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When diving into the realm of signal processing, an active filter is a key player that you'll encounter. Unlike passive filters which rely solely on passive components like resistors, inductors, and capacitors, an active filter includes active components such as transistors or operational amplifiers (op-amps). These active elements allow the filter to not only control the amplitude of signals within certain frequency ranges but also to amplify them.

Active filters have several advantages over their passive counterparts, including the ability to maintain high levels of performance without requiring inductors - components that can be bulky and expensive. Moreover, active filters can provide gain, offer better control over filter characteristics, and can be easily integrated into electronic circuitry.

The frequency response of a filter is essentially a map detailing how the filter affects different frequencies of an input signal. It plots the amplitude of the output signal against the input signal's frequency. In essence, it shows us how the filter 'responds' to varying frequencies. This characteristic is vitally important in applications like audio processing, communications, and instrumentation, where specific frequency components need to be controlled.

Understanding a filter's frequency response allows us to predict how it will behave with complex signals. It tells us which frequencies will be attenuated, which will be passed through unaltered, and how the transition between these areas - the roll-off - occurs. The shape of the frequency response curve, therefore, is crucial and is a defining feature of different types of filters.

The term 'flat response in pass band' refers to a filter's ability to allow signals within a specific frequency range - the pass band - to pass through unaffected; this means the amplitude of these frequencies remains unchanged. This characteristic is desirable in many audio and electronic applications because it allows for the accurate reproduction of signals without coloration or distortion within the pass band.

In the context of an active filter, like the Butterworth filter, this flat response means a smooth, even transmission of frequencies up to the cut-off point, beyond which frequencies are progressively attenuated. The importance of a flat pass band cannot be overstated for applications that require precise signal fidelity, such as in high-fidelity sound systems or precision electronic instruments.