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 Eeng 360 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 Eeng 360 2

|X(f)| -3 d. B 0 3 d. B Bandwidth B 3 d. B 2 B 3 d. B Eeng 360 3

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 |H(0)|2 Equivalent Noise Bandwidth Beq 0 2 Beq Eeng 360 4

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. Eeng 360 5

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. Eeng 360 6

Bandwidth For BPSK Signal Let us evaluate the spectrum of s(t) for the worst case the widest bandwidth). Worst case spectrum occurs when the digital modulating waveform has transitions that occur most often. Hence m(t) must be a square wave. Eeng 360 7

Eeng 360 8

Eeng 360 9

Eeng 360 10

Bandwidth of Signals Null to null Bandwidth Eeng 360 11

Example Problem Eeng 360 12

Example Problem Eeng 360 13