Agilent Technologies 93000 SOC Series Training Manual page 563

Mixed-signal training

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DFT = Discrete

Fourier Transform

FFT = Fast Fourier

Measurements in Frequency Domain

The distortion caused by a device, for example, is determined by

applying a spectrally pure input signal to that device and

measuring the spectrum of the output signal. By separating the

output frequencies, we can distinguish between harmonic and

disharmonic distortions and determine their impact on the whole

output signal.

Phase information cannot be obtained from a usual spectrum

analyzer. But phase information can be obtained, if we convert the

signal into frequency domain with the Fourier transform.

Fourier Transformations

There are two algorithms for numerically calculating the spectrum

of a time-domain signal:

Discrete Fourier Transform (DFT)

Fast Fourier Transform (FFT)

The DFT is a numerical approximation to the Fourier integral,

based on the captured data points. The result of the Fourier

integral is actually a continuous function, but the DFT is only be

able to calculate its values at discrete points.

Unfortunately, the number of operations required for calculating

the DFT rises with the square of the number of samples.

To reduce processing time, FFT has been developed. FFT can be

executed much faster than DFT. The FFT algorithm takes the

symmetries into account that exist in the DFT algorithm.

However, for the FFT algorithm to be applied, it requires that the

number N of data points to be processed is a power of 2 (2

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