EELE445 Exam 1 Review In class Friday March 20 50 minutes
• One 8x11page, both sides • 10 questions, 10 points per question, divided among 5 problems
1 Exam 1 EELE445
The exam covers through lecture 16 and through homework 4.
• Be sure to review and understand the Homework problems. The exam questions center on the material covered by the homework.
•Review the example problems worked in class
•Concepts highlighted in green or blue on the slides.
The following slides are indicative of the areas that will be covered on the exam, BUT ARE NOT ALL INCLUSIVE! You are responsible for the material in the lectures 2 TOPICS
• Review of Signals and Spectra • Analysis and Transmission of Signals • Sampling and pulse code modulation • Principles of Digital Baseband Signals • Bandpass Signaling Principles and Circuits • Bandpass Modulated Systems • Introduction to the theory of probability • Analog systems in the presence of noise • Behavior of digital systems in the presence of noise • Error correcting codes • Example systems
3 TOPICS • Review of Signals and Spectra and information – Shannon’s Channel Capacity Law – LOS tower height – DC, rms, power in time domain – voltage spectra, power spectra , PSD , Fourier series and Fourier transforms – continuous and discreet spectra – power in frequency domain • Analysis and Transmission of Signals – dBm, dBW, dBV, – noise or equivalent bandwidth
– lowpass and bandpass filters- Butterworth filter- 1 pole Beq=B3dBxp/2 – be able to calculate the power of white noise through a filter – waveform through a transfer function, output spectrum and output power for a given input spectrum – total power from a PSD • Sampling and pulse code modulation – impulse, natural, and flat top sampling- what are the spectrum differences – Sample rate – sampled signal in frequency domain- spectra • Principles of Digital Baseband Signals – PAM, PCM – PCM- bit rate, SQNR vs n-bits – m-law compression – line code spectra will not be covered this exam
4 Lecture 1-2 – LOS Line of Sight
d = 2h d in miles, h in feet
5 Lecture 1-2 – Shannon’s Law
H R = bits / s T Channel Capacity : æ S ö C = B · log2 ç1+ ÷ bits / s è N ø B = Bandwith in Hz S = Signal power in watts N = Noise power in watts
6 Lecture 1-2 – Units and dB æ P ö æV 2 R ö dB\10logç 1 ÷ = 10logç 1rms 2 ÷ ç ÷ ç 2 ÷ è P2 ø è R1 V2rms ø æ P in watts ö æ P in milliwatts ö dBm = 10logç ÷ = 10logç ÷ è 0.001 watt ø è 1 milliwatt ø æ P in watts ö dBW = 10logç ÷ è 1 watt ø
æV1 in rmsvolts ö dBV = 20logç ÷ when R1 = R2 è 1 rmsvolt ø æV in rmsvolts ö dBmV = 20logç 1 ÷ when R = R ç -6 ÷ 1 2 è 10 rmsvolt ø 7 Lecture 3-4 – DC,rms, Power, Energy
T 1 2 w(t) = ò w(t)dt = DC or mean of w(t) T T - 2
T 1 2 w2 (t) = ò w2 (t)dt = rms value of w(t) T T - 2 T T 1 2 2 E = ò v2 (t)dt = R ò i2 (t)dt R T T - - 2 2 8 Lecture 5-7 – Frequency Domain
9 Lecture 5-7
10 Lecture 5-7
11 Fourier Series from Fourier Transforms
12 Fourier Series from Fourier Transforms
13 Fourier Series from Fourier Transforms
14 Fourier Series from Fourier Transforms
15 Lecture 8-10 – Power Through a Filter
2 ¥ 2 æ n ö ¥ P = x H ç ÷ = S 2 ( f ) H ( f )2 df y å n ç ÷ ò x n=-¥ è T0 ø -¥
Be able to calculate the noise power at the output of a RC filter with a white noise input
16 Natural Sampling
Duty cycle =1/3
17 Natural Sampling
f Null at s = 3 f d s
18 Lecture 11-13 companding
19 Lecture 11-13 Companding
U=255 U.S
20 Lecture 11-13 Quantization noise
D 1 2 q2 = ò q2dq D -D 2 D2 = 12 ()V 2 = max = P the quantization noise 3M 2 nq
21 SQNR - summary
V 2 P = max quantization noise power nq 3M 2
2 n Px 3M Px 3´ 4 Px SQNR = = 2 = 2 Pnq Vmax Vmax
• M is the number of quantization levels • n is the number of bits
• Vmax is ½ the A/D input range
22 SQNRdB
2 Px £ Vmax The SQNR decreases as Px The input dynamic range 2 £ 1 increases Vmax
æ P ö SQNR | @ 10log ç x ÷ + 6n + 4.8 dB 10 ç 2 ÷ èVmax ø
1 · V is the peak to peak range of the quantizer max 2 · n is the number of bits in the full scale quantizer range 23 Lecture 14-15 SQNR
SQNRdB = 6.02n + a (3 - 25)
æ Vmax ö a = 4.77 - 20logç ÷ (uniform quantizing) (3 - 26a) è xxrms ø a @ 4.77 - 20log[ln(1+ m)] (m - law companding) (3 - 26b) a @ 4.77 - 20log[1+ ln A] (A-law companding) (3 - 26c)
2 Px = xxrms is the input signalpower
Vmax is the peak design voltage level of the quantizer 24 Exam 1 EELE445
•Review the slides for lectures up to and including L16 •concentrate on highlighted information •HW solutions 1-4
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