e would be created by the addition of further odd harmonics. A second common waveshape is the saw tooth waveform which Figure 10.3 Phase difference contains a fundamental frequency and all the odd and even har- monics to infinity. Digital signals 10/5 monics. Therefore the sound waves produced by human voices contain a range of frequencies which is known as bandwidth. Fundamental Voice frequencies lie within the band 100Hz to 10000Hz. The frequency pitch of the voice is determined by the fundamental frequency of the vocal chords and is between 200Hz and 1000Hz for women and between 100Hz and 500Hz for men. The tonal quality and the individuality are determined by the higher frequencies that are produced. Third The power content of speech is small, an average being between harmonic 10 and 20 microwatts. The distribution of the power is not even, with most of it being contained in the region of 500Hz for men and 800Hz for women. The notes produced by musical instruments occupy a much larger frequency band than occupied by speech. Some instruments, such Fifth harmonic as the drum, have a fundamental frequency of 50Hz or less, while others, such as the violin, can produce a note which has a harmonic content in excess of 15000Hz. An orchestra may generate a peak f + 3 f + 5 power in the region of 90 to 100 watts. Resultant In practice not all frequencies produced are transmitted to the square receiver. There are two principal reasons for this. Firstly, it is more t wave economic to use devices in circuits that have a limited bandwidth and, secondly, on long distance routes a number of circuits are transmitted over a single telecommunications link and this provides a further limitation on bandwidth. Figure 10.5 Amplitude addition At the receiving end of the speech or music the sound waves impact on the ear and cause the ear drum to vibrate. The ear can only hear sounds that lie within certain limits. The minimum sound level that can be detected by the ear is known as the threshold or audi- Digital signals bility, with 