Signals, Systems, and Filters

In this chapter, analog signals and systems are treated. Analog circuits, namely, voltage and current ones, must be causal, i.e., physically realizable. The concepts involving linearity, nonlinearity, time-invariant, time-variant, and linear time-invariant are briefly explained in this chapter. In addition, it is dealt with linear time-invariant circuits. Total harmonic distortion is defined, and an NMOS transistor-based simple amplifier is exhibited as an example. Definitions of Laplace and Fourier transforms are given. Ideal transfer functions (TFs) of the low-pass filter (LPF), band-pass filter (BPF), notch filter, high-pass filter (HPF), and all-pass filter are presented. Ideal TFs of the second-order and first-order filters are discussed in which all the non-inverting and inverting phase and gain responses with respect to frequency are demonstrated. Several examples for the second-order ideal filters are given. Gains of the second-order LPF, BPF, and HPF are evaluated. A video filter as a high-order filter is given as an example.