Representations of trigonometric polynomials are given as a preparation for the following chapters, in terms of their Fourier coefficients and as a convolution with a Dirichlet kernel. The computation of the complex coefficients is shown, and the number of zeros of a trigonometric polynomial is calculated. The orthogonality relation is deduced for sine and cosine functions with period T, but different frequencies n/T and m/T. Furthermore, properties of the Dirichlet kernels are discussed, which provide an initial insight into periodic pulse sequences, which play an essential role in discrete signal processing.