I'm currently having issues with my Matlab code for the following problem:

1) The numeric Matlab command, [n,d]=butter(k,w0,'s'), will generate a vector of numerator coefficients, n, and the vector of denominator coefficients, d of a filter. The parameter k is a positive integer, usually less than 10; the parameter w0 is positive.

(a) Use the command pzmap(n,d) to investigate the poles and zeroes of such a filter. Clearly discuss the effect of the parameters k and w0 on the poles and zeroes of the filter. Develop figures that clearly illustrate the behavior of the poles and zeroes of such a filter.

My code is:

syms k w0;
% k is a positive integer, less than 10 
k=0:0.1:9;
% w0 is positive 
w0=0:0.1:inf;
[n,d]=butter(k,w0,'s')

When I run this, I get the error:

??? Maximum variable size allowed by the program is exceeded.

So I tried changing inf to a number such as 0.1, but I get another error:

??? Error using ==> butter at 41
The cutoff frequencies must be greater than zero.

What am I doing wrong here?
Could please help me?

My many thanks in advance

 

Look into the colon notation again. If you replace inf with 0.1, you get a range from 0 to .1 with a step size of .1. In other words, you are probably getting a vector with one element which is zero. You probably want a large number instead of inf (i.e. infinity...)

 

In the colon notation of Matlab if you write
w0=a:b:c
you will get an array from w0 from a to c with b as the increment.
So if you write w0=0:0.1:1.0, you should get a vector from 0 to 1.0 in
steps of 0.1. For reference, take a look at the document here
http://www.mathworks.com/help/techdoc/ref/colon.html

Cheers,
Vahe