## Phase Shift Keying

- Baseband transmission – the transmission of digital information over a low pass / low frequency channel.
- Use nyquist for low pass channel
- Represent binary information with a polar NRZ
- Multiply X
_{1}(t) with sine wave generator - Which transforms

- Represent binary information with a polar NRZ

Into

- To demodulate
- Multiply PSK signal with sine wave generator
- Output can be expressed as

- Multiply PSK signal with sine wave generator

- Filter out the high frequency component
- A
_{k}is retrieved - Trig identities
- 2cos
^{2}(x)= 1 + cos(2x) - 2sin
^{2}(x)= 1 – sin(2x) - 2cos(x)sin(x) = 0 + sin(2x)

- 2cos

- After demodulation of this example we still only end up with W
- Our goal was 2W (nyquist)
- To fix this we put ASK and PSK together
- Send two signals simultaneously on same carrier
- F
_{1}= f - F
_{2}= f + π/2 (shifted 90 degrees) - To do this
- Take the bitstream, split into two sequences f odd and even numbered bits
- Determine the bipolar NRZ B
_{k}for even and A_{k}for odd - Multiply A
_{k}with cosine wave and B_{k}with sin wave: modulate

- Take the bitstream, split into two sequences f odd and even numbered bits
- To demodulate see slides, involved multiplying whole signal by two trig identities which will give you A
_{k}and B_{k }independently

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