I am just begining learning about DFT and I am bit unsure on what is happening mathematically during DFT.
I've sampled a signal , a sine wave sin(1000*2*pi*t). And performed DFT to calculate the Ck-coefficients, by plotting the Ck coefficients with different k values.
The frequency resolution is 8000/205 where 205 is the amount of datapoint/samples and 8000 sample frequency.
I can by using the plot read, where |Ck| is highest and then using my frequency resolution, detemine the frequency.
I see that the amount of samples have alot to say about determining the frequency. If i use a lower amount of samples, or does not use all the samples, will the estimated frequency either be lower, or higher. Why does is do that?
k := Round[1/((8000/100)/1000)] freqres := 8000/100 // N estimated freq = 468.293 k := Round[1/((8000/205)/1000)] freqres := 8000/205// N estimated freq = 992 k := Round[1/((8000/500)/1000)] freqres := 8000/500 estimated freq = 992