Equalizers

Started by sham...@gmail.com February 27, 2008
Hi Group,
Please tell can we connect filters in equalizers in parallel instead of connecting them in cascade. Because we can achieve same effect in both the case(|| or cascade) with adjusting gains of individual filters. Different gains for parallel and cascade.
Shamail,

Yes, you can connect equalizer filters in parallel instead of cascaded; however, the boost/cut (gain/attenuation) filter responses will not be reciprocal as viewed on a log-log scale (dB vs. log of frequency). To get reciprocal boost/cut responses with parallel filters, you must put the filter in a feedforward path for a boost filter, but in a feedback path and subtract for a cut filter. I hope this helps.

Gene Goff
Ashly Audio, Inc.
Gene-

> Yes, you can connect equalizer filters in parallel instead of cascaded;
> however, the boost/cut (gain/attenuation) filter responses will not be
> reciprocal as viewed on a log-log scale (dB vs. log of frequency). To
> get reciprocal boost/cut responses with parallel filters, you must put
> the filter in a feedforward path for a boost filter, but in a feedback
> path and subtract for a cut filter. I hope this helps.

What is the advantage of the parallel architecture? Potentially faster processing
time depending on the device architecture? Is there an SNR or other signal integrity
disadvantage in the add/sub stages?

-Jeff
Jeff,

The advantage of the parallel architecture is that it will give you the same filter combining response as an analog graphic EQ; that is, adjacent filters will interact somewhat because you are *summing* filters rather than multiplying. Imagine that a given frequency, each filter's response can be viewed as a vector having a magnitude and angle. Adjacent filters will interact by summing to a composite vector response. This may seem bad, but people are used to hearing most analog graphic EQ's which do this.

Cascaded filters on the other hand just multiply their transfer functions so there is no filter interaction - the total response magnitude is simply the product of the individual filter magnitudes. This will give a response like that of analog parametric EQ's. Computationally, cascaded is a little more efficient than parallel filters (because the parallel cut {feedback} filters have to be handled differently than the boost {feedforward} filters), but could be noisier because any recursive truncation noise can only get worse as you add more cascaded stages. For summing parallel filters, any recursive truncation noise will add basically geometrically so there is some "cancellation" of noise.

In the end, the main reason to use parallel filters is to get something that behaves like a conventional analog graphic EQ and use cascaded filters to get something that behaves like a conventional parametric EQ.

Gene
Gene-

> The advantage of the parallel architecture is that it will give you the same filter combining response as an analog
> graphic EQ; that is, adjacent filters will interact somewhat because you are *summing* filters rather than
> multiplying. Imagine that a given frequency, each filter's response can be viewed as a vector having a magnitude and
> angle. Adjacent filters will interact by summing to a composite vector response. This may seem bad, but people are
> used to hearing most analog graphic EQ's which do this.
>
> Cascaded filters on the other hand just multiply their transfer functions so there is no filter interaction - the
> total response magnitude is simply the product of the individual filter magnitudes. This will give a response like
> that of analog parametric EQ's. Computationally, cascaded is a little more efficient than parallel filters (because
> the parallel cut {feedback} filters have to be handled differently than the boost {feedforward} filters), but could
> be
> noisier because any recursive truncation noise can only get worse as you add more cascaded stages. For summing
> parallel filters, any recursive truncation noise will add basically geometrically so there is some "cancellation" of
> noise.
>
> In the end, the main reason to use parallel filters is to get something that behaves like a conventional analog
> graphic EQ and use cascaded filters to get something that behaves like a conventional parametric EQ.

Thanks very much for that explanation. We did a TI 5510 based stereo audio equalizer implementation in 2005-2006 for
a customer who wanted to match "analog parametric EQ" performance. Accurate and stable parametric filter frequency
responses were required down to 10 Hz using a 48 kHz sampling rate, so we ended up with 64-bit precision in our IIR
implementation of the parametric filters. After that experience I thought I knew something about audio equalizers,
but clearly it's a deep subject, one you appear to have mastered. Thanks again.

-Jeff
Hi Group
I am having say 10 filters for equalizer and I want to process audio through these. How should I do it ?

1) First convolve all the filters nums and dens coeffs and find a single filter's Num and Den and then process audio through this single filter or

2) process the audio through 1st filter get resultant audio and then process this audio through 2nd filter and so on.

Please guide me what to follow.
I think 2nd approach is batter because convolving all the filters coefficients may make resultant filter unstable. I am I right?
also tell me what is professional approach.
Tx
Shamail

Hi Group,
>Please tell can we connect filters in equalizers in parallel instead of connecting them in cascade. Because we can achieve same effect in both the case(|| or cascade) with adjusting gains of individual filters. Different gains for parallel and cascade.
I am assuming this was for audio application? Why would you require a reponse down to 10 Hz? Human ears cannot hear anything below 20 Hz.
Prajakt.
-----------------
Thanks very much for that explanation. We did a TI 5510 based stereo audio equalizer implementation in 2005-2006 for
a customer who wanted to match "analog parametric EQ" performance. Accurate and stable parametric filter frequency
responses were required down to 10 Hz using a 48 kHz sampling rate, so we ended up with 64-bit precision in our IIR
implementation of the parametric filters. After that experience I thought I knew something about audio equalizers,
but clearly it's a deep subject, one you appear to have mastered. Thanks again.

-Jeff
Prajakt-

> I am assuming this was for audio application? Why would you require a reponse
> down to 10 Hz? Human ears cannot hear anything below 20 Hz.

Yes I agree, but nevertheless that was the spec we were given. I put it in the same
category as 24-bit A/D converters -- you can't hear the difference between 20 and 24
bit in a circuit designed for a consumer audio product, but there is a marketing
aspect to it.

-Jeff

> -----------------
> Thanks very much for that explanation. We did a TI 5510 based stereo audio equalizer implementation in 2005-2006 for
> a customer who wanted to match "analog parametric EQ" performance. Accurate and stable parametric filter frequency
> responses were required down to 10 Hz using a 48 kHz sampling rate, so we ended up with 64-bit precision in our IIR
> implementation of the parametric filters. After that experience I thought I knew something about audio equalizers,
> but clearly it's a deep subject, one you appear to have mastered. Thanks again.
>
> -Jeff
Prajakt-

> I am assuming this was for audio application? Why would you require a reponse
> down to 10 Hz? Human ears cannot hear anything below 20 Hz.

Yes I agree, but nevertheless that was the spec we were given. I put it in the same
category as 24-bit A/D converters -- you can't hear the difference between 20 and 24
bit in a circuit designed for a consumer audio product, but there is a marketing
aspect to it.

-Jeff

> -----------------
> Thanks very much for that explanation. We did a TI 5510 based stereo audio equalizer implementation in 2005-2006 for
> a customer who wanted to match "analog parametric EQ" performance. Accurate and stable parametric filter frequency
> responses were required down to 10 Hz using a 48 kHz sampling rate, so we ended up with 64-bit precision in our IIR
> implementation of the parametric filters. After that experience I thought I knew something about audio equalizers,
> but clearly it's a deep subject, one you appear to have mastered. Thanks again.
>
> -Jeff
I am assuming this was for audio application? Why would you require a reponse down to 10 Hz? Human ears cannot hear anything below 20 Hz.
Prajakt.
-----------------
Thanks very much for that explanation. We did a TI 5510 based stereo audio equalizer implementation in 2005-2006 for
a customer who wanted to match "analog parametric EQ" performance. Accurate and stable parametric filter frequency
responses were required down to 10 Hz using a 48 kHz sampling rate, so we ended up with 64-bit precision in our IIR
implementation of the parametric filters. After that experience I thought I knew something about audio equalizers,
but clearly it's a deep subject, one you appear to have mastered. Thanks again.

-Jeff
Hi Group
I am having say 10 filters for equalizer and I want to process audio through these. How should I do it ?

1) First convolve all the filters nums and dens coeffs and find a single filter's Num and Den and then process audio through this single filter or

2) process the audio through 1st filter get resultant audio and then process this audio through 2nd filter and so on.

Please guide me what to follow.
I think 2nd approach is batter because convolving all the filters coefficients may make resultant filter unstable. I am I right?
also tell me what is professional approach.
Tx
Shamail

Hi Group,
>Please tell can we connect filters in equalizers in parallel instead of connecting them in cascade. Because we can achieve same effect in both the case(|| or cascade) with adjusting gains of individual filters. Different gains for parallel and cascade.
Gene-

> The advantage of the parallel architecture is that it will give you the same filter combining response as an analog
> graphic EQ; that is, adjacent filters will interact somewhat because you are *summing* filters rather than
> multiplying. Imagine that a given frequency, each filter's response can be viewed as a vector having a magnitude and
> angle. Adjacent filters will interact by summing to a composite vector response. This may seem bad, but people are
> used to hearing most analog graphic EQ's which do this.
>
> Cascaded filters on the other hand just multiply their transfer functions so there is no filter interaction - the
> total response magnitude is simply the product of the individual filter magnitudes. This will give a response like
> that of analog parametric EQ's. Computationally, cascaded is a little more efficient than parallel filters (because
> the parallel cut {feedback} filters have to be handled differently than the boost {feedforward} filters), but could
> be
> noisier because any recursive truncation noise can only get worse as you add more cascaded stages. For summing
> parallel filters, any recursive truncation noise will add basically geometrically so there is some "cancellation" of
> noise.
>
> In the end, the main reason to use parallel filters is to get something that behaves like a conventional analog
> graphic EQ and use cascaded filters to get something that behaves like a conventional parametric EQ.

Thanks very much for that explanation. We did a TI 5510 based stereo audio equalizer implementation in 2005-2006 for
a customer who wanted to match "analog parametric EQ" performance. Accurate and stable parametric filter frequency
responses were required down to 10 Hz using a 48 kHz sampling rate, so we ended up with 64-bit precision in our IIR
implementation of the parametric filters. After that experience I thought I knew something about audio equalizers,
but clearly it's a deep subject, one you appear to have mastered. Thanks again.

-Jeff
Jeff,

The advantage of the parallel architecture is that it will give you the same filter combining response as an analog graphic EQ; that is, adjacent filters will interact somewhat because you are *summing* filters rather than multiplying. Imagine that a given frequency, each filter's response can be viewed as a vector having a magnitude and angle. Adjacent filters will interact by summing to a composite vector response. This may seem bad, but people are used to hearing most analog graphic EQ's which do this.

Cascaded filters on the other hand just multiply their transfer functions so there is no filter interaction - the total response magnitude is simply the product of the individual filter magnitudes. This will give a response like that of analog parametric EQ's. Computationally, cascaded is a little more efficient than parallel filters (because the parallel cut {feedback} filters have to be handled differently than the boost {feedforward} filters), but could be noisier because any recursive truncation noise can only get worse as you add more cascaded stages. For summing parallel filters, any recursive truncation noise will add basically geometrically so there is some "cancellation" of noise.

In the end, the main reason to use parallel filters is to get something that behaves like a conventional analog graphic EQ and use cascaded filters to get something that behaves like a conventional parametric EQ.

Gene
Gene-

> Yes, you can connect equalizer filters in parallel instead of cascaded;
> however, the boost/cut (gain/attenuation) filter responses will not be
> reciprocal as viewed on a log-log scale (dB vs. log of frequency). To
> get reciprocal boost/cut responses with parallel filters, you must put
> the filter in a feedforward path for a boost filter, but in a feedback
> path and subtract for a cut filter. I hope this helps.

What is the advantage of the parallel architecture? Potentially faster processing
time depending on the device architecture? Is there an SNR or other signal integrity
disadvantage in the add/sub stages?

-Jeff
Shamail,

Yes, you can connect equalizer filters in parallel instead of cascaded; however, the boost/cut (gain/attenuation) filter responses will not be reciprocal as viewed on a log-log scale (dB vs. log of frequency). To get reciprocal boost/cut responses with parallel filters, you must put the filter in a feedforward path for a boost filter, but in a feedback path and subtract for a cut filter. I hope this helps.

Gene Goff
Ashly Audio, Inc.
Hi Group,
Please tell can we connect filters in equalizers in parallel instead of connecting them in cascade. Because we can achieve same effect in both the case(|| or cascade) with adjusting gains of individual filters. Different gains for parallel and cascade.