Sometimes is grouped with the other " a" coefficients, but ThisĬan be viewed as the amplitude of a cosine wave with zero frequency (aĬonstant value). In addition, theĬoefficient a 0 is used to hold the DC value of the time domain waveform. Imaginary parts of the frequency spectrum, respectively. In other words, the "a" and " b" coefficients are the real and The amplitudes of the cosine waves are held in the variables: a 1, a 2, a 3, a 3, etc., while the amplitudes of the sine waves are held in: b 1, b 2, b 3, b 4, and so on.
The Fourier series synthesis equation creates a continuous periodic signal withĪ fundamental frequency, f, by adding scaled cosine and sine waves withįrequencies: f, 2 f, 3 f, 4 f, etc. Important point is that they do not contribute to forming the time domain signal. In other words, the frequencies between the harmonicsĬan be thought of as having a value of zero, or simply not existing. Harmonics, or (2) the frequency spectrum is discrete, and only defined at the Means that the frequency spectrum can be viewed in two ways: (1) theįrequency spectrum is continuous, but zero at all frequencies except the The time domain repeats itself, is also called the fundamental frequency. The first harmonic, i.e., the frequency that Instance, if the time domain repeats at 1000 hertz, the frequency spectrum willĬontain a first harmonic at 1000 hertz, a second harmonic at 2000 hertz, a third That periodic signals have a frequency spectrum consisting of harmonics. That repeat themselves from negative to positive infinity. Figure 13-10 shows several examples of continuous waveforms The time domain signal used in the Fourier series is periodic andĬontinuous. This brings us to the last member of the Fourier transform family: the Fourier