## labAlive - Virtual Communications Lab

 Tutorial Experiment App MyLabalive Online experiments About

Introduction

Oscilloscope

Spectrum analyzer

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FFT illustrated

Spectrum analyzer

OFDM step-by-step

OFDM Guard interval

OFDM BER vs Eb/N0

QPSK BER

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Equivalent baseband

Wi-Fi IEEE 802.11ac

Doppler shift

Tutorials

Fourier transforms

FFT summary

FFT spectrum analyzer

OFDM step-by-step

OFDM PAPR

OFDM BER vs Eb/N0

QPSK BER

QAM BER

Simulation Apps

Wireless Communications

Telecommunications

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erfc(x) Q(x)

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dB

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# Fast Fourier transform (FFT) illustrated

 Web Start & Java check Download & create desktop icon Java Applet

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 . You find the instruction manual under the link App.

Time domainFrequency domain
DC component
Spectral line at frequency f=0
Time signal - Dirac delta impulse
Constant spectrum
Time signal - cosine with frequency $\frac{{f}_{\mathrm{max}}}{2}$
Spectral lines at frequencies $±\frac{{f}_{\mathrm{max}}}{2}$
Time signal - cosine with frequency ${f}_{\mathrm{max}}$
Spectral line at frequency ${f}_{\mathrm{max}}$
FFT examples (N = 8). The time and frequency domain signals are real and even.
Time domainFrequency domain
Time signal - pulse
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
Single spectral line
FFT examples (N = 8). Complex time domain signal.