Chapter 2 Signal Bandwidth Topics Bandwidth of Signals

Chapter 2 Signal Bandwidth Topics: Ø Bandwidth of Signals. Ø Various definitions of bandwidth Huseyin Bilgekul Eeng 360 Communication Systems I Department of Electrical and Electronic Engineering Eastern Mediterranean University 1

Bandwidth of Signals Ø Ø Spectral bandwidth of signals is very important because of croweded RF bands. We will give six engineering definitions and one legal definition of bandwidth that are often used: 1. Absolute Bandwidth: is f 2 – f 1, where the spectrum is zero outside the interval f 1 < f 2 along the positive frequency axis. Bandlimited |X(f)| Absolute Bandwidth B 0 2 B 2. 3 -d. B BW (Half-power BW): is f 2 – f 1 , where for frequencies inside the band f 1 < f 2 , the magnitude spectra fall no lower than 1/2 times the maximum value , and the maximum value occurs at a frequency inside the band. |X(f)| -3 d. B 0 3 d. B Bandwidth B 3 d. B 2

Bandwidth of Signals 3. Equivalent Noise Bandwidth is the width of a fictitious rectangular spectrum such that the power in that rectangular band is equal to the power associated with the actual spectrum over positive frequencies. Equivalent Noise Bandwidth Beq |H(f)|2 |H(0)|2 0 2 Beq 4. Null-to-null BW (zero-crossing BW): is f 2 – f 1 , where f 2 is the first null in the envelope of the magnitude spectrum above f 0 and, for bandpass systems, f 1 is the first null in the envelope below f 0 , where f 0 is the frequency where the magnitude spectrum is a maximum. For baseband systems, f 1 is usually zero. |X(f)| Null-to-null Bandwidth Bn 0 2 Bn 3

Bandwidth of Signals 5. Bounded Spectrum Bandwidth: is f 2 – f 1 where outside the band f 1 < f 2, the PSD, which is proportional to |H(f)|2, must be down by at least a certain amount, say 50 d. B, below the maximum value of the power spectral density. 6. X% Power Bandwidth: is f 2 – f 1, where f 1 < f 2 defines the frequency band in which x% of the total power resides. (100 -x)% of the total power is outside the bandwidth. Legal Definition of Bandwidth: is defined according to FCC rules and regulations. 7. 4

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Bandwidth of Signals Null to null Bandwidth 6

Example Problem 7

Example Problem 8