Frequency Domain and Fourier Transform

Frequency domain analysis is also called spectrum analysis or spectral analysis. Fourier transform is used to convert signals from time or space domain to the frequency domain. Signal information is converted to a magnitude and phase component of each frequency. The Fourier transform is converted to the magnitude of each frequency component squared, forming a power spectrum. This power spectrum is studied to determine which frequencies are present in the input signal and which are missing. The phase information can also be obtained from the Fourier transform. The cepstrum is a commonly used frequency domain transformation which converts a signal to the frequency domain through Fourier transform. It takes the Fourier transform (FT) of the logarithm of the estimated spectrum of a signal. The name cepstrum is devised by reversing the first four letters of the word spectrum. A very important property of the cepstral domain is that the convolution of two signals can be expressed as the addition of their cepstra.

x₁ * x₂ → x’₁ + x’₂

Frequency Sweep

A swept sine wave, a wave that changes in frequency over a period of time is used to measure the frequency characteristics of an electronic device . The frequency change occurs linearly. It is either in Hz per seconds or logarithmically in Octaves per second. Advanced sweep generators support sweep sequences with selectable start frequency, hold frequency, stop frequency and associated times. A trigger signal is synchronously provided by the signal generator to the sweep for controlling an oscilloscope which measures the output response of the device.

Waveform

According to an English dictionary a waveform is a usually graphic representation of the shape of a wave that indicates its characteristics (as frequency and amplitude).

A waveform is a representation of how alternating current (AC) varies with time, e.g., sine wave. The sine wave represents energy entirely concentrated at a single frequency. An ideal, unmodulated wireless signal has a sine waveform, with a frequency usually measured in megahertz (MHz) or gigahertz (GHz). 

A wave is a pattern of varying quantitative values that repeats over a certain interval of time. They are a periodically repeating phenomena. Signal generators produce electrical (voltage) waves that repeat in a controllable manner. A full repetition of a wave is called a cycle. Waveform graphically represents the activity of the wave and any change in it overtime. Some of the characteristics of waveforms are Amplitude, Frequency, and Phase. Amplitude of a wave measures the strength of the wave from the lowest point that a wave hits to the highest point. In other words it is the maximum disturbance (of a wave) from its undisturbed position. Frequency is the rate at which waveform cycles occur while phase is the time placement of a cycle relative to a reference waveform or point in time.