linear phase fir filter design

Hello,

I want to do some audio filtering using fast convolution. The target is a
adjustable/drawable frequency response and linear phase filtering. As far
as I know, I can create the impulse response for the convolution by doing
a fft over the desired frequency response. And now my question: Is there a
way to get the filter created by a fft over the frequency response become
linear phase?

I would be happy about any tips, links, paper references...

all the best,
Tobias Kurowski

TobiasKurowski wrote:
> Hello,
>
> I want to do some audio filtering using fast convolution. The target is a
> adjustable/drawable frequency response and linear phase filtering. As far
> as I know, I can create the impulse response for the convolution by doing
> a fft over the desired frequency response. And now my question: Is there a
> way to get the filter created by a fft over the frequency response become
> linear phase?
>

Roughly speaking, you would need to do an inverse Fourier Transform (of
the desired continuous frequency response) to get the correct impulse
response, evaluated at integer values, i.e.:

 h[n] = int { H(W) . exp {j . W . n} dW }

An FIR filter is phase-linear if its impulse response is symmetric
(i.e. in the time-domain).

-- 
Oli

TobiasKurowski wrote:
> 
> Hello,
> 
> I want to do some audio filtering using fast convolution. The target is a
> adjustable/drawable frequency response and linear phase filtering.


I'm guessing that adjustable/drawable means some sort of interactive
curve construction so that the user can create a frequency response and
subsequently hear the result. Anyway, to answer your question about
linear phase. All you need to know is a couple of time<->frequency
dualities. In order to get a time domain response that is real and
symmetrical (which is what you have said you want) you need to create
frequency domain response that is real and symmetrical.

-jim



> As far
> as I know, I can create the impulse response for the convolution by doing
> a fft over the desired frequency response. And now my question: Is there a
> way to get the filter created by a fft over the frequency response become
> linear phase?
> 
> I would be happy about any tips, links, paper references...
> 
> all the best,
> Tobias Kurowski

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>TobiasKurowski wrote:
>> I want to do some audio filtering using fast convolution.
>> The target is a adjustable/drawable frequency response
>> and linear phase filtering. As far as I know, I can create
>> the impulse response for the convolution by doing a fft over
>> the desired frequency response. And now my question: Is there a
>> way to get the filter created by a fft over the frequency
>> response become linear phase?
>>
>
>Roughly speaking, you would need to do an inverse Fourier Transform (of
>the desired continuous frequency response) to get the correct impulse
>response, evaluated at integer values, i.e.:
>
> h[n] = int { H(W) . exp {j . W . n} dW }

I think that's what I have done in my matlab script and what is working
very well. I create a nice frequency response that I convert into an
impulse response using an 

>An FIR filter is phase-linear if its impulse response is symmetric
>(i.e. in the time-domain).

that's exactly my problem. the resulting impulse response is not
symmetric. is there a way/trick to get a symmetric impulse response?

thank you,
Tobias

jim wrote:
> In order to get a time domain response that is real and
> symmetrical (which is what you have said you want) you need to create
> frequency domain response that is real and symmetrical.

*Hermitian* symmetrical...

-- 
Oli

TobiasKurowski wrote:
> Oli Filth wrote:
> >Roughly speaking, you would need to do an inverse Fourier Transform (of
> >the desired continuous frequency response) to get the correct impulse
> >response, evaluated at integer values, i.e.:
> >
> > h[n] = int { H(W) . exp {j . W . n} dW }
>
> I think that's what I have done in my matlab script and what is working
> very well. I create a nice frequency response that I convert into an
> impulse response using an
>
> >An FIR filter is phase-linear if its impulse response is symmetric
> >(i.e. in the time-domain).
>
> that's exactly my problem. the resulting impulse response is not
> symmetric. is there a way/trick to get a symmetric impulse response?

What sort of frequency responses are you using/generating?  Are they
definitely real and (Hermitian/conjugate) symmetric?

-- 
Oli

>TobiasKurowski wrote:
>> Oli Filth wrote:
>> >Roughly speaking, you would need to do an inverse Fourier Transform
(of
>> >the desired continuous frequency response) to get the correct impulse
>> >response, evaluated at integer values, i.e.:
>> >
>> > h[n] = int { H(W) . exp {j . W . n} dW }
>>
>> I think that's what I have done in my matlab script and what is
working
>> very well. I create a nice frequency response that I convert into an
>> impulse response using an
>>
>> >An FIR filter is phase-linear if its impulse response is symmetric
>> >(i.e. in the time-domain).
>>
>> that's exactly my problem. the resulting impulse response is not
>> symmetric. is there a way/trick to get a symmetric impulse response?
>
>What sort of frequency responses are you using/generating?  Are they
>definitely real and (Hermitian/conjugate) symmetric?

I used cascaded biquads (lp/hp/peak) and calculate a frequency response
that I use for my impulse response. Probably nobody will use a fast
convolution to simulate biquads, but I thouht if I get them linear phase I
get a good eq. So, unfortunately it's more than just a sharp lopass.

>TobiasKurowski wrote:
>> 
>> I want to do some audio filtering using fast convolution. The target is
>> a adjustable/drawable frequency response and linear phase filtering.
>
>I'm guessing that adjustable/drawable means some sort of interactive
>curve construction so that the user can create a frequency response and
>subsequently hear the result.

that's what I wanted to do.

>Anyway, to answer your question about
>linear phase. All you need to know is a couple of time<->frequency
>dualities. In order to get a time domain response that is real and
>symmetrical (which is what you have said you want) you need to create
>frequency domain response that is real and symmetrical.

If I understand proper, the impulse response gets symmetric when the
frequency response is symmetric, that was used to generate the impulse
response?

thank you,
Tobias

TobiasKurowski wrote:

   ...

> I used cascaded biquads (lp/hp/peak) and calculate a frequency response
> that I use for my impulse response. Probably nobody will use a fast
> convolution to simulate biquads, but I thouht if I get them linear phase I
> get a good eq. So, unfortunately it's more than just a sharp lopass.

Why is linear phase important for this application?

jerry
-- 
Engineering is the art of making what you want from things you can get.
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TobiasKurowski wrote:
> 
> >TobiasKurowski wrote:
> >>
> >> I want to do some audio filtering using fast convolution. The target is
> >> a adjustable/drawable frequency response and linear phase filtering.
> >
> >I'm guessing that adjustable/drawable means some sort of interactive
> >curve construction so that the user can create a frequency response and
> >subsequently hear the result.
> 
> that's what I wanted to do.
> 
> >Anyway, to answer your question about
> >linear phase. All you need to know is a couple of time<->frequency
> >dualities. In order to get a time domain response that is real and
> >symmetrical (which is what you have said you want) you need to create
> >frequency domain response that is real and symmetrical.
> 
> If I understand proper, the impulse response gets symmetric when the
> frequency response is symmetric, that was used to generate the impulse
> response?

No it's the making it real in the frequency domain that corresponds to
the symmetry in the time domain. The symmetry part in the frequency
domains is probably already taken care of. You should be using a
FFT/IFFT implementation that assumes you are only interested real
signals in the time domain, that means half the spectrum is redundant as
far as your needs go. In the half you are interested in the frequency
response of a symmetric time response will be only real.

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