Thread Subject: picewise linear warping function

Hi,
picewise linear warping function has following formula:

f(w) = a*w for 0<=w<w0
f(w) = a*w0 + ((pi-a*w0)/(pi-w0))*(w-w0) for w0<=w<=wb

where w is frequency, wb is boundary frequency, w0 is
breaking frequency and a is warping factor alpha.

Now, I want to draw this function for three alphas, a=1,
a=0.9 and a=1.1. I have wb=4 kHz (so w=1:4000) and w0=2.5
kHz. It's shame there is not possibility of placing image
here, so I will try to describe, what should be result. For
a=1 it's one linear functin for all w=1:4000. For a=1.1
there are two parts, first function is rising faster then
for a=1 till w0, and then it breaks and it should end in
same point as for a=1. For a=0.9 it's same, only first part
is rising slower then a=1, and when it breaks at w0 it goes
steeply up and also it should end in the same point as a=1
and a=1.1.

And now my problem - I tried to solve that by this way:

a=0.9;
w=(1:4000);
w0=2500;
n=zeros(4000,1);
for i=1:2499
    n(i)=a*w(i);
end
for i=2500:4000
    n(i)=a*w0+((pi-a*w0)/(pi-w0))*(w(i)-w0);
end
plot(w,n)
hold on

a=1;
w=(1:4000);
w0=2500;
n=zeros(4000:1);
for i=1:2499
    n(i)=a*w(i);
end
for i=2500:4000
    n(i)=a*w0+((pi-a*w0)/(pi-w0))*(w(i)-w0);
end
plot(w,n)

a=1.1;
w=(1:4000);
w0=2500;
n=zeros(4000:1);
for i=1:2499
    n(i)=a*w(i);
end
for i=2500:4000
    n(i)=a*w0+((pi-a*w0)/(pi-w0))*(w(i)-w0);
end
plot(w,n)
hold off

But that doesn't work, nor a=1.1 nor a=0.9 are braking at w0
fast enough to end at the same point as a=1 and I don't know
why.

Does anyone know, what should be done different, or where is
mistake?

Thank you!

"beda meda" <b.meda@centrum.cz> wrote in message <g0n409$8sd
$1@fred.mathworks.com>...
> Hi,
> picewise linear warping function has following formula:
>
> f(w) = a*w for 0<=w<w0
> f(w) = a*w0 + ((pi-a*w0)/(pi-w0))*(w-w0) for w0<=w<=wb
>
> where w is frequency, wb is boundary frequency, w0 is
> breaking frequency and a is warping factor alpha.
>
> Now, I want to draw this function for three alphas, a=1,
> a=0.9 and a=1.1. I have wb=4 kHz (so w=1:4000) and w0=2.5
> kHz. It's shame there is not possibility of placing image
> here, so I will try to describe, what should be result. For
> a=1 it's one linear functin for all w=1:4000. For a=1.1
> there are two parts, first function is rising faster then
> for a=1 till w0, and then it breaks and it should end in
> same point as for a=1. For a=0.9 it's same, only first part
> is rising slower then a=1, and when it breaks at w0 it goes
> steeply up and also it should end in the same point as a=1
> and a=1.1.
>
> And now my problem - I tried to solve that by this way:
>
> a=0.9;
> w=(1:4000);
> w0=2500;
> n=zeros(4000,1);
> for i=1:2499
> n(i)=a*w(i);
> end
> for i=2500:4000
> n(i)=a*w0+((pi-a*w0)/(pi-w0))*(w(i)-w0);
> end
> plot(w,n)
> hold on
>
> a=1;
> w=(1:4000);
> w0=2500;
> n=zeros(4000:1);
> for i=1:2499
> n(i)=a*w(i);
> end
> for i=2500:4000
> n(i)=a*w0+((pi-a*w0)/(pi-w0))*(w(i)-w0);
> end
> plot(w,n)
>
> a=1.1;
> w=(1:4000);
> w0=2500;
> n=zeros(4000:1);
> for i=1:2499
> n(i)=a*w(i);
> end
> for i=2500:4000
> n(i)=a*w0+((pi-a*w0)/(pi-w0))*(w(i)-w0);
> end
> plot(w,n)
> hold off
>
> But that doesn't work, nor a=1.1 nor a=0.9 are braking at w0
> fast enough to end at the same point as a=1 and I don't know
> why.
>
> Does anyone know, what should be done different, or where is
> mistake?
>
> Thank you!
---------------------------
  What is the relationship between what you have called 'pi' and 'wb'? Unless
these are equal, the three values of 'n' will not match at 'wb'. To see this, just
write out the expression for n at w = wb and force it to be independent of a,
that is, set the coefficient of a to zero, and you will also be forced to set pi
equal to wb.

Roger Stafford

"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid>
wrote in message <g0nopt$pne$1@fred.mathworks.com>...
> "beda meda" <b.meda@centrum.cz> wrote in message <g0n409$8sd
> $1@fred.mathworks.com>...
> > Hi,
> > picewise linear warping function has following formula:
> >
> > f(w) = a*w for 0<=w<w0
> > f(w) = a*w0 + ((pi-a*w0)/(pi-w0))*(w-w0) for w0<=w<=wb
> >
> > where w is frequency, wb is boundary frequency, w0 is
> > breaking frequency and a is warping factor alpha.
> >
> > Now, I want to draw this function for three alphas, a=1,
> > a=0.9 and a=1.1. I have wb=4 kHz (so w=1:4000) and w0=2.5
> > kHz. It's shame there is not possibility of placing image
> > here, so I will try to describe, what should be result. For
> > a=1 it's one linear functin for all w=1:4000. For a=1.1
> > there are two parts, first function is rising faster then
> > for a=1 till w0, and then it breaks and it should end in
> > same point as for a=1. For a=0.9 it's same, only first part
> > is rising slower then a=1, and when it breaks at w0 it goes
> > steeply up and also it should end in the same point as a=1
> > and a=1.1.
> >
> > And now my problem - I tried to solve that by this way:
> >
> > a=0.9;
> > w=(1:4000);
> > w0=2500;
> > n=zeros(4000,1);
> > for i=1:2499
> > n(i)=a*w(i);
> > end
> > for i=2500:4000
> > n(i)=a*w0+((pi-a*w0)/(pi-w0))*(w(i)-w0);
> > end
> > plot(w,n)
> > hold on
> >
> > a=1;
> > w=(1:4000);
> > w0=2500;
> > n=zeros(4000:1);
> > for i=1:2499
> > n(i)=a*w(i);
> > end
> > for i=2500:4000
> > n(i)=a*w0+((pi-a*w0)/(pi-w0))*(w(i)-w0);
> > end
> > plot(w,n)
> >
> > a=1.1;
> > w=(1:4000);
> > w0=2500;
> > n=zeros(4000:1);
> > for i=1:2499
> > n(i)=a*w(i);
> > end
> > for i=2500:4000
> > n(i)=a*w0+((pi-a*w0)/(pi-w0))*(w(i)-w0);
> > end
> > plot(w,n)
> > hold off
> >
> > But that doesn't work, nor a=1.1 nor a=0.9 are braking at w0
> > fast enough to end at the same point as a=1 and I don't know
> > why.
> >
> > Does anyone know, what should be done different, or where is
> > mistake?
> >
> > Thank you!
> ---------------------------
> What is the relationship between what you have called
'pi' and 'wb'? Unless
> these are equal, the three values of 'n' will not match at
'wb'. To see this, just
> write out the expression for n at w = wb and force it to
be independent of a,
> that is, set the coefficient of a to zero, and you will
also be forced to set pi
> equal to wb.
>
> Roger Stafford
>
I solved it at last. The problem was indeed in relationship
between pi and w and wb. The solution is very simple (as
always, when you know it):

a=0.9;
w=(1:4000);
w=w*(pi/4000);
w0=2500;
w=w0*(pi/4000);

And thats it:)