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    <p>Of course there are "gaps". The composite function is identically zero for all t&lt;2184, and for all t>7440. The relationships can only be non-zero inside of that interval. And you have not chosen a function that is zero at the endpoints, so how can you expect there not to be "gaps"?</p> <p>What values does your function take on at the endpoints of the interval?</p> <pre><code>&gt;&gt; t = [2184 7440]; &gt;&gt; (26.045792 + 13.075558*sin(0.0008531214*t - 2.7773943)) ans = 15.689 20.616 </code></pre> <p>So look at the hat function part of this. I'll be lazy and use ezplot.</p> <pre><code>&gt;&gt; ezplot(@(t) ((heaviside(t-2184))-(heaviside(t-7440))),[0,8784]) </code></pre> <p><img src="https://i.stack.imgur.com/z3u6A.jpg" alt="alt text"></p> <p>Now, combine this, multiplying it by a trig piece, and of course the result is identically zero outside of that domain.</p> <pre><code>&gt;&gt; ezplot(@(t) (26.045792 + 13.075558*sin(0.0008531214*t - 2.7773943)).*((heaviside(t-2184))-(heaviside(t-7440))),[0,8784]) </code></pre> <p><img src="https://i.stack.imgur.com/mJV0J.jpg" alt="alt text"></p> <p>But if your goal is some sort of continuous function across the two chosen points in the hat function, you need to chose the trig part such that it is zero at those same two points. Mathematics is not spelled mathemagics. Wishing that you get a continuous function will not make it so.</p> <p>So is your real question how to chose that internal piece (segment) as one such that the final result is continuous? If so, then we need to know why you have chosen the arbitrary constants in there. Surely these numbers, {26.045792, 13.075558, 0.0008531214, 2.7773943} all must have some significance to you. And if they are important, then how can we possibly make the result a continuous function?</p> <p>Perhaps, and I'm just guessing here, you want some other result out of this, such that the function is not identically zero outside of those bounds. Perhaps you wish to extrapolate as a constant function outside of those points. But to help you, you must help us.</p>
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    1. COthanks, actually, my aim is to find the carrier function colored by yellow in this graph: http://www5.0zz0.com/2010/12/31/13/615589208.jpg I divide the whole interval to 3 intervals: 1-constant 2-sinusoidal 3- constant, then I want to find the overall function from the these three functions. regards
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    2. COSo you are trying to write your own regression spline model, composed of various arbitrary functional forms for the pieces? Why not use a tool that already has the required abilities?
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    3. COhttp://www.mathworks.com/matlabcentral/fileexchange/24443
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