Low-pass filter

A low-pass filter (LPF) is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filter design. The filter is sometimes called a high-cut filter, or treble-cut filter in audio applications. A low-pass filter is the complement of a high-pass filter. v in ( t ) − v out ( t ) = R i ( t ) {displaystyle v_{ ext{in}}(t)-v_{ ext{out}}(t)=R;i(t)}     (V) Q c ( t ) = C v out ( t ) {displaystyle Q_{c}(t)=C,v_{ ext{out}}(t)}     (Q) i ( t ) = d ⁡ Q c d ⁡ t {displaystyle i(t)={frac {operatorname {d} Q_{c}}{operatorname {d} t}}}     (I) A low-pass filter (LPF) is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filter design. The filter is sometimes called a high-cut filter, or treble-cut filter in audio applications. A low-pass filter is the complement of a high-pass filter. In the optical domain, high-pass and low-pass have the opposite meanings, with a 'high-pass' filter (more commonly 'long-pass') passing only longer wavelengths (lower frequencies), and vice-versa for 'low-pass' (more commonly 'short-pass'). Low-pass filters exist in many different forms, including electronic circuits such as a hiss filter used in audio, anti-aliasing filters for conditioning signals prior to analog-to-digital conversion, digital filters for smoothing sets of data, acoustic barriers, blurring of images, and so on. The moving average operation used in fields such as finance is a particular kind of low-pass filter, and can be analyzed with the same signal processing techniques as are used for other low-pass filters. Low-pass filters provide a smoother form of a signal, removing the short-term fluctuations and leaving the longer-term trend. Filter designers will often use the low-pass form as a prototype filter. That is, a filter with unity bandwidth and impedance. The desired filter is obtained from the prototype by scaling for the desired bandwidth and impedance and transforming into the desired bandform (that is low-pass, high-pass, band-pass or band-stop).