Filter stability: BIBO and FIR filters

This lecture covers the concept of filter stability, emphasizing the importance of avoiding signal 'explosions' by ensuring bounded input signals. The Bounded-Input Bounded-Output (BIBO) stability criterion is introduced, stating that for a filter to be stable, both the input and output signals must be bounded. The Fundamental Stability Theorem is presented, linking BIBO stability to the absolute summability of a filter's impulse response. The proof for this theorem is detailed, highlighting the conditions under which a filter is considered stable. Additionally, the lecture discusses the stability of Finite Impulse Response (FIR) filters and provides a method for checking the stability of Infinite Impulse Response (IIR) filters, using the example of the Leaky Integrator.