Frequency response analysis is important to us for two primary reasons. First, if we know the frequency response then we can predict the response of the circuit to any input. Sinusoidal waveforms have the elegant property that they can be combined to form other (non-sinusoidal) waveforms. For example, a 50 Hz triangle wave can be expressed as a sum of sinusoids whose frequencies are integer multiples of 50 Hz (called the Fourier Series representation). Therefore the frequency response allows us to understand a circuit's response to more complex inputs. Second, we are often interested in designing circuits with particular frequency characteristics. For example, in the design of an audio 3-way loudspeaker system, we would like to direct low frequency signals to the woofers, high frequency signals to the tweeters, and mid-frequency signals to the mid-range speakers. Therefore we would need a circuit that is capable of passing certain frequencies of a signal and rejecting others.