MATLAB: How to plot a summation signal

urgent

i have a signal summation(exp(-(2t-n)^t)where n has values from -inf to inf. how can i plot this on matlab?

Best Answer

You might as well plot a blank plot.

For any given t, since n goes to infinity, there will be an n value for which (2*t-n) goes negative, leading to a negative number being taken to a power. As t is continuous, t is not going to be confined to the even integers, so (2*t-n)^t will become imaginary. Thus for any given t that is not an even integer, there is an n for which the summation will go imaginary.

Even when t happens to be an even integer, since n goes negative infinity to plus infinity, you can also see that the sum will go infinitely large.

Your plot would thus be infinite and complex everywhere except the even integers, and would be infinite and real at the even integers. I'm not sure how you were thinking to represent that?

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MATLAB: Symbolic limit does not perform the calculation

[N,D] = numden(l11);
limit(D,lambda,1,'left')
simplify(expand(limit(N,lambda,1,'left')))

The denominator goes to 0 (but possibly at a different speed than the numerator). We are therefore risking an infinite or nan value.

The numerator goes to 32*2^n .

With n being an integer, 2^n is positive, so -32*2^n is negative, so the numerator is negative.

The limit is therefore positive/zero which would be +infinity

However, really you need to examine the rate at which both parts go to zero. There is a chance that the infinity should be negative. Maple thinks the limit should be signum(-4/0)*infinity which would get you -infinity .

MATLAB: Plotting Infinite series in matlab

You can plot for various values of t between 0 and 1.

t=.3%not sure what you want to plot against, I held t constant and plotted N vs. error
n=1:2:100000;%have to pick something for infinity (100,000 should be good for about 5 decimal places)
N=1:2:500;%whatever you want N to go up to
x=(4/pi)*sum((1./n).*sin(n*pi*t));
e=arrayfun(@(y)x-(4/pi)*sum((1./(1:2:y)).*sin((1:2:y)*pi*t)),N);
plot(N,e);

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