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

Abstract

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.