Interpolation

Hi

I want to interpolate a complex signal given at points x1,x2,x3....xn
to get signal at points x1+a,x2+a....xn+a.

1) To interpolate complex signal, I am interpolating the magnitude and
phase separately and later combining them. Is this an appropriate
method?

 2) I am trying to get FIR filter coefficients using Spline method. The
equation that i am using is:

   y(i+a)= ((a^3)/6)*(x(i+2))+ ((1 + 3*a +
3*(a^2)-3*(a^3))/6)*(x(i+1))+ ((1 + 3*a +
3*(a^2)-3*(a^3))/6)*(x(i+1))+((4-6*(a^2) + 3*(a^3))/6)*(x(i)) +((1-3*a
+ 3*(a^2)-(a^3))/6)*(x(i-1));

But the values I am getting are far away from the desired one.

Can anybody give me suggestions?

Thanks

Anshu wrote:
> Hi
> 
> I want to interpolate a complex signal given at points x1,x2,x3....xn
> to get signal at points x1+a,x2+a....xn+a.
> 
> 1) To interpolate complex signal, I am interpolating the magnitude and
> phase separately and later combining them. Is this an appropriate
> method?

Kind of depends on your application. Interpoating components that are 
modulo 2pi might have some pitfalls. I think that interpolating real and 
imaginary separately might be easier. Try it both ways and please let us 
know.

> 
>  2) I am trying to get FIR filter coefficients using Spline method. The
> equation that i am using is:
> 
>    y(i+a)= ((a^3)/6)*(x(i+2))+ ((1 + 3*a +
> 3*(a^2)-3*(a^3))/6)*(x(i+1))+ ((1 + 3*a +
> 3*(a^2)-3*(a^3))/6)*(x(i+1))+((4-6*(a^2) + 3*(a^3))/6)*(x(i)) +((1-3*a
> + 3*(a^2)-(a^3))/6)*(x(i-1));
> 
> But the values I am getting are far away from the desired one.
> 
> Can anybody give me suggestions?
> 
> Thanks
> 

Anshu wrote:
> Hi
>
> I want to interpolate a complex signal given at points x1,x2,x3....xn
> to get signal at points x1+a,x2+a....xn+a.
>
> 1) To interpolate complex signal, I am interpolating the magnitude and
> phase separately and later combining them. Is this an appropriate
> method?
>
>  2) I am trying to get FIR filter coefficients using Spline method. The
> equation that i am using is:
>
>    y(i+a)= ((a^3)/6)*(x(i+2))+ ((1 + 3*a +
> 3*(a^2)-3*(a^3))/6)*(x(i+1))+ ((1 + 3*a +
> 3*(a^2)-3*(a^3))/6)*(x(i+1))+((4-6*(a^2) + 3*(a^3))/6)*(x(i)) +((1-3*a
> + 3*(a^2)-(a^3))/6)*(x(i-1));
>
> But the values I am getting are far away from the desired one.
>
> Can anybody give me suggestions?
>
> Thanks

1. Interpolate re and im separately, or
2. Unwrap the phase first

John

Hi

First of all, ALWAYS interpolate the real and imaginary parts.
NEVER the phase and magnitude.
As others said before me, there might be a need to unwrap the phase
first but thats not the only problem.

Consider  the magnitude. Even though it is continuous it's drivative
has steps. When the signal passes through zero (in either the real of
imaginary parts) the magnitude's slope suddenly changes. A signal which
changes its slope abruptly is not band limitted and therefore,
impossible to interpolate.

About your second question, as far as I know, the coefficients of a
cubic spline interpolator depend on the data to be interpolated. If you
don't want to go through the process of finding them, either use a
lower order spline (2nd order) or use a different method. (There are a
variety of methods. For examle, see Lagraunge interpolation in the
following web page -
http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html ).
You can also check -
http://www.mathworks.com/access/helpdesk/help/toolbox/curvefit/ch_fit14.html
for pchip interpolation which has very nice properties.

Good Luck
Tsachi.

Hi

Thanks a lot for your suggestions!!!

1)I am not familiar with phase unwrapping. Can u please explain it to
me.
2) I need to interpolate my data given at given points to get new data
at desired points which are nthg but given points shifted by same
number. I am not sure how to use FIR interpolation with this.

Anshu

Anshu wrote:
> 
> Hi
> 
> I want to interpolate a complex signal given at points x1,x2,x3....xn
> to get signal at points x1+a,x2+a....xn+a.
> 
> 1) To interpolate complex signal, I am interpolating the magnitude and
> phase separately and later combining them. Is this an appropriate
> method?

This is probably a bad idea. The problem is that the phase will
be discontinuous at either the -pi, pi or the 0, 2*pi boundary.

You should probably interpolate the real and imaginary parts
separately.

Erik
-- 
+-----------------------------------------------------------+
  Erik de Castro Lopo
+-----------------------------------------------------------+
"Slavery is a part of Islam. Slavery is part of jihad, and jihad will 
remain as long there is Islam." -- Sheikh Saleh Al-Fawzan, Saudi cleric
http://www.arabianews.org/english/article.cfm?qid=132&sid=2

Anshu wrote:
> Hi
> 
> I want to interpolate a complex signal given at points x1,x2,x3....xn
> to get signal at points x1+a,x2+a....xn+a.
> 
> 1) To interpolate complex signal, I am interpolating the magnitude and
> phase separately and later combining them. Is this an appropriate
> method?
> 
>  2) I am trying to get FIR filter coefficients using Spline method. The
> equation that i am using is:
> 
>    y(i+a)= ((a^3)/6)*(x(i+2))+ ((1 + 3*a +
> 3*(a^2)-3*(a^3))/6)*(x(i+1))+ ((1 + 3*a +
> 3*(a^2)-3*(a^3))/6)*(x(i+1))+((4-6*(a^2) + 3*(a^3))/6)*(x(i)) +((1-3*a
> + 3*(a^2)-(a^3))/6)*(x(i-1));
> 
> But the values I am getting are far away from the desired one.

How do you judge what is desired?

How non-uniform is the sampling?

Jerry
-- 
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯