Problems: (20 points) A signal x(t) is bandlimited to B Hz and is converted to a

Question

Problems: (20 points) A signal x(t) is bandlimited to B Hz and is converted to a discrete-time signal x[n] by using a sampling rate Hz. 1. 40 samples/s which is 4 times the Nyquist Rate. Find the value of B in 2. (20 points) The signal s(t) is bandlimited to 1 KHz. The signal is converted to a discrete-time signal x[n] using a sampling rate 3 times the Nyquist Rate. x[n] is then passed through a Quantizer that uses 10 bits/sample. What is the Bit Rate in Kbps of the resulting digital signal (bit stream)? 3. (20 points) The signal x(t) with spectrum as shown by the figure below is converted to a discrete time signal x [n] using a sampling rate 2 times the Nyquist Rate. Determine the value of the sampling rate f, in samples per second.

Explanation / Answer

1. The sampling theorem states that:

If a signal is limited bandwidth with maximum frequency fmax, then the sampling frequency fs must be greater than twice of the maximum frequency fmax, i.e.,

     fs > 2*fmax   

fs: sampling rate

fmax: maximum frequency

Given: fs=40 samples/s

Accoding to the question ,

2*fmax = 4*fs

fmax= (4*fs)/2 = 2*fs= 80 Hz .

Hence the value of B is 80 Hz.

2. Given: fmax=1Khz

sampling rate:

fs= 2*fmax= 2Khz

Also the quantiser used 10 bits/sample;

Bit rate = sampling rate* 10

= 2Khz * 10 = 20 Kbps

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