[1] Image courtesy of www.maxedtech.com
EQUALIZER REGIONS
All seven regions of the equalizer are discussed in further detail below. Plots of a .mp3 song are used to demonstrate the effect of the filter, which is also shown. For each audio sample, the specific region is boosted by 1dB.
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All the ranges are crudely isolated using bandpass and Discrete Fourier Transform filters, just as other digital post-processing equalizers often are. Low cutoff and high cutoff values are chosen according to the chart above, which are used to make the DFT filters in MatLab. While a function is used in the code, the main idea behind the filtering is the use of time-domain cos() and sinc() functions in order to isolate specific ranges of frequencies below.
For example,
* A lowpass filter is found with sinc(w_c) where w_c is the + and - cutoff frequencies, making a bandwidth of +w_c - (-w_c)
* Two lowpass filters subtract from one another to create a bandpass
- a lowpass filter with the appropriate bandwidth can also be multiplied by fft(cos(w_m)), assuming w_m is the frequency between both cutoffs
* A highpass filter is achieved by subtracting a diract delta for all samples from a low pass that excludes
SUB-BASS
Sub-Bass: 16 - 60 Hz
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At these frequencies, one can expect tubas, bass guitars, and upright basses. Amplifying sound here is made to emphasize the low frequency, rhythmic beats of a song. In the figure, we see just how little of the overall frequency the sub-bass takes up.
Image (c) David Pulido
BASS
Bass: 60 - 250 Hz
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At this frequency range, one can expect to focus on vocals of a song, alongside some bass guitar and other instruments like guitars. More of the song's overall frequency is covered by the bass.
Image (c) David Pulido
LOWER MIDRANGE
Lower Midrange: 250 - 500 Hz
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Brass instruments and woodwind instruments are normally found in this range, giving music a loud and powerful feeling. The lower midrange section is larger than the last two sections, including a distinct downward slope from the filtered song as frequency increases.
Image (c) David Pulido
Image (c) David Pulido
MIDRANGE
Midrange: 500 - 2 kHz
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Though called the Midrange, this region covers higher end frequencies of instruments. Violins, piccolos, and similar sounds are common in this frequency range. The midrange section is one of the most distinct, despite not covering the most instruments when considering the magnitude of the filtered song compared to earlier sections.
HIGHER MIDRANGE
Higher Midrange: 2 - 4 kHz
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Harmonics for the Bass and Lower Midrange instruments can be found here, as the overtones are typically 2 or 3 times the frequency of the sounds they come from. Amplifying can give music a fuller, warmer feeling. Magnitude of the high midrange section is the lowest so far, indicating the very little amount of the song that has sound at this frequency range.
Image (c) David Pulido
Image (c) David Pulido
PRESENCE
Presence: 4 - 6 kHz
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This region normally contains the harmonics of the instruments in the previous Midrange and Higher Midrange fields. These overtones can be maximized or minimized to give certain songs fuller or thinner sounds. Due to the nature of the .mp3 compression, no sound lives in this region.
BRILLIANCE
Brilliance: 6 to 20 kHz
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These are the highest of frequency sounding instruments. Whistles and cymbals are found in this region, and amplifying it is common for energetic music like pop. Similar to the region before, the compression of the .mp3 leaves out this section of music, making the magnitude essentially 0.
Image (c) David Pulido
CONCLUSIONS
The equalizer works well given its role as a basic post-processing music editor. While its ability to strictly manipulate those regions it's supposed to is limited, it can be put to good use with the separated stems from the rest of the project's code. For example, using the equalizer to boost bass on the bass-isolated stem will allow for a greater deal of clear boost.
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The only large item of note is the fact that audio file quality must be incredibly high in order to fully take advantage of the equalizer's upper range modifiers. As such, files like the .mp3 used in the demonstrations above may not be ideal for hobbyists looking to create or edit music. WAV or FLAC files would be better for these purposes.
Citations
1. Image courtesy of https://www.cuidevices.com/blog/understanding-audio-frequency-range-in-audio-design
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2. Jackson, Michael. “PYT.” https://www.youtube.com/watch?v=1ZZQuj6htF4
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Images not cited are from the Wix template images