EELE Lecture 11 Filter example, Bandwidth definitions and BPSK example

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1 EELE Lecture 11 Filter example, Bandwidth definition and BPSK example

2 Example: White noie through filter 0 S n (f) RC LPF fc = 10 MHz Find S n (f) in Watt/Hz The equivalent noie bandwidth of the filter The output PSD, S y (f) The total output noie power in dbm and in Watt The output rm noie voltage. The output Vp-p (aume 6σ noie) What would the filter BW have to be to reduce the noie power by 12 db?

3 Bandlimited Signal

4 Bandwidth Definition 1. Abolute bandwidth: B=f 2 -f 1, when the pectrum i zero outide the interval f 1 <f <f 2 along the poitive frequency axi. Example, white noie through an ideal bandpa filter 2. 3-dB bandwidth (or half-power bandwidth) i B=f 2 -f 1, where for frequencie inde the band f 1 <f <f 2, the power pectra, S(f), fall now lower than ½ the maximum value of S(f), and the maximum value occur at a frequency inide the band. 3 - db bandwidth(or B 3 = S( f S( f ) f 2 ) 2 2 max f for f half, f 1 - power f f 2 bandwidth):

5 Bandwidth Definition

6 Bandwidth Definition

7 Bandwidth Definition

8 Bandwidth Definition

9 BPSK Signal

10 BPSK Signal

11 Figure 2 23 Spectrum of a BPSK ignal. Couch, Digital and Analog Communication Sytem, Seventh Edition 2007 Pearon Education, Inc. All right reerved

12 BPSK Signal

13 BPSK Signal

14 BPSK Signal

15 BPSK Signal

16 Example 2 22 (continued)

17 BPSK Signal Figure 2 24 FCC-allowed envelope for B = 30 MHz.

19 Sampling PAM- Pule Amplitude Modulation PCM- Pule Code Modulation EELE Lecture 12

20 EELE Lecture 12 Sampling

21 Sampling The Cardinal Serie Sampling Theorem: Any phyical waveform may be repreented over the interval t by where f i a parameter aigned ome convenient value greater than zero

22 Sampling The Cardinal Serie ( f ) = 2B min Nyquit Frequency

23 Sampling The Cardinal Serie

24 Figure 2 17 Sampling theorem. Sampling The Cardinal Serie The voltage at t=nt i only due to the voltage at ample nt and i not dependent on any other ample. (Orthogonal in time!)

25 Figure 2 18 Impule ampling. Couch, Digital and Analog Communication Sytem, Seventh Edition 2007 Pearon Education, Inc. All right reerved

26 Impule Sampling T 2 () () [ ] +L = = = = = + + = = = ) 2co(3 ) 2co(2 ) 2co( ) co( ) ( t t t T t T D T D T t n D D nt t t T n n n n n n T ω ω ω δ π ω ϕ ϕ ω δ δ

27 Impule Sampling () ) ( = = n T nt t t δ δ w (t) () [ ] [ ] ) ( 1 ) ( ) ( ) 2co(3 ) 2co(2 ) 2co( 1 ) ( ) ( ) ( = = = = = n T nf f W T t w F f W t t t T t w t t w t w L ω ω ω δ

28 Impule Sampling- text = = = = = = = = n t jn n n n nf f W T f W e T t w t w eq nt t nt w nt t t w t w ) ( 1 ) ( 1 ) ( ) ( ) ( ) ( ) ( ) ( ) ( ω δ δ

29 Impule Sampling The pectrum of the impue ampled ignal i the pectrum of the unampled ignal that i repeated every f Hz, where f i the ampling frequency or rate (ample/ec). Thi i one of the baic principle of digital ignal proceing, DSP. Note: Thi technique of impule ampling i often ued to tranlate the pectrum of a ignal to another frequency band that i centered on a harmonic of the ampling frequency, f. If f >=2B, (ee fig 2-18), the replicated pectra around each harmonic of f do not overlap, and the original pectrum can be regenerated with an ideal LPF with a cutoff of f /2.

30 Figure 2 18 Impule ampling.

31 Impule Sampling Figure 2 19 Underampling and aliaing.

32 Natural Sampling Generation of PAM with natural ampling (gating).

33 Natural Sampling Duty cycle =1/3

34 Natural Sampling Null at f d = 3 f

35 Figure 3 4 Demodulation of a PAM ignal (naturally ampled). n th Nyquit region recovery Couch, Digital and Analog Communication Sytem, Seventh Edition 2007 Pearon Education, Inc. All right reerved

36 Figure 3 5 PAM ignal with flat-top ampling. Impule ample and hold Couch, Digital and Analog Communication Sytem, Seventh Edition 2007 Pearon Education, Inc. All right reerved

37 Figure 3 6 Spectrum of a PAM waveform with flat-top ampling. Couch, Digital and Analog Communication Sytem, Seventh Edition 2007 Pearon Education, Inc. All right reerved

38 Figure 3 7 PCM tramiion ytem. Couch, Digital and Analog Communication Sytem, Seventh Edition 2007 Pearon Education, Inc. All right reerved

39 Figure 3 8 Illutration of waveform in a PCM ytem. Couch, Digital and Analog Communication Sytem, Seventh Edition 2007 Pearon Education, Inc. All right reerved

40 Figure 3 8 Illutration of waveform in a PCM ytem. Couch, Digital and Analog Communication Sytem, Seventh Edition 2007 Pearon Education, Inc. All right reerved

41 Figure 3 8 Illutration of waveform in a PCM ytem. Couch, Digital and Analog Communication Sytem, Seventh Edition 2007 Pearon Education, Inc. All right reerved

42 Figure 3 9 Compreion characteritic (firt quadrant hown). Couch, Digital and Analog Communication Sytem, Seventh Edition 2007 Pearon Education, Inc. All right reerved

43 Figure 3 9 Compreion characteritic (firt quadrant hown). Couch, Digital and Analog Communication Sytem, Seventh Edition 2007 Pearon Education, Inc. All right reerved

44 Figure 3 9 Continued Couch, Digital and Analog Communication Sytem, Seventh Edition 2007 Pearon Education, Inc. All right reerved

45 Figure 3 10 Output SNR of 8-bit PCM ytem with and without companding. Couch, Digital and Analog Communication Sytem, Seventh Edition 2007 Pearon Education, Inc. All right reerved

46 Quantization Noie, Analog to Digital Converter-A/D EELE445 Lecture 13 48

47 Figure 3 7 PCM tramiion ytem. q(x) Couch, Digital and Analog Communication Sytem, Seventh Edition 2007 Pearon Education, Inc. All right reerved

48 Quantization x max Δ x(t) Δ = 2 N x max = x 2 max n 1 Q(x) -x max

49 Quantization Reult in a Lo of Information Δ 2 x(t) Δ = 2 N x max = x 2 max n 1 Q(x) Lot Information Δ 2 After ampling, x(t)=x i R x i After Quantization: Q(x) = xˆ, x R

50 Quantization Noie Quantization function: Define the mean quare ditortion: q( x) = ( x Q( x)) 2 = ~ x 2 and x Q( x) Δ 2

51 Quantization q 2 Δ 2 1 = Δ Δ 2 = = q 2 2 Δ 12 dq ( x ) 2 max 2 3N = P nq the quantization noie where N=2 n and x max i ½ the A/D input range

52 Quantization Noie So we can define the mean quared error ditortion a: The pdf of the error i uniformly ditributed X = X Q( X ) f ~ ) (x ~ 1 Δ Δ 2 Δ 2 x~

53 SQNR Signal to Quantization Noie Ratio

54 SQNR Signal to Quantization Noie Ratio Example of SQNR for full cale inewave done on board

55 SQNR Signal to Quantization Noie Ratio P x may be found uing:

56 SQNR Signal to Quantization Noie Ratio The ditortion, or noie, i therefore: Where P x i the power of the input ignal

57 SQNR Linear Quantization E P x [ 2 X ] x 2 max < 1 x 2 max The SQNR decreae a The input dynamic range increae

58 U-Law Nonuniform PCM ued to increae SQNR for given P x, xmax, and n U=255 U.S

59 a-law Nonuniform PCM a=87.56 U.S

60 u-law v.. Linear Quantization 8 bit P x i ignal power Relative to full cale P x

61 Pule Code Modulation, PCM, Advantage compared with analog ytem b i the number of bit γ i (S/N) baeband Relative to full cale PPM i pule poition modulation

Formatting and Baseband. Formatting & Baseband. Page 1. Formatting and Baseband Modulation. CSE4214 Digital Communications

Formatting and Baseband. Formatting & Baseband. Page 1. Formatting and Baseband Modulation. CSE4214 Digital Communications CSE4214 Digital Communication CSE4214 Digital Communication Chapter 2 Formatting Formatting and Baeband Modulation Formatting & Baeband Formatting and Baeband 3 4 Page 1 1 What i Formatting? Information