Adaptive Filter | ADPCM | ADSP | ADSP-2181 | Aliasing | AMR | Anti-Aliasing | ARMA | Autocorrelation | AutoCovariance | Beamforming | Bessel | Blackfin | Butterworth | C6713 | CCS | Chebyshev | CIC Filter | Circular Convolution | Code Composer Studio | Comb Filter | Compression | Convolution | Cross Correlation | DCT | Decimation | Deconvolution | Demodulation | DM642 | DSP Boards | DSP/BIOS | DTMF | Echo Cancellation | Equalization | Equalizer | ETSI | EZLITE (Ez-kit Lite) | FFT | FFTW | FIR Filter | Fixed Point | FSK | G.711 | G.723 | G.729 | Gaussian Noise | Goertzel | GPIO | Hilbert Transform | IFFT | IIR Filter | Interpolation | Invariance | JTAG | Kalman | Laplace Transform | Levinson | LPC | McBSP | MIPS | Modulation | MPEG | Multirate | Notch Filter | Nyquist | OFDM | Oversampling | Pink Noise | Pitch | PLL | Polyphase | QAM | QDMA | Quantization | Quantizer | Radar | Random Noise | Reed Solomon | Remez | Resampling | RTDX | Sampling | Sharc | TI C6711 | Undersampling | Viterbi | Wavelets | White Noise | Wiener Filter | Windowing | XDS510PP | Z Transform

Hi,

I'm reading about warped filtering using a chain of all-pass filters in
"Frequency Warped Signal Processing for Audio Applications" by Aki Härmä et
al. and have some questions that I hope you can help me with.
I think I have grasped the idea of using an all-pass chain to warp the
frequency of some input signal, but the example the author is using is
giving me a hard time. He uses an example in which three (0.5, 2 & 5 khz)
sinusoidal components are warped using a chain of 1000 all-pass filters with
lambda = 0.723. The results of the warping are shown in three figures - and
this is what confuses me - where the duration of each of the frequency
components has been changed although the input signal contained the
sinusoids with the same duration.  I'm would like to find out where the
zeros after the duration of each sinusoid component come from - is this due
to the group delay so the the additional time (the zeros) is the time it
takes for emptying the all-pass filters?

I hope I've made myself a little more clear than how I feel :)
Thomas S.

______________________________
New DSP Code Snippets Section now Live.   Learn more about the reward program for contributors here.

in article 41a10ace$1...@news.wineasy.se, Heureka at s...@hotmail.com wrote
on 11/21/2004 16:38:

> I'm reading about warped filtering using a chain of all-pass filters in
> "Frequency Warped Signal Processing for Audio Applications" by Aki Härmä et
> al. and have some questions that I hope you can help me with.
> I think I have grasped the idea of using an all-pass chain to warp the
> frequency of some input signal

i don't think that is what it is about.  no kind of "filter" changes the
frequency of an input.

not have read your reference (i *do* remember a Julius Smith presentation of
a similar title), i believe that warped filtering is about substituting one
form of APF for another in a digital filter.

the APF defined by:

    A(z) = (z^-1 - p)/(1 - p*z^-1)

can be substituted for  z^-1  in an already designed digital filter.
similar to the bilinear transform, the new filter will behave just like the
old one but at different frequencies because both A(z) and z^-1 have gain
magnitude of 1 and result in a given phase shift but at different
frequencies.

-- 

r b-j                  r...@audioimagination.com

"Imagination is more important than knowledge."

______________________________
New DSP Code Snippets Section now Live.   Learn more about the reward program for contributors here.

robert bristow-johnson wrote:
> 

> 
> i don't think that is what it is about.  no kind of "filter" changes the
> frequency of an input.
> 

Nope, not true. May not apply to this discussion but lots of filters are
non-linear. The world you live in may have no use for non-linear filters
but open any decent image processing application look at the list of
filters - a whole slew of them will be non-linear. 

-jim

______________________________
New DSP Code Snippets Section now Live.   Learn more about the reward program for contributors here.

in article 3...@uni-berlin.de, jim at "N0sp"@m...@mwt.net
wrote on 11/21/2004 18:16:

> 
> 
> robert bristow-johnson wrote:
>> 
> 
>> 
>> i don't think that is what it is about.  no kind of "filter" changes the
>> frequency of an input.
>> 
> 
> Nope, not true. May not apply to this discussion but lots of filters are
> non-linear. The world you live in may have no use for non-linear filters
> but open any decent image processing application look at the list of
> filters - a whole slew of them will be non-linear.

okay.  semantic difference.  when i say "filter" without qualification, i
mean at least a linear and most of the time a time-invariant filter.  in
practice, we have filters with these things called "quantizers" that make
them, to some extent, non-linear.  but normally we model that as additive,
uniform PDF noise.

-- 

r b-j                  r...@audioimagination.com

"Imagination is more important than knowledge."

______________________________
New DSP Code Snippets Section now Live.   Learn more about the reward program for contributors here.

Hi,

OK, maybe I didn't choose my words carefully enough.

The filter does not change the frequency of the sinusoids,  but a resampling
process is going on along the tabs of the delay line (APF-chain) so the
weighting of each  tab can results in a filter which favours high resolution
in one part of the spectrum and low resolution in another. However, my
question does not concern this issue...... it concerns the alteration of the
duration of each of the three sinusoids!

Thomas S. :)



"robert bristow-johnson" <r...@audioimagination.com> wrote in message
news:BDC6DB9A.2169%r...@audioimagination.com...
> in article 3...@uni-berlin.de, jim at "N0sp"@m...@mwt.net
> wrote on 11/21/2004 18:16:
>
> >
> >
> > robert bristow-johnson wrote:
> >>
> >
> >>
> >> i don't think that is what it is about.  no kind of "filter" changes
the
> >> frequency of an input.
> >>
> >
> > Nope, not true. May not apply to this discussion but lots of filters are
> > non-linear. The world you live in may have no use for non-linear filters
> > but open any decent image processing application look at the list of
> > filters - a whole slew of them will be non-linear.
>
> okay.  semantic difference.  when i say "filter" without qualification, i
> mean at least a linear and most of the time a time-invariant filter.  in
> practice, we have filters with these things called "quantizers" that make
> them, to some extent, non-linear.  but normally we model that as additive,
> uniform PDF noise.
>
> -- 
>
> r b-j                  r...@audioimagination.com
>
> "Imagination is more important than knowledge."
>
>
>
>

______________________________
New DSP Code Snippets Section now Live.   Learn more about the reward program for contributors here.

in article 41a193a7$1...@news.wineasy.se, Heureka at s...@hotmail.com wrote
on 11/22/2004 02:22:

> OK, maybe I didn't choose my words carefully enough.



> The filter does not change the frequency of the sinusoids,  but a resampling
> process is going on along the taps of the delay line (APF-chain) so the
> weighting of each tap can results in a filter which favours high resolution
> in one part of the spectrum and low resolution in another. However, my
> question does not concern this issue...... it concerns the alteration of the
> duration of each of the three sinusoids!

if you're moving tap locations, then it ain't time-invariant and, yes, new
frequencies can be generated.

in article 41a10ace$1...@news.wineasy.se, Heureka at s...@hotmail.com wrote
on 11/21/2004 16:38:

>  He uses an example in which three (0.5, 2 & 5 khz)
> sinusoidal components are warped using a chain of 1000 all-pass filters with
> lambda = 0.723. The results of the warping are shown in three figures - and
> this is what confuses me - where the duration of each of the frequency
> components has been changed although the input signal contained the
> sinusoids with the same duration.  I'm would like to find out where the
> zeros after the duration of each sinusoid component come from - is this due
> to the group delay so the the additional time (the zeros) is the time it
> takes for emptying the all-pass filters?

well, upon re-reading, i am not sure what it is but it sounds to me that you
are bringing up an issue with transient response.  your delay line would be
an FIR system if the elements were z^-1, but if your elements are

    A(z) = (z^-1 - p)/(1 - p*z^-1) ,    (p = 0.723 , i presume)

then your FIR became an IIR.  certainly that changes your finite impulse
response to an infinite impulse response and then changes a finite transient
to an infinite one.  certainly the envelopes of the sinusoidal components
can be smeared and the transient can take forever to get done.

i dunno, that's my guess without seeing more explicitly what it is you are
doing.

-- 

r b-j                  r...@audioimagination.com

"Imagination is more important than knowledge."

______________________________
New DSP Code Snippets Section now Live.   Learn more about the reward program for contributors here.

Heureka wrote:

> The results of the warping are shown in three figures - and this
> is what confuses me - where the duration of each of the frequency
> components has been changed although the input signal contained
> the sinusoids with the same duration.

No such contraction occurs if you observe the value of any single tap 
at successive time instants. The plots show the *contents* of the 
delay lines after 1000 samples (the line length) have been fed in. 
Since low frequency components propagate slower in the warped delay 
line, their beginnings just haven't got so far by that time. The 
wavelength becomes smaller for the same reason. It may be helpful to 
think of the plots' x axis as distance rather than time.


Martin

-- 
Quidquid latine dictum sit, altum viditur.

______________________________
New DSP Code Snippets Section now Live.   Learn more about the reward program for contributors here.

Hi,

I'm sorry looking back at my posts that I'm not that good at writting in 
English. Luckely, you Martin helped me understand what is happening!

Thanks a lot Martin & Robert for the time you spend on my question!

I'm very greateful!
Thomas S:)




"Martin Eisenberg" <m...@udo.edu> wrote in message 
news:1...@ostenberg.wh.uni-dortmund.de...
> Heureka wrote:
>
>> The results of the warping are shown in three figures - and this
>> is what confuses me - where the duration of each of the frequency
>> components has been changed although the input signal contained
>> the sinusoids with the same duration.
>
> No such contraction occurs if you observe the value of any single tap
> at successive time instants. The plots show the *contents* of the
> delay lines after 1000 samples (the line length) have been fed in.
> Since low frequency components propagate slower in the warped delay
> line, their beginnings just haven't got so far by that time. The
> wavelength becomes smaller for the same reason. It may be helpful to
> think of the plots' x axis as distance rather than time.
>
>
> Martin
>
> -- 
> Quidquid latine dictum sit, altum viditur. 

______________________________
New DSP Code Snippets Section now Live.   Learn more about the reward program for contributors here.