frequencies higher than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter. It is sometimes called a high-cut filter, or treble cut filter when used in audio applications. A low-pass filter is the opposite of a high-pass filter, and a band-pass filter is a combination of a low-pass and a high-pass.
The concept of a low-pass filter exists in many different forms, including electronic circuits (like a hiss filter used in audio), digital algorithms for smoothing sets of data, acoustic barriers, blurring of images, and so on.
In the operational amplifier circuit shown in the figure, the cutoff frequency (in hertz) is defined as:
or equivalently (in radians per second):
The gain in the passband is
and the stopband drops off at −6 dB per octave as it is a first-order filter.
Sometimes, a simple gain amplifier (as opposed to the very-high-gain operation amplifier) is turned into a low-pass filter by simply adding a feedback capacitor C. This feedback decreases the frequency response at high frequencies via the Miller effect, and helps to avoid oscillation in the amplifier. For example, an audio amplifier can be made into a low-pass filter with cutoff frequency 100 kHz to reduce gain at frequencies which would otherwise oscillate. Since the audio band (what we can hear) only goes up to 20 kHz or so, the frequencies of interest fall entirely in the passband, and the amplifier behaves the same way as far as audio is concerned.