Spectrum Analysis and the Frequency Domain

Signals can be represented in either the time or frequency domain. Mathematically, the two representations are connected by either Fourier or Laplace transforms. Signals can be measured in the laboratory in either domain, but using different instruments. While the oscilloscope is the most common instrument for time domain measurements, the spectrum analyzer is the most common instrument for frequency domain measurements. Linear systems can likewise be characterized by either their time domain impulse response or by their frequency domain transfer function. The transfer function proves much easier in many circumstances because input signals are simply multiplied by the transfer function to produce the output frequency domain representation, whereas time domain input signals must be convolved with the impulse response to produce the output time domain waveform. Spectrum analyzers allow the frequency domain representation of a signal to be directly viewed, and network analyzers provide direct measurement of the transfer function in the frequency domain. In this laboratory, the spectrum analyzer will be introduced and its basic operation, functions, and measurements will be developed.