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Fast Fourier transform (FFT) illustrated

This experiment illustrates the Fast Fourier transform. Demo examples of time signals and corresponding frequency signals are shown.

Create your individual signal spectra by using the FFT calculator. Click on the start button Green Play Button. You find the instruction manual under the link App.

Time domainFrequency domain
DC component
DC component
Spectral line at frequency f=0
Spectral line at frequency f=0
Time signal - Dirac delta impulse
Time signal - Dirac delta impulse
Constant spectrum
Constant spectrum
Time signal ? cosine with frequency fmax/2
Time signal - cosine with frequency f max 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca WGMbWaaSbaaSqaaiGac2gacaGGHbGaaiiEaaqabaaakeaacaaIYaaa aaaa@3AB8@
Time signal - cosine with frequency +-fmax/2
Spectral lines at frequencies ± f max 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyySae7aaS aaaeaacaWGMbWaaSbaaSqaaiGac2gacaGGHbGaaiiEaaqabaaakeaa caaIYaaaaaaa@3CA6@
Time signal ? cosine with frequency fmax
Time signal - cosine with frequency f max MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaaBa aaleaaciGGTbGaaiyyaiaacIhaaeqaaaaa@39E2@
Spectral line at frequency fmax
Spectral line at frequency f max MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaaBa aaleaaciGGTbGaaiyyaiaacIhaaeqaaaaa@39E2@
FFT examples (N = 8). The time and frequency domain signals are real and even.
Time domainFrequency domain
Time signal - pulse
Time signal - pulse
Spectrum signal - Sinc function
Spectrum signal - Sinc function
FFT examples (N = 32). The time and frequency domain signals are real and even.
Time domainFrequency domain
Time signal - complex rotating phasor
Time signal - complex rotating phasor
Single spectral line
Single spectral line
FFT examples (N = 8). Complex time domain signal.

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