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EQ processing
cool n hot
post Jan 20 2014, 14:02
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Hi. Is there EQ processing that doesn't have compromises like FFT size has? (which is common in audio editing software). Thankyou.
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julf
post Jan 20 2014, 14:55
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QUOTE (cool n hot @ Jan 20 2014, 14:02) *
Hi. Is there EQ processing that doesn't have compromises like FFT size has? (which is common in audio editing software). Thankyou.


What compromises would that be?
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DVDdoug
post Jan 20 2014, 19:13
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As far as I know, most software equalizers don't use FFT. However, there are always compromizes when designing filters, even digital filters. (I don't know enought about DSP to tell you what those compromizes are.)

The big advantage to digital filters is that you can make them more complex, and therefore closer to "ideal filters", without additional physical stages and additional component costs. And, you avoid the noise added by analog gain stages.
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saratoga
post Jan 20 2014, 19:24
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Normal EQs don't use an FFT, so any EQ software would qualify.
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cool n hot
post Jan 21 2014, 00:35
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julf from what i know, a trade off between frequency resolution and time resolution.



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saratoga
post Jan 21 2014, 01:40
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QUOTE (cool n hot @ Jan 20 2014, 18:35) *
julf from what i know, a trade off between frequency resolution and time resolution.


It depends on what you mean. Changing the frequency of a signal via a filter will change it in time too, since any change in one domain must equate to a change in the other. If you do something like brickwall filter an impulse, you will see a definite change in its temporal characteristics.

Generally though an EQ just lets you manipulate frequency content of a signal, so in that sense it has no time "resolution" in that the same EQ will usually be applied to the entire song.
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julf
post Jan 21 2014, 12:22
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QUOTE (cool n hot @ Jan 21 2014, 00:35) *
julf from what i know, a trade off between frequency resolution and time resolution.


That would apply to FFT analysis, but as others have stated, EQ processing doesn't involve a FFT.
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cool n hot
post Jan 23 2014, 06:02
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Sorry I realize now that I should of said filter length.(as it is in audacity)
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AstralStorm
post Feb 12 2014, 05:32
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The main compromise is the delay involved in the convolution and the processing power required for the whole filter.
Doubly so if the filter is to be linear phase. Linear phase implies (filter length)/2 samples processing delay.
A longer filter has higher Q factors of the subbands and allows a more precise frequency domain control with less phase distortion if applicable. (This includes less ringing in FR in min-max filters.)
FIR (finite impulse response) EQ can be done minimum phase too to reduce the delay vastly. (under 100 samples for reasonable non-notch eqs)
FIR filters are unconditionally stable. They also require more coefficients (taps) than the equivalent IIR filter, however long filters can be ran block-wise (with unfortunate delay) using FFT.

The delay in convolution (but not linear phase) can be somewhat alleviated by using partitioned convolution and even mixed time-domain/frequency-domain convolution, at the cost of some more CPU usage.
Lightly partitioned convolution (say, 4 partitions) can be even faster than direct convolution using a long filter.

If you don't know what convolution is: it is applying any impulse response to a signal. This implies it can only handle linear, time-invariant filters; though there are ways to convolve a mildly nonlinear filter via Volterra series (polynomial approximation), or a more complex one with a neural network.

An IIR (infinite impulse response) filter has a very low delay at most frequencies, however it has some at the knee frequency, causing phase response nonlinearities. This can sometimes be compensated with a carefully designed allpass filter. The other issue IIR filters have is the numeric precision problems - error accumulation. That's why they're best done carefully in fixed point, so that you can feed this error back and cancel it out.
The other IIR issue is that higher order IIR filters can be unstable - higher than order 2 (quadratic) specifically. There are stability conditions to solve in general IIR design, pretty tough math.
That's why most IIR equalizers use a biquad (biquadratic filter) or even lower order filters. Alternatively, known stable prototype filters derived from analog ones.
Such "pasted together" filters are not nearly as good as a designed IIR, especially with regards to phase response.
There is also a minor issue where you need to convert said analog filter from s plane (Laplace) to z plane (digital equivalent) - which requires accurate frequency warping or there will be issues at the highest frequencies.


This post has been edited by AstralStorm: Feb 12 2014, 05:44


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