ids and this combination represents the frequency domain description of the signal. The explicit time function x(1) is the time domain description of Figure 10.7 Waveform with the Fourier expression of the signal. 10.17 10/8 Signals and noise - T/2 Odd square wave Figure 10.10 Triangular waveform with the Fourier expression given by Equation 10.22 The triangular waveform is illustrated in Figure 10.10 and the Fourier expression is given in 10.22. Even square wave (10.22) Figure 10.8 Odd and even square waveforms Figure 10.11 illustrates the sawtooth waveform and Equation 10.23 gives the expression corresponding to that figure. (10.17) (10.23) (10.18) There are two varieties of square waveforms that can be described by Fourier series, one being odd and the other even. Figure 10.8 illustrates the two waveforms with expression 10.19 giving the Fourier representation of the odd square wave and expression 10.20 giving the representation for the even square wave. (10.19) Figure 10.11 Sawtooth waveform with the Fourier (10.20) expression given by Equation 10.21 Distortion of signals A regular pulse train, illustrated in Figure 10.9, has the Fourier expression given in 10.21. 10.7.1 Types of distortion (10.21) Distortion of a signal may be expressed in a variety of ways : 1. Distortion has occurred if the output signal from a channel is not the exact replica of the input to that channel. 2. Distortion is the difference in time between the output signal of a receiver and the input signal causing that output. 3. Distortion occurs if there is a change in waveform between the input and output terminals. In general distortion arises when the output waveform contains frequency components that are not present in the original signal, or where complex signals are involved when the phase relationships between the various components of the signal may be altered. The relative amplitudes of the harmonic components may also be al- tered. Figure 10.9 Rectangular pulse train with the Fourier expression given by Equation 10.21 The relati