2.3 Definition and Classification of Signals

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21

ωt

π

2

π

3π

2

2π

{z}

{z}

y(t)

ω0t + φ

ω0t + φ

ω

Fig. 2.10: Projection of a complex pointer onto the imaginary axis in the pointer diagram (left) and

the plot of the resulting harmonic sine function y(t) (right).

Fig. 2.11: Examples of periodic signals: rectangular signal (top left), sawtooth signal (top right),

triangular signal (bottom left) and arbitrary signal from the superposition of two sinusoidal signals

(bottom right).

In the limiting case for k →∞, any periodic signals such as the rectangular, triangular

or sawtooth signal can be represented. In practice, however, when representing these

signals, one works with a finite Fourier series, i.e. with k →N, k ≤N, N ∈ℕ.

The plots of the signals in Figure 2.11 were generated with Matlab (cf. Listing 2.3.2).

In the following applications with Matlab, we omit labelling elements such as axis

labels and titles for reasons of space.

Listing 2.3.2: Matlab example for generating periodic signals with the Fourier series.

f = 1;

% fundamental frequency of signals

N = 1000;

% number of places of support

t = linspace(-pi,2*f*pi,N);

% time vector between -pi and pi