Hz = 22000Hz 4. Recall from the class, what effect the number of Quantization levels has on signal quality? When the number of quantization levels increases it increases the quality of the signal. More quantization levels result in higher resolution so that digital representation can better capture the fine details and nuances of the original analog signal. It also leads a higher signal to noise ratio. Fewer quantization levels can introduce quantization distortion while higher q.l. reduces distortion. Part 2 Analog to Digital Conversion 1. List the steps involved in PCM. Sampling, Quantization & encoding. 2. What is sampling? What are common types of sampling? Sampling is the process of capturing and converting continuous analog signals into discrete digital values at regular intervals. It's a fundamental concept in digital signal processing and allows for the representation, transmission, and processing of real-world signals using digital technology. Ideal Samling Natural Sampling Flat-top Sampling 3. What is Quantization and Quantization noise? How does the Quantization noise affect the quality of signal? Muhammad Masud (Fall 2020) Page 2

Student Name____ __________________ Quantization is the process of approximating a continuous signal by representing it with a limited number of discrete values. Quantization noise is the error or distortion introduced during this process due to the difference between the original continuous signal and its quantized representation. It often appears as random noise in the digital signal. Quantization noise degrades signal quality by introducing errors and unwanted noise, reducing accuracy, fidelity, and the signal-to-noise ratio. 4. What is encoding? How is it related to number of Quantization levels? And what affect it has on the data. Encoding is the process of representing data in a specific format, often in a more efficient or usable way. It is related to the number of quantization levels in that encoding involves assigning digital values to analog signal levels. The number of quantization levels determines the encoding precision. More levels provide finer encoding detail, improving data accuracy, but also increasing data size and complexity. Conversely, fewer levels reduce detail, potentially degrading data quality. Part 3 Simulink (Matlab) project for PCM Create a Simulink (Matlab) project to implement PCM as shown in Figure 1. (Hint: Watch the video at the link https://www.youtube.com/watch?v=cp40kS1nMUI ). Figure 1: Simulink Project Circuit 1. In Figure 1, compare and contrast the signals at output Time Scope. Channel 1 shows input signal and Channel 2 shows output signal? Muhammad Masud (Fall 2020) Page 3

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Student Name____ __________________ 2. What is frequency of Sine wave? 2*pi*2 rad/sec 3. What should be minimum sampling frequency for this signal? Signal frequency = 2*pi*2 = 12.57 Hz Fs ≥ 2 * f Fs ≥ 2 * 12.57 Hz ≈ 25.14 Hz Muhammad Masud (Fall 2020) Page 4

Student Name____ __________________ 4. What sampling frequency is used in this simulation? T = 1/20s f s (sampling frequency) = 1/T= 20Hz Fs = 25.14 Hz 5. How many Quantization states are used in this simulation? L = 2^N_bits = 2^3 = 8 L - the number of quantization levels. N - the number of bits used for quantization. 6. Change the sampling frequency by changing period to ½. Observe the output. 7. Increase the sampling frequency by changing period to 1/40. Observe the output. Muhammad Masud (Fall 2020) Page 5

Student Name____ __________________ 8. Set the period back to 1/20, and now change the encoding bits to 2. Observe the output. Muhammad Masud (Fall 2020) Page 6

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Student Name____ __________________ 9. Change the encoding bits to 8. Observe the output. Muhammad Masud (Fall 2020) Page 7

Student Name____ __________________ Part 4 Supplemental Questions 1. Is under sampling adequate to reproduce the signal at the output? Why or why not. Under-sampling may not be adequate to reproduce the signal accurately at the output because it can lead to aliasing. Aliasing occurs when high-frequency components of the signal are folded back into the lower frequency range, causing distortion and loss of information in the reconstructed signal. To avoid aliasing and faithfully reproduce the original signal, it's generally necessary to sample at or above the Nyquist rate, which is twice the highest frequency component in the signal. 2. What could be a possible drawback of oversampling? A possible drawback of oversampling is the increased data volume, which can consume more storage space and bandwidth. 3. What could be a possible drawback of low number of Quantization levels? A possible drawback of a low number of quantization levels is reduced signal accuracy and loss of fine detail in the digital representation. Muhammad Masud (Fall 2020) Page 8

Student Name____ __________________ 4. Typically how many Quantization levels are used for voice signal? Voice signals are often quantized using 8 to 16 bits per sample. It provides a reasonable balance between audio quality and data efficiency for most communication and recording applications. A higher number of quantization levels, such as 16 bits, offers better audio quality, while a lower number, such as 8 bits, sacrifices some quality for reduced data size. The specific choice depends on the application's requirements and available resources. Muhammad Masud (Fall 2020) Page 9

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