Homework #4 (show your work)
a. Write down a statement of the Sampling Theorem.
b. What is meant by Impulse Sampling?
c. What is aliasing and how is it avoided in a sampling system?
An analog signal that has been sampled to form a PAM waveform can be recovered by a low pass filter. The output of the low pass filter is the original analog signal.
a. Explain in words why this is possible. (i.e. What feature of the PAM signal spectrum allows the recovery of the original signal at the output of the LPF?)
b. What is the advantage of using impulse sampling rather than square wave sampling?
An analog voice signal occupies a bandwidth of 300 – 3,400 Hz.
a. What is the Nyquist sampling frequency for this signal?
b. A sampling system operates at 1.2 times the Nyquist frequency. What is the sampling rate?
c. The sampled signal is transmitted as a PCM signal from a 10 bit ADC to a receiver that has a low pass filter. What cut off (maximum pass band) frequency should this filter have?
The output of a video surveillance camera is an analog signal with a bandwidth that extends from 0 Hz to 1.5 MHz. The signal is sampled at 1.2 times its Nyquist rate. Packets are
transmitted serially over a twisted pair used as the cable for data transmission.
a. What is the sampling frequency?
b. Each sample is encoded as 6 bit PCM. What is bit rate of the transmission on the twisted pair?
c. If the digital outputs of three identical video cameras are combined onto a single cable using time division multiplexing, what is the bit rate on the cable.
A T-1 telephone carrier system transmits 24 sampled PCM telephone channels. Twenty four different phone calls are sampled and each sample contains 8 bits. One extra bit is added to the 24 samples for framing information. The entire package of 193 bits is transmitted at rate of 1.544 Mpbs. (Note that this package represents ONE sample from each phone call.)
a.What is the sampling rate (samples per second) for each individual phone call?
b.Knowing what you know about the range of voice frequencies in a telephone circuit what is a reasonable frequency to set the low pass filter ahead of the sampler. Explain your choice.
The analog to digital converter (ADC) used in a telephone system outputs 8 bit words.
The digital words are transmitted as a serial stream to form a PCM voice signal.
The analog voice signal voltage always lies between -1.0 V and + 1.0 V.
a. Assuming that ADC is linear, what is the step size between quantization levels?
Hint: 28 = 256. This is the number of steps, step size is the voltage each step represents. For instance, 7.84 mV would be encoded digitally as 1, 15.68 mV would be encoded as 2.
b. Why is quantization noise present at the analog output of the PCM voice link?
c.The PCM signal is converted back to an analog waveform. What is the quantization signal to noise ratio (SNR)?
Music CD’s use 16 bit samples to record the music. What is the quantizing SNR on a CD?