### Introduction

Telecommunication is the science of transferring information from one point to another. There are countless ways of encoding, modulating, transmitting and receiving this information; the most common methods may be grouped together under convenient titles, e.g. Amplitude Modulation, Time Division Multiplex, Pulse Code Modulation etc. Another important aspect of telecommunication is the effect of noise and interference upon the information signal, as it traverses the Transmission Lines between transmitter and receiver. The later chapters in this book are each concerned with one of the above aspects of Telecommunications or with other closely related topics.

However, the first chapter is concerned with the basis of all Telecommunication Systems – the information signal itself.

An information signal is generally a voltage or current which is derived from the data to be communicated. If this voltage or current is recorded or displayed over a period of time, the resulting shape is called the waveform. The Telecommunication Engineer needs to know the characteristics of this waveform to be able to design the most effective system for transferring it from one point to another, without significant changes in its shape. This is the reason for waveform analysis.

The main parameters of interest are the amplitude and frequency of the waveform. However, waveforms are made up from a series of component frequencies, the amplitude of the components giving the waveform its shape. For the system to pass the waveform without distortion, the amplitude of the component frequencies must be known so that the system can be designed to pass them all equally.

This experiment enables periodic waveforms to be produced, and their components analyzed. The lowest frequency of a periodic wave is called the fundamental, the others are called harmonics.

### The Apparatus

The Waveform Analysis apparatus consists of a 16-bit recirculating shift register, with the sixteen sliders controlling the amplitude of the output waveform, each slider setting the level of its respective section of the waveform. The reset switch ensures that a single pulse circulates through the register. From time to time it may be necessary to operate this switch if an extra pulse is injected into the shift register. This is shown by the sliders affecting more than one section of the waveform.

The following additional equipment is required:

1. Audio signal generator.
2. Audio amplifier and speaker.
3. An oscilloscope.

### Observation of Waveforms

Connect the oscilloscope and audio amplifier to the blue output terminal of the 16-bit Waveform Generator. Connect the 'External Trigger' socket to external trigger on the oscilloscope, and switch the oscilloscope to 'external trigger'.

Set the sliders 1-8 at the top of their travel, and 9-16 at the bottom of their travel. Switch ON and operate the 'Reset switch'. With the oscilloscope set to about 1mS/cm time base and 5volts/cm amplitude, observe the reproduction of the waveform, and listen to the output of the audio amplifier with the volume control set to a convenient level.

The periodicity of a waveform is the time between exactly equivalent points on the waveform. Measure the periodicity of this waveform.

The waveform is symmetrical (i.e. any half period is a mirror image of the other half period about the horizontal mean axis) and therefore has no even harmonics. However, all odd harmonics contribute to the waveform the lowest of which has the periodicity measured.

This lowest note is the basic pitch or fundamental, and the harmonics give the note its harsh tone. We will call this fundamental frequency f0.

If the eighth slider is moved to the bottom of the panel, the waveform becomes asymmetrical and the second harmonic can be heard. This is a sine wave component at a frequency of twice the fundamental, i.e. 2f0.

A tone with a fundamental at 2f0 i.e. half the periodicity previously measured may be set up by having sliders 1-4 and 9-12 up and 5-8 and 3-16 down.

Set up waveforms on the panel which have fundamentals at:

a) 4f0. b) 8f0.

Set 15 of the sliders at the bottom of the panel, with the remaining one at the top. What is the fundamental frequency of this impulse waveform? Set up a symmetrical saw tooth waveform of fundamental frequency f0 e.g. sliders 1 and 16 at the bottom of the panel, 8 and 9 at the top, and the remainder linearly displaced between them. Compare the tone quality of this waveform with the impulse waveform. Which waveform do you consider to have the higher harmonic content?

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