in the time domain? Assume sampling at TWICE the Nyquist rate. Figure Q4.2 The input 6. Plot the output of a sampler in frequency given: The input signal has maximum frequency 5,300 Hz. Ideal sampling is used. Sampling is at a rate of 5,300 Hz. The input signal in the frequency domain is triangular (i.e., it is a maximum at 0 Hz and degrades to 0 linearly as frequency increases to 5,300 Hz (and to -5,300 Hz). 7. Consider a quantizer with an input described in Figure Q4.3. (a) Draw a quantizer with 7 levels. Make it mid-tread, let it have -3 as its smallest output value, and make sure that the step size is 1. (b) Evaluate the mse of your quantizer given the input. (c) Evaluate the SQNR. (d) If the input to the quantizer has an amplitude with a probability distribution uniform between -3.5 and +3.5, what is the SQNR of the quantizer? Source Coding and Decoding: Making it Digital Figure Q4.3 The input pdf 8. Find out how many levels a quantizer must use to achieve an SQNR greater than 30 dB given: The incoming audio signal is sampled at its Nyquist rate of 8,000 samples/ The amplitudes output from the sampler have a uniform probability distri- bution function. A uniform quantizer is used. 9. Determine the optimal compression characteristic for the input X whose prob- ability density function is provided in Figure Q4.4. (a) Plot the u=10 compressor characteristic given that the input values are in the range [-2.5,2.5]. (b) Plot the corresponding expander. p (x) Figure Q4.4 The input pdf Chapter Four 11. Evaluate the symbol rate and the bit rate of the PCM system described by the following: The sampling rate is 5,300 Hz The quantizer is an 8-level quantizer. 12. A computer sends: 100 letters every 4 seconds 8 bits to represent each letter the bits enter a special coding device that takes in a set of bits and puts out one of 32 possible symbols. What is the bit rate and what is the symbol rate out of the special coding device? 13. Over the time 0 S to 2 S, determine (1) the input to the DM, (2) the output of the DM, an