E5 Frequency Analysis and Fourier Transform

Topic

Frequency analysis shifts the study of a circuit from the time domain to the frequency domain, where many problems become simpler to solve. The Fourier transform is the tool that enables this shift: any signal—whether periodic or not—can be decomposed into a sum of pure sinusoidal components with varying frequencies and amplitudes; for instance, a square wave comprises its fundamental frequency plus a series of harmonics at integer multiples of that frequency.

A circuit's transfer function describes how it modifies the amplitude and phase of the frequencies passing through it; a filter is simply a circuit whose transfer function attenuates certain frequencies while allowing others to pass. To represent very wide gain ranges in a manageable way, a logarithmic gain scale—decibels—is used; this allows a single graph to display gains ranging from virtually no change to massive amplification. The cutoff frequency of a simple filter is the point at which the signal has lost a characteristic fraction of its original amplitude; depending on the filter type, the signal passes with minimal attenuation either below or above this frequency.

Thus, this module—which begins by shifting analysis from the time domain to the frequency domain—concludes with the tool that makes this shift practical on an industrial scale: the Fast Fourier Transform (FFT). The FFT calculates the frequency content of a digitized signal with extreme efficiency and is arguably the most widely used algorithm in digital electronics and signal processing.

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