# Question based on scaling property of dft

Can you please tell how use the scaling property to solve this question?? i am new to dsp subject

• Welcome to DSP.SE! Where are you having trouble? Do you know how to solve for $X_1[k]$ (This is the formula for the DFT, you must certainly have access to that?) Then if you do, you use that to solve for $X_1[8]$ and $X_1[9]$--- with that do you not know how to solve for the magnitude of the ratio of the two? Dec 26 '19 at 17:53
• We avoid giving answers that look like homework problems (please see this: dsp.stackexchange.com/help/how-to-ask ) but help those that have already done some amount of research and study on their own but still having trouble---- it doesn't appear that you have done the first part of this yet? Or maybe you need some math help in understanding the DFT equation? Would like to help you! Dec 26 '19 at 17:56
• (And may help you to see the periodic frequency property of the DFT when you insert zeros in time ) Dec 26 '19 at 18:08
• I can solve this question by using the basic formula of dft, but i want to use scaling property of dft. Here x1(n)=x(n/3), then what how to calculate X1(k)?? Dec 26 '19 at 20:34
• And X(k)=Xk+N) so using this property i can find X(8) and X(11) easily, but how is X(8) = X1(8) here?? Dec 26 '19 at 20:37

• @AmanSinha Very similar—-the other thing to know is that whatever is in the DFT from 0 to N-1 must repeat if you extended the DFT samples beyond that (you can see this by looking at the DFT equation carefully and noting how $e^{jn2\pi/N}$ is cyclical.). So if you compress time by decimating you stretch the frequency samples out—- any frequency samples with non zero values that extend beyond N-1 will therefore roll into the equivalent periodic location in 0 to N-1 (aliasing) Dec 26 '19 at 21:19