Chapter 2 Signal Bandwidth

1. 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

2. Bandlimited |X(f)| Absolute Bandwidth B 0 2B Bandwidth of Signals • 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 < f2along the positive frequency axis.

3. |X(f)| -3dB 3dB Bandwidth B3dB 0 2B3dB

4. Bandwidth of Signals Equivalent Noise Bandwidth Beq |H(f)|2 |H(0)|2 3. Equivalent Noise Bandwidthis 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. 0 2Beq

5. Null-to-null BW (zero-crossing BW): is f2 – f1 , where f2is 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.

6. 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 < f2defines the frequency band in which x% of the total power resides. (100-x)% of the total power is outside the bandwidth.

7. 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.

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11. Bandwidth of Signals Null to null Bandwidth

12. Example Problem

13. Example Problem