Todays Schedule

1
Todays Schedule

• Reading Lathi 11.4, 11.5
• Quiz 2
• Lecture
• Calculating Signal to Noise Ratio
• Equivalent Noise Bandwidth
• Bandpass Random Processes
• Activity

2
Example RC Low Pass Filter

• Input is thermal white noise
• Use

R
C
y(t)
n(t)
3
Computing the SNR

• Input SNR is ratio of the input signal to input
  noise
• Output SNR is ratio of the output signal to
  output noise

4
RC LPF

• Same filter as before, assume x(t)si(t)ni(t)
• si(t) A cos(w0t q0), deterministic
• ni(t) is white noise, flat PSD over all
  frequencies
• ergodic noise (time avgstatistical avg)
• Input SNR is zero
• Signal Power A2/2
• Noise Power

5
Output SNR

• Output is y(t)so(t)no(t)
• Output Signal Power
• Output Noise Power (from previous example)

6
Noise Equivalent Bandwidth

• Input white noise with a PSD of No/2 to a low
  pass filter
• The Noise Equivalent Bandwidth is the filter
  bandwidth of H(f) that gives the same average
  noise power as an ideal low pass filter of DC
  gain H(0)

7
Noise Equivalent BW Calculation
LP Filter
H(f)
B
Noise Equivalent Bandwidth
8
Bandpass Random Process

• What happens to a signal at a receiver? How does
  the PSD of the signal after a BPF correspond to
  the signal before the BPF?

Sx(w)
-wc
w
wc
0
9
Next Time

• Reading Lathi 11.5,13.1
• Mini-Lecture 1
• Bandpass Random Processes
• Mini-Lecture 2
• Optimal Threshold Detection
• Mini-Lecture 3
• Optimum Binary Receivers-Introduction