Chapter 2 Signal Bandwidth Topics: Bandwidth of Signals. Various definitions of bandwidth Huseyin Bilgekul Eeng360 Communication Systems I Department of Electrical and Electronic Engineering Eastern Mediterranean University

Bandwidth of Signals |X(f)| |X(f)| 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: Absolute Bandwidth: is f2 – f1, where the spectrum is zero outside the interval f1 < f < f2 along the positive frequency axis. |X(f)| 2B Bandlimited Absolute Bandwidth B 2. 3-dB BW (Half-power BW): is f2 – f1 , where for frequencies inside the band f1 < f < f2 , 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)| 2B3dB 3dB Bandwidth B3dB -3dB

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. |H(f)|2 Equivalent Noise Bandwidth Beq |H(0)|2 2Beq Null-to-null BW (zero-crossing BW): is f2 – f1 , where f2 is the first null in the envelope of the magnitude spectrum above f0 and, for bandpass systems, f1 is the first null in the envelope below f0 , where f0 is the frequency where the magnitude spectrum is a maximum. For baseband systems, f1 is usually zero. |X(f)| Null-to-null Bandwidth Bn 2Bn

Bandwidth of Signals 5. Bounded Spectrum Bandwidth: is f2 – f1 where outside the band f1 < f < f2, the PSD, which is proportional to |H(f)|2, must be down by at least a certain amount, say 50 dB, below the maximum value of the power spectral density. X% Power Bandwidth: is f2 – f1, where f1 < f < f2 defines the frequency band in which x% of the total power resides. (100-x)% of the total power is outside the bandwidth. 7. Legal Definition of Bandwidth: is defined according to FCC rules and regulations.

Bandwidth of Signals Null to null Bandwidth

Example Problem

Example Problem