A low-pass filter is a filter that passes signals with a frequency lower than a certain cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The amount of attenuation for each frequency 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 opposite of a high-pass filter. A band-pass filter is a combination of a low-pass and a high-pass filter.
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.
An optical filter can correctly be called a low-pass filter, but conventionally is called a longpass filter (low frequency is long wavelength), to avoid confusion.
RC filter:
Passive, first order low-pass RC filter
One simple low-pass filter circuit consists of a resistor in series with a load, and a capacitor in parallel with the load. The capacitor exhibits reactance, and blocks low-frequency signals, forcing them through the load instead. At higher frequencies the reactance drops, and the capacitor effectively functions as a short circuit. The combination of resistance and capacitance gives the time constant of the filter \scriptstyle \tau \;=\; RC (represented by the Greek letter tau). The break frequency, also called the turnover frequency or cutoff frequency (in hertz), is determined by the time constant:
f_\mathrm{c} = {1 \over 2 \pi \tau } = {1 \over 2 \pi R C}
or equivalently (in radians per second):
\omega_\mathrm{c} = {1 \over \tau} = {1 \over R C}
This circuit may be understood by considering the time the capacitor needs to charge or discharge through the resistor:
At low frequencies, there is plenty of time for the capacitor to charge up to practically the same voltage as the input voltage.
At high frequencies, the capacitor only has time to charge up a small amount before the input switches direction. The output goes up and down only a small fraction of the amount the input goes up and down. At double the frequency, there's only time for it to charge up half the amount.
Another way to understand this circuit is through the concept of reactance at a particular frequency:
Since direct current (DC) cannot flow through the capacitor, DC input must flow out the path marked \scriptstyle V_\mathrm{out} (analogous to removing the capacitor).
Since alternating current (AC) flows very well through the capacitor, almost as well as it flows through solid wire, AC input flows out through the capacitor, effectively short circuiting to ground (analogous to replacing the capacitor with just a wire).
The capacitor is not an "on/off" object (like the block or pass fluidic explanation above). The capacitor variably acts between these two extremes. It is the Bode plot and frequency response that show this variability.
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.
An optical filter can correctly be called a low-pass filter, but conventionally is called a longpass filter (low frequency is long wavelength), to avoid confusion.
RC filter:
Passive, first order low-pass RC filter
One simple low-pass filter circuit consists of a resistor in series with a load, and a capacitor in parallel with the load. The capacitor exhibits reactance, and blocks low-frequency signals, forcing them through the load instead. At higher frequencies the reactance drops, and the capacitor effectively functions as a short circuit. The combination of resistance and capacitance gives the time constant of the filter \scriptstyle \tau \;=\; RC (represented by the Greek letter tau). The break frequency, also called the turnover frequency or cutoff frequency (in hertz), is determined by the time constant:
f_\mathrm{c} = {1 \over 2 \pi \tau } = {1 \over 2 \pi R C}
or equivalently (in radians per second):
\omega_\mathrm{c} = {1 \over \tau} = {1 \over R C}
This circuit may be understood by considering the time the capacitor needs to charge or discharge through the resistor:
At low frequencies, there is plenty of time for the capacitor to charge up to practically the same voltage as the input voltage.
At high frequencies, the capacitor only has time to charge up a small amount before the input switches direction. The output goes up and down only a small fraction of the amount the input goes up and down. At double the frequency, there's only time for it to charge up half the amount.
Another way to understand this circuit is through the concept of reactance at a particular frequency:
Since direct current (DC) cannot flow through the capacitor, DC input must flow out the path marked \scriptstyle V_\mathrm{out} (analogous to removing the capacitor).
Since alternating current (AC) flows very well through the capacitor, almost as well as it flows through solid wire, AC input flows out through the capacitor, effectively short circuiting to ground (analogous to replacing the capacitor with just a wire).
The capacitor is not an "on/off" object (like the block or pass fluidic explanation above). The capacitor variably acts between these two extremes. It is the Bode plot and frequency response that show this variability.
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