The earliest synthesizers used simple oscillators to generate "stupid" waveforms, such as sine waves and triangular waves, as well as brighter sawtooth waves and pulse waves. Then they are modified by deformation and modulation. Filters are very important tools. Nowadays, the synthesizer technology is very different from that in the early days, but both analog and digital synthesizers and software synthesizers are inseparable from the signal processing means of filtering. With the development of electronic technology, filters are no longer circuits composed of capacitors, resistors and inductors, but mostly become digital circuits and even software. Four types of filters are usually used in synthesizers: low-pass, Qualcomm, bandpass and notch. As the name implies, low-pass means letting low frequencies pass and filtering high frequencies; Qualcomm lets the high frequency pass and filters out the low frequency; Bandpass is to let a certain range of frequencies pass and filter out the rest; Notching is to filter out a certain range of frequencies and let the rest pass. [Illustration] By the way, several commonly used terms are also introduced here: the frequency range blocked by the filter is called stopband; The frequency range that can pass through the filter smoothly is called passband; The beginning of the forbidden band is called the half power point. The filter allows or prevents a certain frequency from passing. This frequency does not change suddenly like a knife, but has a transition, which is a diagonal line. The inclination of the diagonal is expressed by the slope. When the output signal drops by 3 decibels, it is a half-power point, also called a negative 3 decibel point. You may be more familiar with its other name "cut-off frequency". The cut-off frequency of the filter in the synthesizer can usually be moved at will. Band-pass filter and notch filter each have two half-power points, and the center of these two points is called the center frequency. The most common synthesizer is a low-pass filter. If a synthesizer has only one filter, it is undoubtedly a low-pass filter. The slope of the filter should be expressed by frequency and output decibel. Here "octave" is often used as the unit of frequency. The meaning of octave in synthesizer technology and sound technology is exactly the same as that in music. For example, every octave to 3 decibels is a diagonal line that is not too steep; And every octave -6 dB or-12 dB or even -24 dB is steeper. The slope is usually determined by the structure of each filter and cannot be changed at will. Software filters are not subject to this restriction. Slope will affect the auditory impression of sound. For example, if we send a sawtooth wave of 100Hz into a low-pass filter with a cutoff frequency of 300Hz (just equal to the frequency of the third harmonic), then at the output end of the filter, the third harmonic will be 3 decibels lower than the original level. If the slope of the filter is 6 dB/ octave, the level of the sixth harmonic will be reduced by 6 dB, the twelfth harmonic will be reduced by 6db, and so on. This is a diagonal line that is not too steep, and many higher harmonics can still be heard. If a filter with a slope of 24db/ octave is used, the diagonal is much steeper and many higher harmonics cannot be heard. There is also a control in the filter, which is represented by a capital Q, also called * * * oscillation or regeneration. Q is defined as the ratio of center frequency to bandwidth: Q=fo/BW. As can be seen from the formula, if the center frequency remains unchanged, changing q will change the bandwidth. Increasing q will narrow the bandwidth. In this way, the bandwidth can be concentrated in a limited range in the spectrum, even on a harmonic. Of course, it also depends on how to control Q. Adjusting q may affect the slope. Q control and bandwidth control are not the same thing. If Q is constant, changing the center frequency can change the bandwidth. This technique can track a harmonic of each pitch in the whole range when making timbre. Q can also do an amazing thing: it can turn a filter into an oscillator! As long as q is high enough, the filter will ring around the center frequency, and the output waveform is an attenuated sine wave with a frequency equal to the center frequency of the filter. Therefore, the controller is sometimes called "resonant filter". In particular, the function of the filter is not bad at all, and it is a white "standby" oscillator. "Wow", which was popular for a while a few years ago, uses a very simple * * * vibration filter. A similar phenomenon can also be found in acoustic instruments, such as Malimba. When it is excited, the tune can vibrate at several frequency points. If the q of the filter becomes infinite, it can really be used as an oscillator, and the output waveform is a stable sine wave. In the sixties and seventies, the famous timbres of some analog synthesizers were made by adjusting Q to be close to oscillation. Filters are widely used. Equalizer, an important tool for us to decorate sound, is to combine several filters together. Equalizers can be basically divided into two types, one is parametric equalizer and the other is graphic equalizer. A parametric equalizer is a combination of several bandpass filters, each of which controls the center frequency, Q, boost or attenuation. Graphic equalizer is a series of parallel band-pass filters, which receive the same input signal, but each filter has its fixed center frequency and bandwidth, which manages the promotion or attenuation of this frequency band. Usually, graphic equalizer is not as detailed as parametric equalizer, but it has more filters than parametric equalizer, and the equalization curve is clear at a glance. In the process of mixing various parts of music, the allocation of equalizer is very knowledgeable. I believe many people have had this experience: a single voice sounds good, but it becomes ugly when played together. Equalizers can solve similar problems. You may not be familiar with the name all-pass filter, but when it comes to guitar Faz, many people know it. All-pass filter has a flat frequency response. Is this filter also useful? Its main purpose is to change the phase of the signal spectrum. The principle of Faz filter is to let the sound pass through several all-pass filters, and then mix the output signal with the original signal. Because of different phases, some overlap and some cancel, many peaks and valleys appear in the spectrum, which changes the original sound. That's not enough. Then the all-pass filter is controlled by a low-frequency oscillator, and the magnitude of the phase difference is changed periodically, thus creating a "tumbling" effect, which is the familiar "Faz" sound. Time-varying filters (TAF) are widely used in synthesizers. Because the sound always changes with time, not only the volume is changing, but also the timbre is changing. Take the piano as an example. At the beginning of pronunciation, the noise of hammer striking the strings and the excited higher harmonics are transformed into attenuated vibration of the strings, and the waveform is gradually close to sine wave. Therefore, the low-pass filter of piano timbre should be set accordingly. At first, a large number of high-frequency components should be let through, and then the cutoff frequency will be lowered soon. Time-varying filters usually have various variable parameters, such as q, lifting or attenuation, and even slope. There are many sources of control information, such as low frequency oscillator, function generator, envelope generator or MIDI controller. The Z-Plane filter introduced by E-mu company a few years ago pushed the time-varying filter to a new height, and it can be found in several products of E-mu at present. There are six cascaded parameter equalizer groups in the Z-plane filter, and each group can dynamically control the center frequency, bandwidth and gain. E-mu also developed a database with complex frequency response curves, called Frame (Structure), which are stored in the ROM of the synthesizer. Some of these frames simulate acoustic instruments or human voices, while others are purely electronic. What's more amazing about Z-Plane filter is that it can insert and transform more than two frames, that is, it can smoothly connect two completely different frequency response curves. For example, it can unconsciously turn an "oh" sound into an "yi", which really uses up the filter.