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```How does an FIR asymmetric bandpass filter perform differently than a
symmetric bandpass filter with the same magnitude and phase response at
positive frequencies?

```
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```On 21 Jan, 14:15, "clayss" <cshe...@gmail.com> wrote:
> How does an FIR asymmetric bandpass filter perform differently than a
> symmetric bandpass filter with the same magnitude and phase response at
> positive frequencies? =A0

Depends on what kind of asymmetry you mean:

Time-domain symmetry means that the frequency response has
linear phase. So a FIR that is asymmetric in time domain
will have non-linear phase in frequency domain.

Conjugate symmetry in frequency domain means the time-domain
impulse response is real-valued. If the frequency response
is not conjugate symmetric, the time-domain impulse response
becomes complex-valued.

Rune
```
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```On Jan 21, 8:15=A0am, "clayss" <cshe...@gmail.com> wrote:
> How does an FIR asymmetric bandpass filter perform differently than a
> symmetric bandpass filter with the same magnitude and phase response at
> positive frequencies? =A0

FIR filter is easily decomposed into the sum of a symmetric and an
antisymmtric FIR filter. The antisymmtric part has a 90 degree phase
shift. So if your filter is asymmetric how can it both simultaneously
match the magnitude and phase response of a symmetric FIR filter even
if just looking at positive frequencies. The symmetric FIR filter's
phase repsonse is a zero degree phase shift apart from the overall
delay required for causality.

IHTH,

Clay
```
 0

```>On Jan 21, 8:15=A0am, "clayss" <cshe...@gmail.com> wrote:
>> How does an FIR asymmetric bandpass filter perform differently than a
>> symmetric bandpass filter with the same magnitude and phase response at
>> positive frequencies? =A0
>
>FIR filter is easily decomposed into the sum of a symmetric and an
>antisymmtric FIR filter. The antisymmtric part has a 90 degree phase
>shift. So if your filter is asymmetric how can it both simultaneously
>match the magnitude and phase response of a symmetric FIR filter even
>if just looking at positive frequencies. The symmetric FIR filter's
>phase repsonse is a zero degree phase shift apart from the overall
>delay required for causality.
>
>IHTH,
>
>Clay
>

Rune, Clay

about responses to my inquiry, hence my extremely late reply.  The reason I
am looking at it presently is because the issue has surfaced once again.
I'm basically using some matlab code that was given to me, and I need to
understand it better.  It's a part of an ultrasound image reconstruction
algorithm, where the signal being filtered is an A-line.  Here his method
of removing negative frequency components:

lpf = fir1(nf,bw/fs,'low').';
B = lpf.*exp(j*2*pi*f0/fs*(1:length(lpf)).');

Where he has created an FIR lowpass filter and shifted it with a complex
exponential.  What I have done is just use the fir1 command to generate a
bandpass filter for the same frequencies, which has a very similar phase
and magnitude response (from what i can tell by using freqz.m).  However
they seem to perform in significantly different ways.  Would you happen to
know the practical difference between the two filters?

```
 0

```clayss wrote:
>> On Jan 21, 8:15=A0am, "clayss" <cshe...@gmail.com> wrote:
>>> How does an FIR asymmetric bandpass filter perform differently than a
>>> symmetric bandpass filter with the same magnitude and phase response at
>>> positive frequencies? =A0
>> FIR filter is easily decomposed into the sum of a symmetric and an
>> antisymmtric FIR filter. The antisymmtric part has a 90 degree phase
>> shift. So if your filter is asymmetric how can it both simultaneously
>> match the magnitude and phase response of a symmetric FIR filter even
>> if just looking at positive frequencies. The symmetric FIR filter's
>> phase repsonse is a zero degree phase shift apart from the overall
>> delay required for causality.
>>
>> IHTH,
>>
>> Clay
>>
>
> Rune, Clay
>
> about responses to my inquiry, hence my extremely late reply.  The reason I
> am looking at it presently is because the issue has surfaced once again.
> I'm basically using some matlab code that was given to me, and I need to
> understand it better.  It's a part of an ultrasound image reconstruction
> algorithm, where the signal being filtered is an A-line.  Here his method
> of removing negative frequency components:
>
> lpf = fir1(nf,bw/fs,'low').';
> B = lpf.*exp(j*2*pi*f0/fs*(1:length(lpf)).');
>
> Where he has created an FIR lowpass filter and shifted it with a complex
> exponential.  What I have done is just use the fir1 command to generate a
> bandpass filter for the same frequencies, which has a very similar phase
> and magnitude response (from what i can tell by using freqz.m).  However
> they seem to perform in significantly different ways.  Would you happen to
> know the practical difference between the two filters?

The only practical difference that jumps out at me is that your method
gives you (I assume) a real-valued filter, while his gives a complex
valued one.

How is the frequency-domain response very similar?  And what are the
differences you see that makes you say they "perform in significantly
different ways"?  And how is he (or is he) getting rid of the imaginary
component to his filter?

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
```
 0

```>clayss wrote:
>>> On Jan 21, 8:15=A0am, "clayss" <cshe...@gmail.com> wrote:
>>>> How does an FIR asymmetric bandpass filter perform differently than a
>>>> symmetric bandpass filter with the same magnitude and phase response
at
>>>> positive frequencies? =A0
>>> FIR filter is easily decomposed into the sum of a symmetric and an
>>> antisymmtric FIR filter. The antisymmtric part has a 90 degree phase
>>> shift. So if your filter is asymmetric how can it both simultaneously
>>> match the magnitude and phase response of a symmetric FIR filter even
>>> if just looking at positive frequencies. The symmetric FIR filter's
>>> phase repsonse is a zero degree phase shift apart from the overall
>>> delay required for causality.
>>>
>>> IHTH,
>>>
>>> Clay
>>>
>>
>> Rune, Clay
>>
>> Thanks for your response on this.  I never received any email
>> about responses to my inquiry, hence my extremely late reply.  The
reason I
>> am looking at it presently is because the issue has surfaced once
again.
>> I'm basically using some matlab code that was given to me, and I need
to
>> understand it better.  It's a part of an ultrasound image
reconstruction
>> algorithm, where the signal being filtered is an A-line.  Here his
method
>> of removing negative frequency components:
>>
>> lpf = fir1(nf,bw/fs,'low').';
>> B = lpf.*exp(j*2*pi*f0/fs*(1:length(lpf)).');
>>
>> Where he has created an FIR lowpass filter and shifted it with a
complex
>> exponential.  What I have done is just use the fir1 command to generate
a
>> bandpass filter for the same frequencies, which has a very similar
phase
>> and magnitude response (from what i can tell by using freqz.m).
However
>> they seem to perform in significantly different ways.  Would you happen
to
>> know the practical difference between the two filters?
>
>The only practical difference that jumps out at me is that your method
>gives you (I assume) a real-valued filter, while his gives a complex
>valued one.
>
>How is the frequency-domain response very similar?  And what are the
>differences you see that makes you say they "perform in significantly
>different ways"?  And how is he (or is he) getting rid of the imaginary
>component to his filter?
>
>--
>Tim Wescott
>Control system and signal processing consulting
>www.wescottdesign.com
>

I basically get a much smoother waveform by using the complex coefficients
and then taking the absolute value of the filtered result (to convert to
back to real) than i do with just using the real coefficients.  I suppose
frequency-domain response do you mean the frequency content of the filtered
signal?
```
 0

```>>clayss wrote:
>>>> On Jan 21, 8:15=A0am, "clayss" <cshe...@gmail.com> wrote:
>>>>> How does an FIR asymmetric bandpass filter perform differently than
a
>>>>> symmetric bandpass filter with the same magnitude and phase response
>at
>>>>> positive frequencies? =A0
>>>> FIR filter is easily decomposed into the sum of a symmetric and an
>>>> antisymmtric FIR filter. The antisymmtric part has a 90 degree phase
>>>> shift. So if your filter is asymmetric how can it both simultaneously
>>>> match the magnitude and phase response of a symmetric FIR filter even
>>>> if just looking at positive frequencies. The symmetric FIR filter's
>>>> phase repsonse is a zero degree phase shift apart from the overall
>>>> delay required for causality.
>>>>
>>>> IHTH,
>>>>
>>>> Clay
>>>>
>>>

correction: I basically get a rippled version of the original when I use
the real coefficients.  i.e., the waveform after using the complex
coefficients seems like an envelope of that using the real.
>>> Rune, Clay
>>>
>>> Thanks for your response on this.  I never received any email
>>> about responses to my inquiry, hence my extremely late reply.  The
>reason I
>>> am looking at it presently is because the issue has surfaced once
>again.
>>> I'm basically using some matlab code that was given to me, and I need
>to
>>> understand it better.  It's a part of an ultrasound image
>reconstruction
>>> algorithm, where the signal being filtered is an A-line.  Here his
>method
>>> of removing negative frequency components:
>>>
>>> lpf = fir1(nf,bw/fs,'low').';
>>> B = lpf.*exp(j*2*pi*f0/fs*(1:length(lpf)).');
>>>
>>> Where he has created an FIR lowpass filter and shifted it with a
>complex
>>> exponential.  What I have done is just use the fir1 command to
generate
>a
>>> bandpass filter for the same frequencies, which has a very similar
>phase
>>> and magnitude response (from what i can tell by using freqz.m).
>However
>>> they seem to perform in significantly different ways.  Would you
happen
>to
>>> know the practical difference between the two filters?
>>
>>The only practical difference that jumps out at me is that your method
>>gives you (I assume) a real-valued filter, while his gives a complex
>>valued one.
>>
>>How is the frequency-domain response very similar?  And what are the
>>differences you see that makes you say they "perform in significantly
>>different ways"?  And how is he (or is he) getting rid of the imaginary
>>component to his filter?
>>
>>--
>>Tim Wescott
>>Control system and signal processing consulting
>>www.wescottdesign.com
>>
>
>I basically get a much smoother waveform by using the complex
coefficients
>and then taking the absolute value of the filtered result (to convert to
>back to real) than i do with just using the real coefficients.  I suppose
>frequency-domain response do you mean the frequency content of the
filtered
>signal?
>
```
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