ECE511FL_activity1a1.doc

___________________ ___________________ ECE511FL ___________________

ACTIVITY NO. 1 SOURCE CODING Part 1

Date Performed: ______________ Date Submitted: ______________

I. Problem Set 1. Determine the binary stream for the message 511FL Dgcom if 7-bit ASCII is used for encoding. Show the bit stream with order of the arrow to the left. Message bit stream:  10101101000110100011001100010011001000001000100011110011110001111110 111011011 2. Determine the message for the given binary stream if 7-bit ASCII is used and the bits are shown with order of the arrow to the left.  1100001 1111011 0000111 1001111 0000010 0001011 0000110 0001111 0100110 1001110 0000111 Message: Copy h0x29p 3. A pulse-code modulation (PCM) system has an ADC that samples with a sampling frequency of 8000 samples/second. Its resolution is 20mV and uses 8-bit, foldedbinary encoding. Assuming the input signal is defined as x(t) = 2sin(1200πt)volts and the sampling starts at t=0. (a) Complete the table below for the pulse-code modulation process.

x(t) - analog input signal , x[n] - value of nth sample xqn[n] - quantized value of the nth sample b[n] - 8-bit, folded binary code for the nth sample PCM Table: n 1 2 3 4 5 6 7 8

x[n], mV 0 907.981 1618.0340 1975.3767 1902.1130 1414.2136 618.0340 -312.8689

xq[n], mV 0 45 81 99 95 71 31 -16 1

b[n] 1000 0000 1010 1101 1101 0001 1110 0011 1101 1111 1100 0111 1001 1111 0001 0000

___________________ ___________________ ECE511FL ___________________

ACTIVITY NO. 1 SOURCE CODING Part 1

Date Performed: ______________ Date Submitted: ______________

(b) Determine the output bit stream b[n] for the 8 samples taken. The least significant magnitude bit is transmitted first and the sign bit is transmitted last for each of the samples. Show the output bit stream with order of the arrow to the left. Output bit stream: 0000000110110101100010111100011111111011111000111111100100001000 (c) Determine the output bit rate of the ADC. ADC output bit rate =

64000

bits/second

4. The following bit stream arrives at the input of the digital-to-analog converter (DAC) of a PCM system at a rate of 64,000 bits/second. The DAC has a resolution of 25mV and uses 8-bit, folded binary format. During transmission, the least significant magnitude bit is transmitted first and the sign bit is transmitted last for each of the PCM codes.

The received bit stream is shown with order of the arrow to the left. Received bit stream:  1001 0110 1010 1100 1001 0101 1011 1010 1110 0110 0100 1001 Sketch the staircase waveform of the output signal of the DAC. Indicate all significant amplitude values and time values. Assume that the 8th bit of the received bit stream is received by the DAC at t=0.

II. Laboratory Work 2

___________________ ___________________ ECE511FL ___________________

ACTIVITY NO. 1 SOURCE CODING Part 1

Date Performed: ______________ Date Submitted: ______________

1. Familiarization with SCILAB functions used for the simulation of source coding. (a) Open the SCILAB file source_coding_functions.sci and familiarize with the SCILAB functions declared in the file. Understand their operation and the syntax for calling them. (b) Use the SCILAB functions declared in source_coding_functions.sci to solve the problems in the problem set. Compare the results you get from using the SCILAB functions with your answers. Are the results obtained using the SCILAB functions similar to your answers? Yes. 2. Perform a simulation of the ADC/DAC process to observe the closeness of the waveform of the signal reconstructed by the DAC to the analog input signal of the ADC for different sampling frequencies. (a) Open the simulation program simulation.sce and perform the necessary editing to perform the required simulation. Sample the input signal using the following sampling frequencies: Fsmin, 5Fsmin, 10Fsmin, 15Fsmin, 20Fsmin, and 30Fsmin where Fsmin=2fmax. The DAC sample reconstruction rate Fs' is always equal to the ADC sampling frequency Fs. Sample 3 periods of the input signal and plot the signal reconstructed at the output of the DAC. (b) Based on your observations, answer the following: (b.1) Describe the reconstructed signal if the sampling frequency is Fsmin. A square wave with an amplitude of 0.2V, a frequency of 100Hz. (b.2) Is there an improvement on the reconstructed signal as the sampling frequency is increased? Yes, the number of staircases in the reconstructed signal increases. (b.3) In your assessment, what should be the minimum sampling frequency such that the reconstructed signal is an acceptable reconstruction of the analog input signal (i.e. if the input is a sine wave, the reconstructed signal should be an acceptable sine wave)? The sampling frequency must be at least 5 times the critical sampling frequency or it must be 10 times the highest frequency of the signal. (b.4) In relation to your answer for (b.3), what should be the minimum sampling frequency for an analog signal x(t) = 2 +sin(1200πt) + 2cos(2500πt) volts such that the reconstructed is an acceptable reconstruction of x(t)? The minimum sampling frequency should be at least 12,500Hz. 3

___________________ ___________________ ECE511FL ___________________

ACTIVITY NO. 1 SOURCE CODING Part 1

Date Performed: ______________ Date Submitted: ______________

3. Perform a simulation of the ADC/DAC process to observe the closeness of the waveform of the signal reconstructed by the DAC to the analog input signal of the ADC for different input frequencies. (a) Open the simulation program simulation.sce and perform the necessary editing to perform the required simulation. Vary the frequency of the input signal to the following values: Fs/2, Fs/4, Fs/10, Fs/20, and Fs/50 where Fs is the ADC sampling frequency. Sample 3 periods of the input signal and plot the signal reconstructed at the output of the DAC. (b) Based on your observations, answer the following: (b.1) Describe the reconstructed signal if the frequency of the input signal is Fs/2. The reconstructed signal is a continuous signal with an amplitude of 0.2V (b.2) Is there an improvement on the reconstructed signal as the frequency of the input signal is decreased. None. (b.3) In your assessment, what should be the highest frequency of the input signal such that for the reconstructed signal is an acceptable reconstruction of the analog input signal? The highest frequency of the input signal to have an acceptable reconstruction must be of at least Fs/5. (b.4) In relation to your answer for (b.3), what should be the highest frequency content of the input analog signal such that the reconstructed signal is an acceptable reconstruction if the sampling frequency is 2500Hz? The highest frequency content of the input analog signal must be 500 Hz. 4. Perform a simulation of the ADC/DAC process to observe the closeness of the waveform of the signal reconstructed by the DAC to the analog input signal of the ADC for different sample reconstruction rates of the DAC. (a) Open the simulation program simulation.sce and perform the necessary editing to perform the required simulation. Vary the sample reconstruction rate Fs' of the DAC to the following values: 0.25Fs, 0.5Fs, 0.75Fs, Fs, 1.25Fs, and 2Fs where Fs is the ADC sampling rate. Sample 3 periods of the input signal and plot the signal reconstructed at the output of the DAC. (b) Based on your observations, answer the following: 4

___________________ ___________________ ECE511FL ___________________

ACTIVITY NO. 1 SOURCE CODING Part 1

Date Performed: ______________ Date Submitted: ______________

(b.1) Describe the reconstructed signal if the sample reconstruction rate of the DAC is 0.25Fs. The frequency of the reconstructed signal is 25Hz (b.2) What should be the sample reconstruction rate of the DAC such that the reconstructed signal is the best reconstruction of the analog input signal? The sample reconstruction frequency should be equal to sampling frequency to have the best reconstruction of the analog input signal. (b.3) Describe the reconstructed signal if the DAC sample reconstruction rate is higher than the sampling frequency of the input. The frequency must have a higher than a factor equal to the reconstruction rate and sample rate. (b.4) In relation to your answer for (b.3), what is the freq reconstructed signal y(t) if the input signal is x(t)=2sin(250πt), the ADC samples at 12000Hz, and the DAC sample reconstruction rate is 8000Hz.? 125*8000/12000 = 83.333Hz y(t)=2sin(166.67πt) 5. Perform a simulation of the ADC/DAC process to observe the closeness of the waveform of the signal reconstructed by the DAC to the analog input signal of the ADC for different sample reconstruction rates of the DAC. (a) Open the simulation program simulation.sce and perform the necessary editing to perform the required simulation. Vary the resolution Vlsb' of the DAC to the following values: 0.25Vlsb, 0.5Vlsb, 0.75Vlsb, Vlsb, 1.25Vlsb, and 2Vlsb where Vlsb is the resolution of the ADC. Sample 3 periods of the input signal and plot the signal reconstructed at the output of the DAC. (b) Based on your observations, answer the following: (b.1) Describe the reconstructed signal if the resolution of the DAC is 0.25Vlsb. The reconstructed signal has an amplitude of 0.05v. (b.2) What should be the resolution of the DAC such that the reconstructed signal is the best reconstruction of the analog input signal? The resolution of DAC should be equal to the resolution of the ADC to have the best reconstruction of the analog input signal. (b.3) Describe the reconstructed signal if the DAC resolution is higher than the resolution of the input. The amplitude of reconstructed signal will be higher by a factor of Vlsb’/Vlsb 5

___________________ ___________________ ECE511FL ___________________

ACTIVITY NO. 1 SOURCE CODING Part 1

Date Performed: ______________ Date Submitted: ______________

(b.4) In relation to your answer for (b.3), what is the reconstructed signal y(t) if the input signal is x(t)=2sin(250πt), the ADC resolution is 50mV, and the DAC resolution is 75mV? 75mV/50mV = 1.5V y(t) = 3sin(250πt)

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