# Determine Frequency Resolution samples

Can someone tell me if the way I solved this problem is right?

Suppose I have a signal $X_a(t)= 0.5cos(700πt)+0.6cos(720πt)+0.1cos(780πt)$ where $F_s=8000Hz$

I want to determine the minimum samples which must be available in order the frequency resolution of DFT be ok.

I did this:

• Firstly calculate each frequency of the signal: $F_1=350Hz$, $F_2=360Hz$, $F_3=390Hz$
• Calculate the differences: $F_2$-$F_1$=$10Hz$ ,$F_3$-$F_2$= $30Hz$ , $F_3$-$F_1$= $40Hz$
• $ΔF_{min}$=$10Hz$
• $ΔF$ = $\frac{f_s}{N}$, so $N\geq\frac{8000Hz}{10}$=800 samples

Can someone tell me if my solution is right and explain why we choose the minimum difference

Thanks

• It could be argued that you need 5 Hz resolution rather than 10 Hz, otherwise F1, F2 will appear in adjacent bins and will be indistinguishable from a single peak that straddles both bins. – Paul R Jan 27 '15 at 22:07
• @PaulR I don't understand my answer is right? – Aris Chrisak Jan 27 '15 at 22:21
• It depends on what you mean by "right". ;-) I would say that your peaks in the frequency domain need to be at least two bins apart, in order for them to be distinct, in which case you would need 5 Hz resolution, not 10 Hz. – Paul R Jan 27 '15 at 22:43
• @jojek I have seen you 've experience in this topic for similar threads which you have give answers, could you help me If my thought is wrong/right? – Aris Chrisak Jan 28 '15 at 14:41