BIBO Stability and Decomposition Analysis of Signals and System with Convolution Techniques

In this paper control system’s stability is arrived based on Bounded Input Bounded Output (BIBO) when bounded input is given in the form of discrete values. The control system allows the state estimation constraints to reach the convergence even when fluctuations in the parameters of the input system occur. To overcome this DTFT (Discrete Time Fourier Transform) is used when the signal is completely absolutely summable. Stability of the LTI (Linear time invariant) system is showed and is depending on the absolute summable of their impulse response. Simultaneously for continuous signal the stability occurs if it is absolutely integrable . LTI system is steady if their impulse responses encounter the Dirichlet conditions. In addition to that the linearity and time-invariance properties are discussed. This provide a new way to decompose the periodic signals into Fourier series by convolving the fundamental signals. Continuous and discrete time signals are focused in this paper to get linear time invariant system (LTI) through complex exponentials. Finally filtering techniques were used to eliminate the noisy frequency component in a signal.