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Help me to understand filters


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Steep brickwall linear-phase FIR introduces delay, for example 65535 taps linear FIR causes 32768 samples (0.7 seconds on 44.1kHz signal) delay. This means when digital signal is inputted to the FIR filter, the filter stores those signal for 0.7 seconds in its FIFO memory then output it.

 

One of the practical usage of short delay digital filter is for musical instruments such as digital piano or vocal reverb. Short response time from pressing keys to emitting sound is preferable for players. Something below 10 milliseconds is desirable.

 

Also short delay FIR is used on sub-woofer lowpass digital filter, where shorter delay is desirable to synchronize to main speakers.

 

Short delay sharp roll-off digital filters are used for those purposes.

 

While there is a slow roll-off leaky filters. It seems those filters are early days approach to reproduce original analog sound before low-pass filtering of ADC. There was "Pioneer Legato Link" and "Wadia Spline". I think it is very 1990s way to solve the problem. Nowadays people developing deep learning audio super resolution, more accurate high frequency-component restoration, something like: record various music with high-resolution, convert it to low-resolution and train the neural network of low-resolution input and high-resolution output. Compare the network output with original high resolution sound and adjust network parameters until the neural network learns how typical musical instruments sound and outputs high resolution sound 😁.

Sunday programmer since 1985

Developer of PlayPcmWin

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Minimum-phase IIR filter is designed using analog lowpass filter design techniques: Design analog lowpass filter circuit then convert it to digital IIR filter circuit using impulse invariance method. So it succeeds all the knowledge of old and well-studied analog filter design techniques, also there is always equivalent analog circuit of the IIR filter exists and it can be realized as analog filter circuit, it is nice to imagine about it 🙂

 

I think, when analog lowpass filter circuit is converted to digital IIR using bilinear transform, resulted filter is not minimum-phase because poll is placed on the unit circle. But it is short delay and impulse response shape is very similar to minimum-phase so it is called as short-delay sharp roll-off or something.

 

It is not possible to see real filter performance using your null-test method because frequency-phase response is not zero-phase for those filters.

 

Also I'd like to add, typically leaked aliasing noise sound is very unmusical and super annoying if you can hear it (I test it with down-sampling to 11.025Hz PCM).

Sunday programmer since 1985

Developer of PlayPcmWin

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6 hours ago, manisandher said:

OK, but why is zero-phase (linear-phase?) not 'good enough'? What problem are these 'minimum-phase', 'minimum-ringing' and 'non-ringing' filters fixing? I just can't see it.

 

Minimum-phase IIR filter is able to achieve the same filtering performance to FIR filter, except frequency-phase response, and IIR filters are more computationally efficient than the same performance FIR. It is something like the order of 100x to 1000x difference so it is not negligible difference. On low-power device, IIR filter can be only option with given filter specification. (Also there is something romantic characteristic on minimum-phase filter: when matching maximum-phase filter is cascaded to the minimum-phase filter, original signal before filtering is completely recovered, theoretically:) )

 

But on PC, massively parallel cores (GPU) become available and FIR is able to use those functionality fully to accelerate FIR computation and now super overkill brickwall linear-phase FIR filter can be run on realtime speed

Sunday programmer since 1985

Developer of PlayPcmWin

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