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Spectral Analysis

The Fourier Transform is used to convert time domain signals into the frequency domain.

Using SystemView

To perform spectral analysis:

  1. Set the number of samples in the System Time Specification window to a power of 2
  2. Set the sampling rate at least 4 times the highest frequency in the model (exactly 4 times higher will place the spectrum in the middle of the display window)
  3. Make certain to capture one or more complete cycles of the signal of interest (It may be necessary to adjust the stop time to do this, however this will affect the sampling rate if the number of samples remains fixed.)

Sinewave

A sinewave has only one spectral component.

Although the amplitude of the sinewave in the time domain is 1, its magnitude in the frequency domain is . This difference is a natural result of the FFT. The calculated value will vary as a function of the sampling rate and number of samples.

In this case the sampling rate is 64 and the number of samples is 64.

Notice that the power spectrum in 50 W is 10 dBm.

This model is identical except the number of samples is increased to 128.

The sinewave magnitude in the frequency domain is now 1 and the power spectrum in 50 W remains at 10 dBm.

If it is necessary to calculate the (voltage) magnitude of a spectrum, in order to compare the magnitude with a standard waveform in a math handbook, add a globally linked gain token of 2/(dt*ns).

Square Wave

A square wave is composed of many sine waves (the odd harmonics of the fundamental).

The spectrum of any signal represents the value of all sine waves which when added duplicate the signal being analyzed

Pulse Wave

A pulse wave is composed of many harmonics (even and odd) of the fundamental.

The amplitude of some harmonics may equal zero. This phenomenon is a function of the pulse duty cycle.

The overall shape of the harmonic envelope is known as the sinc or function.

Ramp Wave

A ramp waveform has fewer spectral components than a pulse. From this we observe that the number and amplitude of spectral components are directly related to the number of rapid transitions in the signal.

Triangle Wave

This txt file is needed to run this model.

Arbitrary Wave

This txt file is needed to run this model.

Product of Sine Waves

Multiplying two sine waves in the time domain creates sum and difference frequencies in the frequency domain.

Spectral Amplitude Coefficients

The amplitudes of spectral components in SystemView are generally different from those seen on a spectrum analyzer. This is because the computer is analyzing only a small time portion of the signal, whereas the spectrum analyzer sees a continuous signal.

If it is necessary to see the same values as a spectrum analyzer, place a gain token of 2/(dt*ns) at the measuring point. This distorts the amplitude in the time domain, but compensates for the time scale in the Time Specification Window.

Student Tasks

  1. Modify each of the above models by changing the input signal frequency to 1 KHz and perform the FFT on 1cycle.
  2. Perform the FFT on 2.5 cycles of the pulse model and explain the change in the calculated spectrum.
  3. Perform the FFT on 1 cycle of the pulse model, but set the number of samples to something other than a power of 2. Explain the change in the calculated spectrum.
  4. Create a SystemView model of a triangle wave.


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