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Section E.2. SOME USEFUL DECIBEL NUMBERS

E 2 SOME USEFUL DECIBEL NUMBERS

If the reader uses dB scales on a regular basis, there are a few constants worth committing to memory. A power difference of 3 dB corresponds to a power factor of 2; that is, if the magnitude-squared ratio of two different frequency components is 2, then from Eq. (E-2),

Likewise, if the magnitude-squared ratio of two different frequency components is 1/2, then the relative power difference is –3 dB because

Table E-1. Some seful Logarithmic Relationships

Magnitude ratio

Magnitude-squared power (P1/P2) ratio

Relative dB (approximate)

 

10–1/2

10–1

–10

P1 is one-tenth P2

2–1

2–2 = 1/4

–6

P1 is one-fourth P2

2–1/2

2–1 = 1/2

–3

P1 is one-half P2

20

20 = 1

0

P1 is equal to P2

21/2

21 = 2

3

P1 is twice P2

21

22 = 4

6

P1 is four times P2

101/2

101 = 10

10

P1 is ten times P2

101

102 = 100

20

P1 is one hundred times P2

103/2

103 = 1000

30

P1 is one thousand times P2

Equation E-9

Table E-1 lists several magnitude and power ratios vs. dB values worth remembering. Keep in mind that decibels indicate only relative power relationships. For example, if we're told that signal A is 6 dB above signal B, we know that the power of signal A is four times that of signal B, and that the magnitude of signal A is twice the magnitude of signal B. We may not know the absolute power of signals A and B in watts, but we do know that the power ratio is PA/PB = 4.

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Chapter One. Discrete Sequences and Systems

Chapter Two. Periodic Sampling

Chapter Three. The Discrete Fourier Transform

Chapter Four. The Fast Fourier Transform

Chapter Five. Finite Impulse Response Filters

Chapter Six. Infinite Impulse Response Filters

Chapter Seven. Specialized Lowpass FIR Filters

Chapter Eight. Quadrature Signals

Chapter Nine. The Discrete Hilbert Transform

Chapter Ten. Sample Rate Conversion

Chapter Eleven. Signal Averaging

Chapter Twelve. Digital Data Formats and Their Effects

Chapter Thirteen. Digital Signal Processing Tricks

Appendix A. The Arithmetic of Complex Numbers

Appendix B. Closed Form of a Geometric Series

Appendix C. Time Reversal and the DFT

Appendix D. Mean, Variance, and Standard Deviation

Appendix E. Decibels (dB and dBm)

Appendix F. Digital Filter Terminology

Appendix G. Frequency Sampling Filter Derivations

Appendix H. Frequency Sampling Filter Design Tables

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Understanding Digital Signal Processing
Understanding Digital Signal Processing (2nd Edition)
ISBN: 0131089897
EAN: 2147483647
Year: 2004
Pages: 183
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