By Speakman J

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38¥10-23 J/K), T is the absolute temperature (K). Calculate the rms value of the noise voltage across the terminals of the resistor at room temperature (290 K) in a frequency range of 0 to 10 kHz. 9 Find the frequency spectrum (amplitude and phase diagrams) of the signal given below (single-sided rectified sine) A signal x(t) is characterized as: x(t) = e-at for t > 0 x(t) = 0 for t > 0 a. Prove that the Fourier transform of x(t) exists, b. Determine the Fourier transform, c. Draw the amplitude and phase spectrum.

5 shows the power spectra of two different signals. One signal varies gradually over the course of time while the other is much faster. One can imagine the first signal being composed of sinusoidal signals with relatively low frequencies. Signal (b) contains components with frequencies that are higher. This is clearly illustrated in the corresponding frequency spectra of the signals: the spectrum of signal (a) covers a small range of frequency and its bandwidth is low. Signal (b) has a much wider bandwidth.

Each periodic signal can be written as a collection of sinusoidal signals with amplitudes given by the Fourier coefficients and frequencies that are multiples of the fundamental signal frequency. 1) is nothing other than the mean value of the signal x(t): the mean value must be equal to that of the complete series, and the mean of each sine signal is zero. e. if the signal were made audible by a loudspeaker a perfect "harmonic" sound would be heard). The component with a frequency of 2f0 is the second harmonic, 3f0 is the third harmonic, and so on.

### An introduction to the electronic theory of valency by Speakman J

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