Signal Processing, Part 1
Introduction
Any variation to a signal can be referred to as signal processing. If audio signals were perfect direct from the microphone, there would be no need for signal processing. This is seldom the case however, and signals are altered in a variety of ways to suit listener taste, to optimize signal to noise ratio, and for other reasons. In this section we’ll look at equalization, or the act of shifting the level of various frequency ranges, as well as compression and limiting.
Equalization
Perhaps the most widely used signal processing function apart from gain/level control is equalization, or EQ for short. The basic idea is to alter the spectral balance of the signal, that is, to change the timbre of the source. This is achieved with some form of filter or shaped response amplifier. Of the classic filter structures (high pass, low pass, band pass, band reject) the one used most frequently is the high pass. The usage is primarily to remove rumble and other low frequency noises. Most other EQ jobs are handled by specialized audio circuits.
There are three basic types of audio equalizers: Shelving, graphic, and parametric. Shelving EQ is familiar to most people in the form of the bass and treble controls found on most stereo equipment. Essentially these circuits offer cut and boost to a specified frequency range, and exhibit a frequency response curve that looks like a shelf. For example, a bass control might be effective below 200 Hz, not affecting anything above that frequency. Depending on the position of the bass control, the response will then rise (or fall) to a second frequency (for example 100 Hz). Below the second frequency the response will stay constant. Typical boost/cut limits are in the +/-15 dB range. Some more sophisticated shelving EQs also have adjustable hinge points (i.e., the frequency where the response begins to be effective).
Graphic EQ consists of a series of individual EQ subsections. Each subsection effects only a limited range of frequencies, typically from 1 octave to 1/3 octave wide. These subsections are spaced evenly across the spectrum and allow either cutting or boosting the associated range by several dB (again, perhaps +/- 15 dB). With a 1 octave bandwidth, 10 subsections will cover the entire audible range. 1/3 octave units require approximately 30 subsections to do the same job. The subsections are normally arrayed across the front panel of the EQ unit with slide pots oriented vertically. The resulting knob positions “draw out” the effective frequency response of the EQ unit, hence the name graphic EQ. Graphic EQ (particularly 1/3 octave) are very common for equalizing large PA systems.
Parametric EQ normally offers far fewer bands than graphic EQs (perhaps just 2 to 4), but offer far greater flexibility. Instead of using fixed center frequencies with fixed bandwidths (Qs), parametrics allow control over both the center frequency and Q. The tuning frequency may be adjustable over several octaves and the bandwidth may be adjustable from aa broad as a few octaves to as narrow as 1/10 octave. Parametrics tend to be more difficult to use for the beginner although they allow for a very wide range of response curves.
There is also a somewhat odd EQ called the semi-parametric. These are a cross between the graphic and the true parametric. They normally offer fewer bands than a graphic but more than a parametric. They normally do not have bandwidth control but they do exhibit limited tuning frequency control. This is a reasonable cost compromise for many people as several bands of a graphic EQ may be set to 0 dB to in any given situation. By having movable center frequencies, fewer bands are required to do the job.
The circuitry for EQ is usually based on an op amp gain stage for analog systems. For example, a simple parallel-parallel inverting amplifier may be used for a bass control. Along with the normal fixed Rf and Ri resistor values, a potentiometer may be placed between them, with the wiper arm being connected to the input of the op amp. In this configuration the pot is split between the Rf and Ri positions, and thus controls the gain. If a capacitor is placed across the pot, the pot is effectively shorted out at high frequencies yielding a gain of unity no matter what the position of the wiper arm. Thus, only low frequencies are controlled by the pot position. EQ may also be implemented in digital systems through the use of FIR and IIR filter techniques, although discussion of these techniques is beyond the scope of this paper. It is sufficient to say that it has been successfully implemented in a variety of systems.
It is worthwhile to remember that any alteration to the frequency content (including phase) of a signal will also show up as a change in the shape of the waveform in the time domain. This is particularly easy to see with square wave test signals. As a square wave consists of a fundamental along with a sequence of harmonics, EQ will alter the relative amplitudes of the harmonics and fundamental, and thus change the shape of the waveform. Generally, reducing high frequency content will slow the edges of the square wave, while boosting high frequencies will tend to produce some peaking and possibly ringing of the waveform edges. Reduction of low frequency content tends to make the flat tops of the square wave droop. As a rule, the more extensive and complex the equalization curve, the greater the effect on the time domain response.
Compression and Limiting
Signals often need to be restrained in amplitude in order to prevent overload of certain circuit subsections, to maximize signal to noise ratio, or to increase intelligibility. Examples include the need to prevent the mechanical overload of vinyl albums, excessive tape saturation, digital clipping, and over modulation in radio and TV broadcasts. This is also done at times for effect (i.e., making an instrument sound “different” on purpose). Compressors and limiters can be thought of as controlled gain amplifiers. The gain is a function of the signal level. Limiters and compressors differ primarily in the severity of gain control. Limiters are in essence, extreme compressors.
The two prime characteristics for a compressor are the threshold level and compression ratio. If the short-term average signal level is below the threshold level then the compressor behaves as a normal buffer (amplifier with a gain of unity). Once the threshold is exceeded, the gain begins to drop at a predetermined rate, the compression ratio. A compression ratio of 2:1 means that for every 2 dB of input signal change there will only be a 1 dB change in output level. Very high compression ratios (typically beyond about 5 or 10 to 1) are referred to as limiting. The circuit that detects the average signal and which initiates the compression process normally includes the ability to adjust the attack and release times of the amplifier. The attack time refers to how long it will take before the compressor responds to a sudden transient, while the release time refers to how long it will take for the amplifier to recover (i.e., return to normal gain) once the large signal is removed. Attack times are usually measured in milliseconds, and release times somewhat longer (as much as a few seconds). The attack and release times are adjusted depending on the program material. Incorrect settings may lead to an effect known as pumping and/or breathing in which the material takes on an unnatural dynamic characteristic (e.g., the background noise may appear to grow, swell, and subside as if the circuit was breathing).
Compressors can be used to enhance dynamics as well. It is common, for example, for bass players to use compressors set for high compression and slow attack times. This will tend to accentuate the beginning transient of each note, leading to a more distinct, aggressive, “popping” sound. Guitar players may also use compression along with distortion to increase sustain, or the ability of a note to “hang”[1].
The opposite of compression and limiting are expansion and peak unlimiting. These are similar in operation except that the ratios are reversed (i.e., 1 dB of input change may turn into 2 dB of output change). These are used to restore dynamic range in overly compressed and limited signals.
Example Problem
1. Q: A compressor is set for 3:1 compression and a threshold level of -10 dBu. If the input signal is +8 dBu, what is the output level? A: Compression is applied because the input level is above the threshold level. For every 3 dB of input above the threshold, the output will increase only 1 dB (3:1 ratio). The input is 18 dB above the threshold, therefore the output will rise only 6 dB, yielding a level of –4dBu.
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ET163 Audio Technology Lecture Notes: Signal Processing, Part 1
[1] Unlike wind or bowed instruments, plucked instruments have no way to lengthen the intrinsic sustain time of a note; they can only reduce it via muting. Consequently, if the instrumentalist desires to play a piece with long notes and legato phrasing, the inherent sustain of the instrument needs to be maximized.