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I am trying to simulate a 10-band graphic equalizer based on 10 octaves. For each channel, I tried to cascade 4 -20 dB active low-pass filter and 4 +20 dB active high pass filters (I cascaded these many filters so that the phase shift equations are somewhat simpler and identical to simple all pass filters) to form a 80 dB band-pass. But now the issue is about the phase shift, which I thought would be simpler if I cascaded these many filters.

The phase shift caused by a low-pass filter is $$-\arctan(\omega RC) $$

whereas the phase shift caused by an all-pass filter incorporating a low-pass filter is $$-2\arctan(\omega RC)$$

I thought cascading these all-pass filters with low pass filter would negate the phase shift, but later realized that they are rather creating more phase shift, since both of them are causing the same lagging phase shift. Is there any other way to design an active pass filter that could compensate this phase shift?

Another thing to know is that, does these cascading 8 filters(excluding the phasers) cause serious issue by delaying the time between input and output? I could use Butterworth filters as well, but their phase shift equation seemed a bit complex.

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    \$\begingroup\$ if this is for audio, then phase shift is irrelevant, inaudible. \$\endgroup\$
    – Neil_UK
    Commented Oct 7 at 10:09
  • \$\begingroup\$ Yes I'm trying to simulate for audio. But shouldn't this phase shift cause incoherence between different frequency components? \$\endgroup\$
    – MSKB
    Commented Oct 7 at 10:51
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    \$\begingroup\$ You would expect the change in relationship between different frequencies, causing a change in waveform shape, to be audible, wouldn't you? AFAIK, listening experiments have shown it to be inaudible. I don't have any citations to hand, perhaps somebody could spend a few minutes on a sutable search engine. As Andy's answer below is true (summarised as filters are causal, output must lag input), and that countless audio systems use filter-based tone controls without problems, this supports what I assert. \$\endgroup\$
    – Neil_UK
    Commented Oct 7 at 11:22
  • \$\begingroup\$ Putting a suitable allpass filter behind a lowpass/highpass filter equalizes the time delay (=linear phase shift) of all frequency components present inside the passband. There are certain situations where equal delay/linear phase is important but I don't know if it really makes a noticeable difference with audio/music sources. \$\endgroup\$
    – Raonoke
    Commented Oct 7 at 11:51
  • \$\begingroup\$ if two different frequency components lag differently then shouldn't the output waveform be completely different from the input? \$\endgroup\$
    – MSKB
    Commented Oct 7 at 12:21

1 Answer 1

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Filters create a natural time-lag between input and output. This is most readily seen in low-pass filters so, what you are asking for is realistically impossible to achieve. This statement doesn't just apply to electronics but to any mechanical system too.

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  • \$\begingroup\$ I don't have any issue if all the frequency components lag equally but they lag differently based on their frequency and that causes a difference between the input and output. I want to minimize the disparity \$\endgroup\$
    – MSKB
    Commented Oct 7 at 12:19
  • \$\begingroup\$ @MSKB unfortunately, you are not going to get what you want. The best that can be achieved is a fairly constant time delay from 0 Hz up to a frequency that is lower than the cut-off frequency but, at the expense of a low quality factor. Try looking up Bessel filters to see what I mean. \$\endgroup\$
    – Andy aka
    Commented Oct 7 at 12:51
  • \$\begingroup\$ I'm curious how does practical graphic equalizers deal with this issue? \$\endgroup\$
    – MSKB
    Commented Oct 7 at 12:54
  • \$\begingroup\$ I mean, the time delay from speaker across the room to the ear means that all sorts of spectral phase shifts happen and, do you notice those things? If you recorded the speaker output close to the speaker and also tried it further away, apart from the obvious amplitude reduction, the waveforms won't bear hardly any similarity for complex audio. \$\endgroup\$
    – Andy aka
    Commented Oct 7 at 12:56
  • \$\begingroup\$ I just want one clarification about an issue, let me elaborate lets assume the for an audio the 1kHz component has a phase shift of 45° and that of 2kHz is nearly 90°. Doesn't that distort the whole audio input to something totally different? if not then I guess I wouldn't have to fix much about the circuit I'm trying to build \$\endgroup\$
    – MSKB
    Commented Oct 7 at 13:00

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