# Category: Uncategorized #### (5 pts) Pulse Code Modulation A compact disc (CD) records audio signal bandwidth equals 15 kHz. (a) (2 pts) Determine the sampling rate it the signal is to be sampled at a rate 20% above the Nyquist rate. (b) (1 pt) If the samples are uniformly quantized into M=65.536 levels, determine the average signal to noise ratio (SNR). Assume uniform distribution for the audio signal as well. (c) (1 pt) Assuming binary encoding, determine the number of bits per second required to encode the audio signal. (d) (1 pt) Assuming square pulses, determine the first null bandwidth of the PCM signal.

... #### 2) A signal with bandwidth 20KHz is sampled and digitally transmitted. (a) If the maximum acceptable quantization error in sample amplitudes is 0.25% of the peak signal voltage, find the minimum number of bits needed for a uniform quantizer. (b) If the sampling rate must be 20% higher than the minimum rate, find the minimum bit rate of the multiplexed data stream based on the quantizer of part (a). (c) If 5% more bits are added to the multiplexed data for error protection and synchronization, determine the minimum bandwidth needed to transmit the final data stream

... #### 6.2-3 In a satellite radio system, 128 station of stereo quality are to be package in one data stream. For each station, Two (left and right) signals of bandwidth 15,000 Hz are sampled, quantized, and binary-cooled into PCM signals. The transmitter must multiplex the data from the 128 stations into a single stream via time multiplexing. (a) If the maximum acceptable quantization error in sample amplitude is 0.25% of the peak signal voltage, find the minimum number of bits needed for a uniform quantizer. (b) If the sampling rate must be 20% higher than the Nyquist rate, find the minimum bit rate of the multiplexed data stream based on the quantizer of part (a). (c) If 5% more bits are added to the multiplexed data for error protection and synchronization, determine the minimum bandwidth needed to transmit the final data stream to receivers.

... #### 5.2-3 In a satellite radio system, 500 stations of stereo quality are to be multiplexed in one data stream. For each station, two (left an right) signal channels each of bandwidth 15,000 Hz are sampled, quantized, and binary-coded into PCM signals. (a) If the maximum quantized error in sample amplitudes is 1% of the peak signal voltage, find the minimum number of bits needed for a uniform quantizer. (b) If the sampling rate must be 8% higher than the Nyquist rate, find the minimum bit rate of the multiplexed data stream based on the quantizer of part (a). (c) If 2% more bits are added to the multiplexed data for error protection and synchronization, determine the minimum bandwidth needed to transmit the final data stream to receivers.

... #### 6.2-4 Five telemetry signals, each of bandwidth 1 KHz, are quantized and binary coded. These signals are time-division multiplexed (signal bits interleaved). Choose the number of quantization levels so that the maximum error in sample amplitudes is no greater than 0.2% of the peak signal amplitude. The signal must be sampled at least 20% above the Nyquist rate. Determine the data rate (bits per second) of the multiplexed signal.

... #### 5.1-4 Two signals are applied at the inputs of ideal LPFs. The outputs y1(t) and y2(t) of these filters are multiplied to obtain the signal y(t)=y1(t)y2(t). Find the Nyquist rate of y1(t),y2(t) and y(t). Use the convolution property and the width property of convolution to determine the bandwidth of y1(t)y2(t).

... #### 6.1-5 Signals are applied at the inputs of ideal low-pass filters. The outputs y1(t) and y2(t) of these filters are multiplied to obtain the signal y(t) = y1(t)y2(t). Find the Nyquist rate of y1(t),y2(t), and y(t). Use the convolution property and the width property of convolution to determine the bandwidth of y1(t)y2(t). See also Prob. 6.1-1.

... #### Problem A: Suppose you want to sample the signal. Determine the sampling rate needed to avoid aliasing. Hint: The Fourier transform of x(t) form constant W. (This is problem 5.1-2b from the book by Lathi cited in the syllabus.)

... #### 2. Determine the Nyquist sampling rate and the Nyquist sampling interval for the following signals.

... #### 6.1-1 Figure P6.1-1 shows Fourier spectra of signals g1(t) and g2(t). Determine the Nyquist interval and the sampling rate for signals. Hint: Use the frequency convolution and the width property of the convolution.

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