half band filter

Hi All

I need to interpolate a signal by 2. I am using a half band filter with 15 
taps. What is the best implementation of this filter in order to minimize 
the number of multiplications and additions.

Regards

Tom 

> I need to interpolate a signal by 2. I am using a half band filter with 15
> taps. What is the best implementation of this filter in order to minimize
> the number of multiplications and additions.

Since you're interpolating the signal, your first step will be to
upsample by inserting a zero between each sample that you have. When
filtering the data, you can then take advantage of the fact that every
other sample is zero and prevent doing needless multiplications and
additions with the zeros. I can't find a decent link explaining this,
but most practical DSP texts would describe this approach.

Jason

I forgot to note in my previous message: this implementation method is
called "polyphase" FIR filtering.

Jason

Tom wrote:
> Hi All
> 
> I need to interpolate a signal by 2. I am using a half band filter with 15 
> taps. What is the best implementation of this filter in order to minimize 
> the number of multiplications and additions.
> 
> Regards
> 
> Tom 
> 
> 

An efficient way to proceed in the general case for a filter of length N 
is to split the filtering up into two MAC loops. The first loop 
multiplies N/2 samples of data with the even taps to get the first 
output. The second loop multiplies the same N/2 samples of data with the 
odd taps to get the second output.

I suspect that there is a better way for the halfband case. I'm sure 
somebody will chime in.

John

Is your signal sufficiently bandlimited already so that a halfband
filter makes sense to use?

Dirk

Tom wrote:
> Hi All
>
> I need to interpolate a signal by 2. I am using a half band filter with 15
> taps. What is the best implementation of this filter in order to minimize
> the number of multiplications and additions.
> 
> Regards
> 
> Tom

"dbell" <bellda2005@cox.net> wrote in message 
news:1164735419.913767.96610@n67g2000cwd.googlegroups.com...
> Is your signal sufficiently bandlimited already so that a halfband
> filter makes sense to use?
>
> Dirk
>

Dirk,

Doesn't need to be ... that's really the point of a halfband filter.
Of course, this assumes that you have an OK sampled signal in the first 
place.
First you double the sample rate by stuffing zeros. This really has no 
affect on the spectrum except now you naturally "look at" two periods of it. 
Then, you filter at that higher rate to get rid of the energy surrounding 
the old fs aka the new fs/2.

Fred 

Fred,

Sure it does. Otherwise, if there is signal near the original fs/2,
there will be imaged signal near the new fs/4. The transition band may
be fairly wide; these filters are good in the passband, good in the
stopband, and not very good in the transition band.  Definitely not
suitable for general bandlimiting. For best results, the input signal
bandwidth should be contained in the passband of the halfband filter
defined at the new rate, so the image created by the zero padding falls
in the stopband.

You usually bandlimit before interpolating with a halfband filter or
series of them, and bandlimit after decimating with a halfband filter
or series of them.

Dirk

Fred Marshall wrote:
> "dbell" <bellda2005@cox.net> wrote in message
> news:1164735419.913767.96610@n67g2000cwd.googlegroups.com...
> > Is your signal sufficiently bandlimited already so that a halfband
> > filter makes sense to use?
> >
> > Dirk
> >
>
> Dirk,
>
> Doesn't need to be ... that's really the point of a halfband filter.
> Of course, this assumes that you have an OK sampled signal in the first
> place.
> First you double the sample rate by stuffing zeros. This really has no
> affect on the spectrum except now you naturally "look at" two periods of it.
> Then, you filter at that higher rate to get rid of the energy surrounding
> the old fs aka the new fs/2.
> 
> Fred

"dbell" <bellda2005@cox.net> wrote in message 
news:1164747514.516409.64410@80g2000cwy.googlegroups.com...
> Fred,
>
> Sure it does. Otherwise, if there is signal near the original fs/2,
> there will be imaged signal near the new fs/4. The transition band may
> be fairly wide; these filters are good in the passband, good in the
> stopband, and not very good in the transition band.  Definitely not
> suitable for general bandlimiting. For best results, the input signal
> bandwidth should be contained in the passband of the halfband filter
> defined at the new rate, so the image created by the zero padding falls
> in the stopband.
>
> You usually bandlimit before interpolating with a halfband filter or
> series of them, and bandlimit after decimating with a halfband filter
> or series of them.
>
> Dirk

Dirk,

You're correct.  I should have known you would be!

Fred 

cincydsp@gmail.com wrote:
> > I need to interpolate a signal by 2. I am using a half band filter with 15
> > taps. What is the best implementation of this filter in order to minimize
> > the number of multiplications and additions.

since the OP is using a half-band filter, the OP already has eliminated
nearly half of the multiplications. (every other sample of the impulse
response of a half-band is zero, except for the one at the center.)

> Since you're interpolating the signal, your first step will be to
> upsample by inserting a zero between each sample that you have. When
> filtering the data, you can then take advantage of the fact that every
> other sample is zero and prevent doing needless multiplications and
> additions with the zeros.

then you also don't need to bother sticking in those extraneous zeros.
we do that *conceptually*, but since we actually avoid multiplying by
them in the convolution summation, we don't *actually* bother to stick
them in.

> I can't find a decent link explaining this,

maybe
http://ccrma-www.stanford.edu/~jos/resample/

r b-j

cincydsp@gmail.com wrote:
> I can't find a decent link explaining this,
> but most practical DSP texts would describe this approach.

This is a pretty good treatment of the topic.
http://www.dspguru.com/info/faqs/mrfaq.htm

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Jim Thomas            Principal Applications Engineer  Bittware, Inc
jthomas@bittware.com  http://www.bittware.com    (603) 226-0404 x536
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