Guide to Spectrum and Signal Analysis

Guide to Spectrum and Signal Analysis
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Guide to Spectrum and Signal Analysis

  • 28 | Guide to Spectrum and Signal AnalysisFor voice communication a higher degree of distortion can be tolerated; that is, we can ignore all side bands with less that 10% of the carrier voltage (20 dB). We can calculate the necessary bandwidth B using the approximation:So far our discussion of FM sidebands and bandwidth has been based on having a single sine wave as the modulating signal. Extending this to complex and more realistic modulating signals is difficult. We can extend this to look at an example of single tone modulation for some useful information.An FM broadcast station has a maximum frequency deviation (determined by the maximum amplitude of the modulation signal) of Δf = 80 kHz. The highest modulation frequency fm is 15 kHz. This yields a modulation index of m = 5.33 and the resulting signal has eight significant sideband pairs. Thus the required bandwidth can be calculated as 190 kHz. For modulation frequencies below 15 kHz (with the same amplitude), the modulation index increases above 5 and the bandwidth eventually approaches 2Δf kHz = 160 for very low modulation frequencies.Therefore, we can calculate the required transmission bandwidth using the highest modulation frequency and the maximum frequency deviation Δfpk.Figure 33B = 2ΔFpk + 2Fmor B = 2Fm (1 + m)ΔFpk = m x fm maximum frequency deviation