1. Worst case sequence 101010 – period of two interval 110110- period of three interval 101010 has the shortest period and so highest fundamental freq comp This is called worst case sequence

2. Limited Bandwidth (d) – (e) Successive approximations to the original signal.

3. Limited Bandwidth Relation between data rate and harmonics.

4. Limited Bandwidth Let coding scheme of n-bit Bit rate = b bps Time required to send b-bits = 1sec So,……………………. 8 bits = 8/b sec T= 8/b f= b/8 No of harmonics = fc/b/8 Voice grade line fc=3000Hz b=300bps T=8/300=26.67 ms Fundamental freq = 1/T= 1/26.67 = 37.5 Hz No of harmonics = 3000/300/8 = 24000/300=80

5. Delay Distortion Various freq comp of the signal arrive at different Time at the receiver

6. Noise Nyquist: Maxm data rate for finite bandwidth noiseless channel: A noiseless 3-kHz ( H =3000) channel cannot transmit binary (V = 2) signals at a rate Exceeding 6000 bps

7. Noise Shannon: Maximum data rate for finite bandwidth noisy channel: A noiseless 3-kHz ( H =3000) channel with SNR = 1000 = 10 log 10 (1000) =30 db cannot transmit binary (V = 2) signals at a rate Exceeding 30000 bps

8. Noise Crosstalk: Unwanted electrical coupling between adjacent lines. Near End Crosstalk (NEXT): Caused by the strong signal output by a transmitter circuit being coupled with the much weaker signal at the input of the local receiver circuit

9. Noise Adaptive NEXT canceller: It adaptively forms an attenuated replica of the crosstalk signal and this is subtracted from the received signal