ABSTRACT
Before we can proceed with digital šlters, we šrst need to review a major DSP system level concept. Previously, we have seen that Fourier analysis breaks down complex signals by looking at them as a sum of sinusoidal waves, which enables us to perform signal analysis in an easier fashion. Similarly, we can simplify complex waveforms in the digital domain by looking at them as a sum of individual pulses. After all, once a signal is digitized, it is merely a series of digital pulses. If we can break down and analyze how a system responds to a single pulse, we can apply that same response when a series of pulses is applied. If a system is linear and time invariant, then once we know how it reacts to one pulse, we can determine how it will respond to multiple pulses, based on the principle of superposition. Thus, the analysis can be broken down and simplišed. An unknown system is characterized by how it responds to a simple impulse. To see how the same unknown system responds to a complex sampled signal, we merely consider the sampled signal to be a series of impulses that can be scaled and added.
