Low pass filtering

Low-pass filtering can be simply considered: set a frequency point, when the signal frequency is higher than this frequency can not pass, in the digital signal, this frequency point is also the cut-off frequency, when the frequency domain is higher than this cut-off frequency, all assignment is 0. Because in this process, the low-frequency signal is passed through.It is called low pass filtering.

The concept of low pass filter exists in various fields, such as electronic circuits, data smoothing, acoustic blocking, image blurring and so on.

In the field of digital image processing, from the frequency domain, low-pass filtering can smooth and denoise the image.

For different filters, the attenuation degree of each frequency is different. When used in audio applications, it is sometimes referred to as a high frequency shear filter or a high pitch cancellation filter.

There are many different forms of low-pass filter concepts, including electronic circuits (such as his filter used in audio equipment, digital algorithms for smoothing data, acoustic barriers, image blurring, etc.), both of which are guaranteed by eliminating short-term fluctuations.The trend of long-term development provides a smooth form of signal.

The function of low-pass filter in signal processing is equal to that of other fields such as finance; there are many kinds of low-pass filters. Among them, Butterworth filter and Chebyshev filter are the most common ones.

Filtering circuit is often used to filter out the ripple in the rectifier output voltage. It is usually composed of reactance elements, such as capacitor C at both ends of load resistance, inductor L in series with load, and various complex filtering circuits composed of capacitor and inductor. The simplest filtering circuit is as follows:

The formula of critical frequency is:

The commonly used filter circuits are two categories: passive filtering and active filtering. If the filter circuit components are only composed of passive components (resistance, capacitance, inductance), it is called passive filter circuit. The main forms of passive filtering are capacitive filtering, inductance filtering and complex filtering (including inverted L type, LC filtering, LC PI type filtering andRC PI type filtering, etc.) If the filter circuit is composed of not only passive components, but also active components (bipolar transistor, monopole transistor, integrated operational amplifier), it is called active filter circuit. Active filter is the main form of active RC filtering, also known as electronic filters.

Passive filter circuit is simple in structure and easy to design, but its pass-band amplification factor and cut-off frequency vary with the load, so it is not suitable for high signal processing requirements. Passive filter circuits are usually used in power circuits, such as DC power rectified filter, or high current load using LC (electricity)The circuit is filtered.

The load of active filter circuit does not affect the filtering characteristics, so it is often used in situations where signal processing is required. Active filter circuit is generally composed of RC network and integrated operational amplifier, so it must be used in the case of suitable DC power supply, but also can be amplified. But the composition and design of the circuit are also complex.. Active filter circuit is not suitable for high voltage and high current applications, but only for signal processing.

According to the characteristics of the filter, the amplitude-frequency characteristics of its voltage amplification multiple can accurately describe whether the circuit is a low-pass, high-pass, band-pass or band-stop filter. Therefore, if the pass-band and stopband can be qualitatively analyzed in which frequency band, the type of filter can be determined.

The method to identify the filter is as follows: if the signal frequency tends to zero and the voltage amplification factor tends to zero when the signal frequency tends to infinity, then the low-pass filter; otherwise, if the signal frequency tends to infinity, there is a definite voltage amplification factor, and the signal frequency tends to zero when the voltage amplification factor tends to zero.If the signal frequency tends to zero and infinity, the voltage amplification factor tends to zero, then the band-pass filter; if the signal frequency tends to zero and infinity, the voltage amplification factor has the same definite value, and the voltage amplification factor tends to zero in a certain frequency range, then the band-stop filter..

There are many different types of filter circuits with different frequency response. The frequency response of filters is usually represented by the Bode diagram.

For example, the first-order filter reduces the signal strength by half (about – 6dB) when the frequency doubles (increasing octave). The amplitude wave diagram of the first order filter is a horizontal line below the cut-off frequency and a slant line above the cut-off frequency. There is also a “knee Cu” at the boundary.Rve “transforms smoothly between two straight lines.Refer to the RC circuit.The two order filter has a higher effect on reducing the high frequency signal. The Potter diagram of this type of filter is similar to that of a first order filter, but its roll down rate is faster. For example, a second-order Butterworth filter (which is a critical decay RLC circuit without spikes) doubles the frequency of the signalThe intensity is reduced to the initial 1/4 (-12dB per frequency). The initial roll-off speed of other second-order filters may depend on their Q-factors, but the final speed is – 12 dB per octave. Refer to the RLC circuit. Three and higher order filters are also similar. In conclusion, the last n step filter.The roll off rate of the wave is 6ndB per frequency.

For any Butterworth filter, if the horizontal line is extended to the right and the diagonal line is extended to the left (the asymptote of the function, they will intersect at the cut-off frequency). The frequency response of the first order filter at the cut-off frequency is -3dB below the horizontal line. Different types of filters — Butterworth filter and Chebyshev filterWave devices, etc., all have different shapes of “knee curves”. Many second-order filters are designed to have a “peak” or resonance to obtain a frequency response above the horizontal line at the cut-off frequency.Refer to other types of filters in electronic filters.

‘The meaning of “low” and “high”, such as cutoff frequency, depends on the characteristics of filters. The term “lowpass filter” refers only to the shape of the filter response. A high pass filter can be designed to cut off the cut-off frequency lower than any low-pass filter. Different frequency responses are the basis for distinguishing them..) Electronic filters can be designed to any desired frequency range – up to microwave frequencies (more than 1000MHz) or higher.