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Manually calculate DFT

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derick007

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Please find my attempt to manually calculate the dft of the Hann function.

I have built a model in MATLAB - Simulink in order to verify the results and included them in the attachment. As you can see the is a substantial difference ?

Apparently the amplitude at zero frequency/dc should be 1v, 1w, 0dB or 30dBw.

I cannot understand this as the HANN function in the time domain, clearly produces a dc amplitude of 0.5v, 0.25w, -6dB or 24dBw.

Any help at all would be very welcome.

I can email the original spreadsheet to help with the calculations.

Regards, Derek
 

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  • squarespectrumDFT9(1).pdf
    198.8 KB · Views: 53

I think your calculation for DC is correct. How did you get the Matlab results?
The DFT is not a low pass filter. Why should the amplitude at DC be 1V?
 

In my example of N=8,

X(1) = -1.92 -0.8i

|X(1)| = 2.08

|X(1)|/N = 0.26

POWER (w) = |X(1)|^2/N^2 = 0.0676 w = 30 + (10*log(0.0676)) = 18.3 dBm

My guess is Simulink's spectrum analyser does a similar conversion, but comes up with 23.979 dBm for a double sided spectrum and 26.99 dBm for single sided.
 

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