2 replaced http://dsp.stackexchange.com/ with https://dsp.stackexchange.com/ edited Apr 13 '17 at 12:47 The DFT of a discrete-time sinusoid will only have components at the sinusoid's frequency if there are an integer number of periods inside the window. I.e., you must figure out the period $$M$$ of the sinusoid and choose the number of points $$N$$ as an integer multiple of $$M$$ ($$N=kM$$). I'm sure you can figure out the period of the given sinusoid. Also have a look at this answerthis answer to a related question. The DFT of a discrete-time sinusoid will only have components at the sinusoid's frequency if there are an integer number of periods inside the window. I.e., you must figure out the period $$M$$ of the sinusoid and choose the number of points $$N$$ as an integer multiple of $$M$$ ($$N=kM$$). I'm sure you can figure out the period of the given sinusoid. Also have a look at this answer to a related question. The DFT of a discrete-time sinusoid will only have components at the sinusoid's frequency if there are an integer number of periods inside the window. I.e., you must figure out the period $$M$$ of the sinusoid and choose the number of points $$N$$ as an integer multiple of $$M$$ ($$N=kM$$). I'm sure you can figure out the period of the given sinusoid. Also have a look at this answer to a related question. 1 answered Sep 19 '16 at 7:38 Matt L. 55.5k22 gold badges4040 silver badges103103 bronze badges The DFT of a discrete-time sinusoid will only have components at the sinusoid's frequency if there are an integer number of periods inside the window. I.e., you must figure out the period $$M$$ of the sinusoid and choose the number of points $$N$$ as an integer multiple of $$M$$ ($$N=kM$$). I'm sure you can figure out the period of the given sinusoid. Also have a look at this answer to a related question.