Re: Piecewise constant approximation

erudite wrote:

Let s(t) be a continuous bandlimited signal. Let p(t) be its best
piecewise constant approximation on the uniformly partitioned unit
interval [0,1],

i.e p(t) = \sum_{i=1}^n c_i I_i(t)

where I_i(t) is the indicator function which takes 1 on the interval
[(i-1)/n , i/n) and 0 elsewhere.

Now how does the MSE ||s(t)-p(t)||^2 vary with n ?

It doesn't if c_i = <a constant> for all i.

You need to know something about how the c_i are selected before you
can answer the question. For example: what does "best" mean in the
phrase "best piecewise constant approximation"? Does it mean minimum
MSE?

Are there any restrictions on s(t) other than that it is continuous and
bandlimited?

Ciao,

Peter K.

.

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