8 signals, each limited to 2 kHz and sampled at Nyquist rate, are converted into binary PCM signal using 256 quantization levels. The data rate for TDM signal will be:

Explanation:

1. Nyquist Sampling Theorem:

According to the Nyquist sampling theorem, the sampling rate for a signal must be at least twice the highest frequency present in the signal to avoid aliasing. For each signal:

• Signal bandwidth = 2 kHz
• Nyquist sampling rate = 2 × 2 kHz = 4 kHz

2. Bits per Sample:

The number of quantization levels is given as 256. The number of bits required to represent each sample is calculated as:

• Bits per sample = log₂(Number of quantization levels)
• Bits per sample = log₂(256) = 8 bits

3. Data Rate for a Single Signal:

The data rate for a single signal is the product of the sampling rate and the number of bits per sample:

• Data rate for one signal = Sampling rate × Bits per sample
• Data rate for one signal = 4 kHz × 8 bits
• Data rate for one signal = 32 kbps

4. Data Rate for 8 Signals:

Since there are 8 signals, the total data rate for the TDM signal is:

• Total data rate = Data rate for one signal × Number of signals
• Total data rate = 32 kbps × 8
• Total data rate = 256 kbps

Final Answer:

Based on the calculations, the data rate for the TDM signal is 256 kbps.