Learn SDR 07: Frequency Spectra and the Fast Fourier Transform (FFT)

Learn SDR with Professor Jason Gallicchio at Harvey Mudd College
Lesson 7: Frequency Spectra and the Fast Fourier Transform (FFT)
What is the frequency spectrum -- amount of each component, starting with constant, then one cycle, then 2 cycles, etc, all the way up to up-down-p-down.
Show this by hitting each bin in a 100 or 1000 bin FFT.
Talk about FFT and limits of FFT. What sets the highest frequency? What sets frequency resolution?
What happens when the input isn't exactly on one of the bins? What's the point of the window? (rectangular gives 0dB, but things mush around -- zoom in on the top and go up by 1Hz with scroll wheel)
Convert to dB: relative and absolute power. Power is the square of amplitude. For whatever reason, RF power isn't given in dbW (relative to 1 Watt), but dBm (relative to 1mW)
HW: Show that by sampling twice as fast (2MHz vs 1MHz), everything scales as it should: max freq x2, resolution unchanged, noise level unchanged, but there's twice as much of it because it goes twice as high in frequency.
HW: Show that fast waves look really crappy, but still contain enough information to recover a smooth wave -- do this by upsampling and filtering (or not, because we haven't discussed filters yet).
HW: By what factor must you multiply a signal by to get 10x the power out. How many dB does this correspond to?
HW: We talked about dB in increments of 10, corresponding to powers of 10. Do the same for powers of 2.
gallicchio.github.io/learnSDR...
All GNURadio flowgraphs are at:
github.com/gallicchio/learnSDR
--- Learn SDR with Professor Jason Gallicchio

[@preuton]

fft size 100 i get this error: Assertion "not (fftsize & (fftsize -1))#The FFT Size should be a power of 2" failed.

[@hanimakannan6870]

I cannot give fft size 100

[@IsraelGoldstein1983]

Who understands this well ?