High-pass filter

A high-pass filter (HPF) is an electronic filter that passes signals with a frequency higher than a certain cutoff frequency and attenuates signals with frequencies lower than the cutoff frequency. The amount of attenuation for each frequency depends on the filter design. A high-pass filter is usually modeled as a linear time-invariant system. It is sometimes called a low-cut filter or bass-cut filter. High-pass filters have many uses, such as blocking DC from circuitry sensitive to non-zero average voltages or radio frequency devices. They can also be used in conjunction with a low-pass filter to produce a bandpass filter. A high-pass filter (HPF) is an electronic filter that passes signals with a frequency higher than a certain cutoff frequency and attenuates signals with frequencies lower than the cutoff frequency. The amount of attenuation for each frequency depends on the filter design. A high-pass filter is usually modeled as a linear time-invariant system. It is sometimes called a low-cut filter or bass-cut filter. High-pass filters have many uses, such as blocking DC from circuitry sensitive to non-zero average voltages or radio frequency devices. They can also be used in conjunction with a low-pass filter to produce a bandpass 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'). The simple first-order electronic high-pass filter shown in Figure 1 is implemented by placing an input voltage across the series combination of a capacitor and a resistor and using the voltage across the resistor as an output. The product of the resistance and capacitance (R×C) is the time constant (τ); it is inversely proportional to the cutoff frequency fc, that is, where fc is in hertz, τ is in seconds, R is in ohms, and C is in farads. Figure 2 shows an active electronic implementation of a first-order high-pass filter using an operational amplifier. In this case, the filter has a passband gain of -R2/R1 and has a cutoff frequency of Because this filter is active, it may have non-unity passband gain. That is, high-frequency signals are inverted and amplified by R2/R1. Discrete-time high-pass filters can also be designed. Discrete-time filter design is beyond the scope of this article; however, a simple example comes from the conversion of the continuous-time high-pass filter above to a discrete-time realization. That is, the continuous-time behavior can be discretized. From the circuit in Figure 1 above, according to Kirchhoff's Laws and the definition of capacitance: where Q c ( t ) {displaystyle Q_{c}(t)} is the charge stored in the capacitor at time t {displaystyle t} . Substituting Equation (Q) into Equation (I) and then Equation (I) into Equation (V) gives: